diff --git a/.github/docker/Dockerfile b/.github/docker/Dockerfile
index d6a907f8..f7655aaa 100755
--- a/.github/docker/Dockerfile
+++ b/.github/docker/Dockerfile
@@ -17,6 +17,7 @@ RUN micromamba install -y -n base -c conda-forge \
coverage">=7.1.0" \
mpich \
petsc"<=3.19" \
+ scipy \
python=3.11 && \
micromamba clean --all --yes
diff --git a/.github/workflows/codeql-analysis.yml b/.github/workflows/codeql-analysis.yml
index e4bfe703..72e82715 100644
--- a/.github/workflows/codeql-analysis.yml
+++ b/.github/workflows/codeql-analysis.yml
@@ -37,7 +37,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
# Initializes the CodeQL tools for scanning.
- name: Initialize CodeQL
diff --git a/.github/workflows/docker.yml b/.github/workflows/docker.yml
index b4c00581..b09d1bca 100644
--- a/.github/workflows/docker.yml
+++ b/.github/workflows/docker.yml
@@ -16,7 +16,7 @@ jobs:
TAG_PREFIX: ${{ steps.tag_name.outputs.TAG_PREFIX }}
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Get tag name
id: tag_name
@@ -47,7 +47,7 @@ jobs:
runs-on: ubuntu-latest
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Log into the Dockerhub registry
run: echo ${{ secrets.DOCKERHUB_TOKEN }} | docker login -u ${{ secrets.DOCKERHUB_USERNAME }} --password-stdin
diff --git a/.github/workflows/docker_ghcr.yml b/.github/workflows/docker_ghcr.yml
index c4827a16..01164c0c 100644
--- a/.github/workflows/docker_ghcr.yml
+++ b/.github/workflows/docker_ghcr.yml
@@ -30,7 +30,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Log in to the Container registry
uses: docker/login-action@v3
@@ -51,7 +51,7 @@ jobs:
type=semver,pattern={{major}}.{{minor}}
- name: Build and push Docker image
- uses: docker/build-push-action@v5
+ uses: docker/build-push-action@v6
with:
context: .
file: ./.github/docker/Dockerfile
diff --git a/.github/workflows/ossar-analysis.yml b/.github/workflows/ossar-analysis.yml
index 61bfc925..05c026b3 100644
--- a/.github/workflows/ossar-analysis.yml
+++ b/.github/workflows/ossar-analysis.yml
@@ -21,7 +21,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
# Ensure a compatible version of dotnet is installed.
# The [Microsoft Security Code Analysis CLI](https://aka.ms/mscadocs) is built with dotnet v3.1.201.
diff --git a/.github/workflows/publish.yml b/.github/workflows/publish.yml
index 4c85eea4..88d5275a 100644
--- a/.github/workflows/publish.yml
+++ b/.github/workflows/publish.yml
@@ -22,7 +22,7 @@ jobs:
rm -R /home/mambauser/cashocs
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install cashocs
shell: bash
@@ -45,7 +45,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Get tag name
@@ -63,7 +63,7 @@ jobs:
- name: Create Github release
id: create_release
- uses: softprops/action-gh-release@v1
+ uses: softprops/action-gh-release@v2
with:
name: cashocs ${{ steps.tag_name.outputs.TAG_PREFIX }}
generate_release_notes: ${{ steps.check_version.outputs.is_stable == 'true' }}
@@ -80,7 +80,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Set up Python 3.11
uses: actions/setup-python@v5
diff --git a/.github/workflows/test_demos.yml b/.github/workflows/test_demos.yml
index e3901d97..5f2bdbcf 100644
--- a/.github/workflows/test_demos.yml
+++ b/.github/workflows/test_demos.yml
@@ -17,7 +17,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install micromamba
uses: mamba-org/setup-micromamba@v1
@@ -30,6 +30,7 @@ jobs:
gmsh>=4.8
matplotlib
petsc<=3.19
+ scipy
python=3.11
- name: Install package
@@ -55,7 +56,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install micromamba
uses: mamba-org/setup-micromamba@v1
@@ -69,6 +70,7 @@ jobs:
mpich
matplotlib
petsc<=3.19
+ scipy
python=3.11
- name: Install package
diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index ad56bb62..60cbb126 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -27,7 +27,7 @@ jobs:
rm -R /home/mambauser/cashocs
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install cashocs
shell: bash
diff --git a/.github/workflows/tests_macos.yml b/.github/workflows/tests_macos.yml
index 07824c6d..55a6b85c 100644
--- a/.github/workflows/tests_macos.yml
+++ b/.github/workflows/tests_macos.yml
@@ -20,7 +20,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install micromamba
uses: mamba-org/setup-micromamba@v1
@@ -33,6 +33,7 @@ jobs:
pytest>=7.2.0
gmsh>=4.8
petsc<=3.19
+ scipy
- name: Install package
run: |
diff --git a/.github/workflows/tests_parallel.yml b/.github/workflows/tests_parallel.yml
index 8f27d36e..f7d819f0 100644
--- a/.github/workflows/tests_parallel.yml
+++ b/.github/workflows/tests_parallel.yml
@@ -24,7 +24,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install micromamba
uses: mamba-org/setup-micromamba@v1
@@ -36,6 +36,7 @@ jobs:
pytest>=7.2.0
gmsh>=4.8
petsc<=3.19
+ scipy
${{ matrix.mpi }}
python=${{ matrix.python-version }}
diff --git a/.github/workflows/tests_serial.yml b/.github/workflows/tests_serial.yml
index 8cd9d904..6a1b2b74 100644
--- a/.github/workflows/tests_serial.yml
+++ b/.github/workflows/tests_serial.yml
@@ -21,7 +21,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4.1.1
+ uses: actions/checkout@v4.1.7
- name: Install micromamba
uses: mamba-org/setup-micromamba@v1
@@ -33,6 +33,7 @@ jobs:
pytest>=7.2.0
gmsh>=4.8
petsc<=3.19
+ scipy
python=${{ matrix.python-version }}
- name: Install package
diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index 2a4c217e..4b979792 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -1,60 +1,47 @@
-repos:
+default_language_version:
+ python: python3.11
+repos:
- repo: https://github.com/regebro/pyroma
rev: "4.2"
hooks:
- id: pyroma
-
- repo: https://github.com/psf/black
- rev: 24.1.1
+ rev: 24.4.2
hooks:
- id: black
-
-
- repo: https://github.com/PyCQA/isort
rev: 5.13.2
hooks:
- id: isort
-
-
- repo: https://github.com/PyCQA/pydocstyle
rev: 6.3.0
hooks:
- id: pydocstyle
additional_dependencies: ["tomli"]
files: cashocs/
-
-
- repo: https://github.com/PyCQA/flake8
- rev: 7.0.0
+ rev: 7.1.0
hooks:
- id: flake8
files: cashocs/
-
-
- repo: https://github.com/PyCQA/bandit
- rev: 1.7.7
+ rev: 1.7.9
hooks:
- id: bandit
files: cashocs/
-
-
- repo: https://github.com/PyCQA/pylint
- rev: v3.0.3
+ rev: v3.2.5
hooks:
- id: pylint
files: cashocs/
-
-
- repo: https://github.com/pre-commit/mirrors-mypy
- rev: v1.8.0
+ rev: v1.10.1
hooks:
- id: mypy
files: cashocs/
additional_dependencies: ["numpy"]
args: [--config-file, pyproject.toml]
-
-
- repo: https://github.com/PyCQA/prospector
rev: v1.10.3
hooks:
diff --git a/.zenodo.json b/.zenodo.json
index e75df2d3..57b59a5c 100755
--- a/.zenodo.json
+++ b/.zenodo.json
@@ -1,8 +1,8 @@
{
"description": "
cashocs is a computational, adjoint-based shape optimization and optimal control software.
",
"license": "GPL-3.0+",
- "title": "cashocs v2.1.4",
- "version": "v2.1.4",
+ "title": "cashocs v2.2.0-dev",
+ "version": "v2.2.0-dev",
"upload_type": "software",
"creators": [
{
diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index 109d76eb..5e430668 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -7,6 +7,33 @@ of the maintenance releases, please take a look at
``_.
+2.2.0 (in development)
+----------------------
+
+* Add a wrapper for PETSc's SNES solver for nonlinear equations. This is used internally in cashocs whenever possible. For the solution of the state system, our own Newton solver is the default for backwards compatibility. Users can use the new SNES backend by specifying :ini:`backend = petsc` in the Section StateSystem of the configuration.
+
+* Allows nesting of PETSc Fieldsplit PCs with the command line option "pc_fieldsplit_%d_fields , as explained at ``_
+
+* Increase the precision of the Gmsh output from cashocs
+
+* Add mesh quality constraints for shape optimization: These ensure that the angles of the (solid) angles of triangles and tetrahedrons cannot fall below a specified threshold.
+
+* New configuration file parameters:
+
+ * Section StateSystem
+
+ * :ini:`backend` specifies which backend is used for solving nonlinear equations. The default is :ini:`backend = cashocs`, which is the "old" behavior, and :ini:`backend = petsc` uses the new PETSc SNES interface.
+
+ * Section ShapeGradient
+
+ * :ini:`test_for_intersections` is used to disable the (post mesh movement) check for intersections of the mesh, which ensures physically reasonable designs. This should not be set to `False`.
+
+ * Section MeshQualityConstraints
+
+ * This section includes parameters for the new mesh quality constraints for shape optimization. These are described in the documentation at ``_
+
+
+
2.1.0 (February 6, 2024)
------------------------
diff --git a/README.rst b/README.rst
index 4c302d2f..f2e82244 100755
--- a/README.rst
+++ b/README.rst
@@ -76,13 +76,13 @@ we can recommend the textbooks
.. readme_end_disclaimer
-However, the `cashocs tutorial `_ also gives many references either
+However, the `cashocs tutorial `_ also gives many references either
to the underlying theory of PDE constrained optimization or to relevant demos
and documentation of FEniCS.
An overview over cashocs and its capabilities can be found in `Blauth - cashocs: A Computational, Adjoint-Based
-Shape Optimization and Optimal Control Software `_. Moreover, note that
-the full cashocs documentation is available at ``_.
+Shape Optimization and Optimal Control Software `_ and `Blauth - Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software `_. Moreover, note that
+the full cashocs documentation is available at ``_.
.. readme_start_installation
@@ -111,7 +111,7 @@ where `` is the desired name of the new environment.
.. note::
- `Gmsh `_ is now (starting with release 1.3.2) automatically installed with anaconda.
+ `Gmsh `_ is automatically installed with anaconda.
@@ -125,7 +125,7 @@ Manual Installation
version that matches the HDF5 version used in FEniCS, and `matplotlib `_.
The version of meshio should be at least 4, but for compatibility it is recommended to use meshio 4.4.
-- You might also want to install `Gmsh `_, version 4.8.
+- You might also want to install `Gmsh `_, version 4.8 or later.
cashocs does not necessarily need this to work properly,
but it is required for the remeshing functionality.
@@ -191,18 +191,17 @@ Manual Installation
Usage
=====
-The complete cashocs documentation is available here ``_. For a detailed
-introduction, see the `cashocs tutorial `_. The python source code
+The complete cashocs documentation is available here ``_. For a detailed
+introduction, see the `cashocs tutorial `_. The python source code
for the demo programs is located inside the "demos" folder.
-.. readme_start_citing
.. _citing:
Citing
======
-If you use cashocs for your research, please cite the following papers
+If you use cashocs for your research, please cite the following paper
.. code-block:: text
@@ -211,45 +210,7 @@ If you use cashocs for your research, please cite the following papers
SoftwareX, Volume 13, 2021
https://doi.org/10.1016/j.softx.2020.100646
-as well as
-
-.. code-block:: text
-
- Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software
- Sebastian Blauth
- SoftwareX, Volume 24, 2023
- https://doi.org/10.1016/j.softx.2023.101577
-
-
-Additionally, if you are using the nonlinear conjugate gradient methods for shape optimization implemented in cashocs, please cite the following paper
-
-.. code-block:: text
-
- Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
- Sebastian Blauth
- SIAM Journal on Optimization, Volume 31, Issue 3, 2021
- https://doi.org/10.1137/20M1367738
-
-If you are using the space mapping methods for shape optimization, please cite the paper
-
-.. code-block:: text
-
- Space Mapping for PDE Constrained Shape Optimization
- Sebastian Blauth
- SIAM Journal on Optimization, Volume 33, Issue 3, 2023
- https://doi.org/10.1137/22M1515665
-
-and if you are using the topology optimization methods implemented in cashocs, please cite the paper
-
-.. code-block:: text
-
- Quasi-Newton Methods for Topology Optimization Using a Level-Set Method
- Sebastian Blauth and Kevin Sturm
- Structural and Multidisciplinary Optimization, Volume 66, 2023
- https://doi.org/10.1007/s00158-023-03653-2
-
-
-If you are using BibTeX, you can use the following entries
+or use the following bibtex entry
.. code-block:: bibtex
@@ -264,73 +225,8 @@ If you are using BibTeX, you can use the following entries
doi = {https://doi.org/10.1016/j.softx.2020.100646},
keywords = {PDE constrained optimization, Adjoint approach, Shape optimization, Optimal control},
}
-
-.. code-block:: bibtex
-
- @Article{Blauth2023Version,
- author = {Sebastian Blauth},
- journal = {SoftwareX},
- title = {{Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software}},
- year = {2023},
- issn = {2352-7110},
- pages = {101577},
- volume = {24},
- doi = {https://doi.org/10.1016/j.softx.2023.101577},
- keywords = {PDE constrained optimization, Shape optimization, Topology optimization, Space mapping},
- }
-
-
-.. code-block:: bibtex
-
- @Article{Blauth2021Nonlinear,
- author = {Sebastian Blauth},
- journal = {SIAM J. Optim.},
- title = {{Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov-Poincaré-Type Metrics}},
- year = {2021},
- number = {3},
- pages = {1658--1689},
- volume = {31},
- doi = {10.1137/20M1367738},
- fjournal = {SIAM Journal on Optimization},
- }
-
-
-.. code-block:: bibtex
-
- @Article{Blauth2023Space,
- author = {Blauth, Sebastian},
- journal = {SIAM J. Optim.},
- title = {{Space Mapping for PDE Constrained Shape Optimization}},
- year = {2023},
- issn = {1052-6234,1095-7189},
- number = {3},
- pages = {1707--1733},
- volume = {33},
- doi = {10.1137/22M1515665},
- fjournal = {SIAM Journal on Optimization},
- mrclass = {49Q10 (35Q93 49M41 65K05)},
- mrnumber = {4622415},
- }
-
-
-.. code-block:: bibtex
-
- @Article{Blauth2023Quasi,
- author = {Blauth, Sebastian and Sturm, Kevin},
- journal = {Struct. Multidiscip. Optim.},
- title = {{Quasi-Newton methods for topology optimization using a level-set method}},
- year = {2023},
- issn = {1615-147X,1615-1488},
- number = {9},
- pages = {203},
- volume = {66},
- doi = {10.1007/s00158-023-03653-2},
- fjournal = {Structural and Multidisciplinary Optimization},
- mrclass = {99-06},
- mrnumber = {4635978},
- }
-
-.. readme_end_citing
+
+For more details on how to cite cashocs please take a look at ``_.
.. readme_start_license
@@ -361,8 +257,9 @@ along with cashocs. If not, see ``_.
Contact / About
===============
-I'm `Sebastian Blauth `_, a scientific employee at `Fraunhofer ITWM
-`_. I have developed this project as part of my PhD thesis.
+I'm `Sebastian Blauth `_, a researcher at `Fraunhofer ITWM
+`_. I started developing cashocs during my PhD studies and have
+further developed and refined it as part of my employment at Fraunhofer ITWM.
If you have any questions / suggestions / feedback, etc., you can contact me
via `sebastian.blauth@itwm.fraunhofer.de
`_. For more information, visit my website at ``_.
diff --git a/cashocs/__init__.py b/cashocs/__init__.py
index 7dd05a54..f8a48d8c 100755
--- a/cashocs/__init__.py
+++ b/cashocs/__init__.py
@@ -58,8 +58,9 @@
from cashocs.nonlinear_solvers import linear_solve
from cashocs.nonlinear_solvers import newton_solve
from cashocs.nonlinear_solvers import picard_iteration
+from cashocs.nonlinear_solvers import snes_solve
-__version__ = "2.1.4"
+__version__ = "2.2.0-dev"
__citation__ = """
@Article{Blauth2021cashocs,
@@ -155,4 +156,5 @@
"linear_solve",
"TopologyOptimizationProblem",
"interpolate_levelset_function_to_cells",
+ "snes_solve",
]
diff --git a/cashocs/_exceptions.py b/cashocs/_exceptions.py
index a7a62b13..43b0cdda 100755
--- a/cashocs/_exceptions.py
+++ b/cashocs/_exceptions.py
@@ -61,8 +61,8 @@ def __str__(self) -> str:
return main_msg + post_msg
-class PETScKSPError(CashocsException):
- """This exception is raised when the solution of a linear problem with PETSc fails.
+class PETScError(CashocsException):
+ """This exception is raised when the solution of a problem with PETSc fails.
Also returns the PETSc error code and reason.
"""
@@ -70,7 +70,7 @@ class PETScKSPError(CashocsException):
def __init__(
self,
error_code: int,
- message: str = "PETSc linear solver did not converge.",
+ message: str = "The PETSc solver did not converge.",
) -> None:
"""Initializes self.
@@ -82,7 +82,35 @@ def __init__(
super().__init__()
self.message = message
self.error_code = error_code
+ self.error_dict: dict[int, str] = {}
+
+ def __str__(self) -> str:
+ """Returns the string representation of the exception."""
+ return (
+ f"{self.message} ConvergedReason = "
+ f"{self.error_code} {self.error_dict[self.error_code]}"
+ )
+
+
+class PETScKSPError(PETScError):
+ """This exception is raised when the solution of a linear problem with PETSc fails.
+
+ Also returns the PETSc error code and reason.
+ """
+
+ def __init__(
+ self,
+ error_code: int,
+ message: str = "The PETSc linear solver did not converge.",
+ ) -> None:
+ """Initializes self.
+
+ Args:
+ error_code: The error code issued by PETSc.
+ message: The message, detailing why PETSc issued an error.
+ """
+ super().__init__(error_code, message)
self.error_dict = {
-2: " (ksp_diverged_null)",
-3: " (ksp_diverged_its, reached maximum iterations)",
@@ -102,12 +130,48 @@ def __init__(
"it was not possible to build / use the preconditioner)",
}
- def __str__(self) -> str:
- """Returns the string representation of the exception."""
- return (
- f"{self.message} KSPConvergedReason = "
- f"{self.error_code} {self.error_dict[self.error_code]}"
- )
+
+class PETScSNESError(PETScError):
+ """This exception is raised if the solution of a nonlinear problem with PETSc fails.
+
+ Also returns the PETSc error code and reason.
+ """
+
+ def __init__(
+ self,
+ error_code: int,
+ message: str = "The PETSc nonlinear solver did not converge.",
+ ) -> None:
+ """Initializes self.
+
+ Args:
+ error_code: The error code issued by PETSc.
+ message: The message, detailing why PETSc issued an error.
+
+ """
+ super().__init__(error_code, message)
+ self.error_dict = {
+ -1: (
+ " (snes_diverged_function_domain, "
+ "the new x location passed to the function is not in the domain)"
+ ),
+ -2: " (snes_diverged_function_count)",
+ -3: " (snes_diverged_linear_solve, linear solve failed)",
+ -4: " (snes_diverged_fnorm_nan)",
+ -5: " (snes_diverged_max_it, maximum number of iterations exceeded)",
+ -6: " (snes_diverged_line_search, the line search failed)",
+ -7: " (snes_diverged_inner, inner solve failed)",
+ -8: (
+ " (snes_diverged_local_min, ||J^T b|| is small, "
+ "implies converged to local minimum)"
+ ),
+ -9: " (snes_diverged_dtol, ||F|| > divtol*||F_initial||)",
+ -10: (
+ " (snes_diverged_jacobian_domain, "
+ "Jacobian calculation does not make sense)"
+ ),
+ -11: " (snes_diverged_tr_delta)",
+ }
class InputError(CashocsException):
diff --git a/cashocs/_forms/control_form_handler.py b/cashocs/_forms/control_form_handler.py
index 054a7531..b8aeff47 100644
--- a/cashocs/_forms/control_form_handler.py
+++ b/cashocs/_forms/control_form_handler.py
@@ -192,6 +192,16 @@ def _compute_gradient_equations(self) -> None:
for i in range(len(self.db.function_db.controls))
]
+ def apply_shape_bcs(self, function: fenics.Function) -> None:
+ """Applies the geometric boundary conditions / constraints to a function.
+
+ Args:
+ function: The function onto which the geometric constraints are imposed.
+ Must be a vector CG1 function.
+
+ """
+ pass
+
class HessianFormHandler:
"""Form handler for second order forms and hessians."""
diff --git a/cashocs/_forms/form_handler.py b/cashocs/_forms/form_handler.py
index f6115519..66eed754 100644
--- a/cashocs/_forms/form_handler.py
+++ b/cashocs/_forms/form_handler.py
@@ -107,3 +107,14 @@ def scalar_product(
def update_scalar_product(self) -> None:
"""Updates the scalar product."""
pass
+
+ @abc.abstractmethod
+ def apply_shape_bcs(self, function: fenics.Function) -> None:
+ """Applies the geometric boundary conditions / constraints to a function.
+
+ Args:
+ function: The function onto which the geometric constraints are imposed.
+ Must be a vector CG1 function.
+
+ """
+ pass
diff --git a/cashocs/_forms/shape_form_handler.py b/cashocs/_forms/shape_form_handler.py
index f74c2ce8..1f4b8b3e 100644
--- a/cashocs/_forms/shape_form_handler.py
+++ b/cashocs/_forms/shape_form_handler.py
@@ -411,6 +411,12 @@ def _setup_assembler_failsafe(
ufl_algorithms.estimate_total_polynomial_degree(modified_scalar_product),
ufl_algorithms.estimate_total_polynomial_degree(shape_derivative),
)
+ fenics_quadrature_degree = fenics.parameters["form_compiler"][
+ "quadrature_degree"
+ ]
+ if fenics_quadrature_degree is not None:
+ estimated_degree = np.minimum(estimated_degree, fenics_quadrature_degree)
+
assembler = fenics.SystemAssembler(
modified_scalar_product,
shape_derivative,
@@ -728,3 +734,21 @@ def _compute_mu_elas(self) -> None:
PDE Constrained Shape Optimization `_.
"""
self.stiffness.compute()
+
+ def apply_shape_bcs(self, function: fenics.Function) -> None:
+ """Applies the geometric boundary conditions / constraints to a function.
+
+ Args:
+ function: The function onto which the geometric constraints are imposed.
+ Must be a vector CG1 function.
+
+ """
+ for bc in self.bcs_shape:
+ bc.apply(function.vector())
+ function.vector().apply("")
+
+ if self.use_fixed_dimensions:
+ function.vector().vec()[self.fixed_indices] = np.array(
+ [0.0] * len(self.fixed_indices)
+ )
+ function.vector().apply("")
diff --git a/cashocs/_optimization/line_search/__init__.py b/cashocs/_optimization/line_search/__init__.py
index 067bd684..fb8f019f 100644
--- a/cashocs/_optimization/line_search/__init__.py
+++ b/cashocs/_optimization/line_search/__init__.py
@@ -23,4 +23,8 @@
PolynomialLineSearch,
)
-__all__ = ["ArmijoLineSearch", "LineSearch", "PolynomialLineSearch"]
+__all__ = [
+ "ArmijoLineSearch",
+ "LineSearch",
+ "PolynomialLineSearch",
+]
diff --git a/cashocs/_optimization/line_search/armijo_line_search.py b/cashocs/_optimization/line_search/armijo_line_search.py
index f4a03fcf..013edcc6 100644
--- a/cashocs/_optimization/line_search/armijo_line_search.py
+++ b/cashocs/_optimization/line_search/armijo_line_search.py
@@ -29,6 +29,9 @@
from cashocs._optimization.line_search import line_search
if TYPE_CHECKING:
+ import numpy as np
+ from scipy import sparse
+
from cashocs import _typing
from cashocs._database import database
from cashocs._optimization import optimization_algorithms
@@ -90,6 +93,9 @@ def search(
solver: optimization_algorithms.OptimizationAlgorithm,
search_direction: List[fenics.Function],
has_curvature_info: bool,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: sparse.csr_matrix | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> Tuple[Optional[fenics.Function], bool]:
"""Performs the line search.
@@ -120,7 +126,12 @@ def search(
)
self.stepsize = (
self.optimization_variable_abstractions.update_optimization_variables(
- search_direction, self.stepsize, self.beta_armijo
+ search_direction,
+ self.stepsize,
+ self.beta_armijo,
+ active_idx,
+ constraint_gradient,
+ dropped_idx,
)
)
@@ -128,13 +139,23 @@ def search(
objective_step = self._compute_objective_at_new_iterate(
current_function_value
)
+ _loggers.debug(
+ f"Line search - Trial stepsize {self.stepsize:.3e} - "
+ f"Function value {objective_step:.3e}"
+ )
decrease_measure = self._compute_decrease_measure(search_direction)
if self._satisfies_armijo_condition(
objective_step, current_function_value, decrease_measure
):
+ _loggers.debug("Stepsize satisfies the Armijo decrease condition.")
if self.optimization_variable_abstractions.requires_remeshing():
+ _loggers.debug(
+ "The mesh quality was sufficient for accepting the step, "
+ "but the mesh cannot be used anymore for computing a gradient."
+ "Performing a remeshing operation."
+ )
is_remeshed = (
self.optimization_variable_abstractions.mesh_handler.remesh(
solver
@@ -147,6 +168,9 @@ def search(
break
else:
+ _loggers.debug(
+ "Stepsize does not satisfy the Armijo decrease condition."
+ )
self.stepsize /= self.beta_armijo
self.optimization_variable_abstractions.revert_variable_update()
@@ -199,5 +223,6 @@ def _compute_objective_at_new_iterate(self, current_function_value: float) -> fl
raise error
else:
objective_step = 2.0 * abs(current_function_value)
+ self.state_problem.revert_to_checkpoint()
return objective_step
diff --git a/cashocs/_optimization/line_search/line_search.py b/cashocs/_optimization/line_search/line_search.py
index 07cd88cb..c9f3fabe 100644
--- a/cashocs/_optimization/line_search/line_search.py
+++ b/cashocs/_optimization/line_search/line_search.py
@@ -26,9 +26,12 @@
import numpy as np
from petsc4py import PETSc
+from cashocs import _loggers
from cashocs import _utils
if TYPE_CHECKING:
+ from scipy import sparse
+
from cashocs import _typing
from cashocs._database import database
from cashocs._optimization import optimization_algorithms
@@ -92,23 +95,38 @@ def perform(
solver: optimization_algorithms.OptimizationAlgorithm,
search_direction: List[fenics.Function],
has_curvature_info: bool,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: sparse.csr_matrix | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> None:
"""Performs a line search for the new iterate.
Notes:
This is the function that should be called in the optimization algorithm,
it consists of a call to ``self.search`` and ``self.post_line_search``
- afterwards.
+ afterward.
Args:
solver: The optimization algorithm.
search_direction: The current search direction.
has_curvature_info: A flag, which indicates, whether the search direction
is (presumably) scaled.
+ active_idx: The list of active indices of the working set. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
+ constraint_gradient: The gradient of the constraints for the mesh quality.
+ Only needed for shape optimization with mesh quality constraints.
+ Default is `None`.
+ dropped_idx: The list of indicies for dropped constraints. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
"""
deformation, is_remeshed = self.search(
- solver, search_direction, has_curvature_info
+ solver,
+ search_direction,
+ has_curvature_info,
+ active_idx,
+ constraint_gradient,
+ dropped_idx,
)
if deformation is not None and self.config.getboolean(
"ShapeGradient", "global_deformation"
@@ -154,9 +172,17 @@ def initialize_stepsize(
)
if has_curvature_info:
+ _loggers.debug(
+ "Stepsize computation has curvature information. "
+ "Setting trial stepsize to 1.0."
+ )
self.stepsize = 1.0
if solver.is_restarted:
+ _loggers.debug(
+ "Solver has been restarted. "
+ "Using initial_stepsize from config as trial stepsize."
+ )
self.stepsize = self.config.getfloat("LineSearch", "initial_stepsize")
num_decreases = (
@@ -164,6 +190,11 @@ def initialize_stepsize(
search_direction, self.stepsize
)
)
+ if num_decreases > 0:
+ _loggers.debug(
+ "Stepsize is too large for the angle_change parameter in "
+ "section MeshQuality. Making the step smaller to be feasible."
+ )
self.stepsize /= pow(self.beta_armijo, num_decreases)
if self.safeguard_stepsize and solver.iteration == 0:
@@ -173,6 +204,9 @@ def initialize_stepsize(
self.stepsize = float(
np.minimum(self.stepsize, 100.0 / (1.0 + search_direction_norm))
)
+ _loggers.debug(
+ "Performed a safeguarding of the stepsize to avoid too large steps."
+ )
@abc.abstractmethod
def search(
@@ -180,6 +214,9 @@ def search(
solver: optimization_algorithms.OptimizationAlgorithm,
search_direction: List[fenics.Function],
has_curvature_info: bool,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: sparse.csr_matrix | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> Tuple[Optional[fenics.Function], bool]:
"""Performs a line search.
@@ -188,6 +225,13 @@ def search(
search_direction: The current search direction.
has_curvature_info: A flag, which indicates, whether the search direction
is (presumably) scaled.
+ active_idx: The list of active indices of the working set. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
+ constraint_gradient: The gradient of the constraints for the mesh quality.
+ Only needed for shape optimization with mesh quality constraints.
+ Default is `None`.
+ dropped_idx: The list of indicies for dropped constraints. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
Returns:
The accepted deformation or None, in case the deformation was not
diff --git a/cashocs/_optimization/line_search/polynomial_line_search.py b/cashocs/_optimization/line_search/polynomial_line_search.py
index 605de8a2..79157ade 100644
--- a/cashocs/_optimization/line_search/polynomial_line_search.py
+++ b/cashocs/_optimization/line_search/polynomial_line_search.py
@@ -32,6 +32,8 @@
from cashocs._optimization.line_search import line_search
if TYPE_CHECKING:
+ from scipy import sparse
+
from cashocs import _typing
from cashocs._database import database
from cashocs._optimization import optimization_algorithms
@@ -101,6 +103,9 @@ def search(
solver: optimization_algorithms.OptimizationAlgorithm,
search_direction: List[fenics.Function],
has_curvature_info: bool,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: sparse.csr_matrix | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> Tuple[Optional[fenics.Function], bool]:
"""Performs the line search.
@@ -109,6 +114,13 @@ def search(
search_direction: The current search direction.
has_curvature_info: A flag, which indicates whether the direction is
(presumably) scaled.
+ active_idx: The list of active indices of the working set. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
+ constraint_gradient: The gradient of the constraints for the mesh quality.
+ Only needed for shape optimization with mesh quality constraints.
+ Default is `None`.
+ dropped_idx: The list of indicies for dropped constraints. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
Returns:
The accepted deformation / update or None, in case the update was not
@@ -133,7 +145,12 @@ def search(
)
self.stepsize = (
self.optimization_variable_abstractions.update_optimization_variables(
- search_direction, self.stepsize, self.beta_armijo
+ search_direction,
+ self.stepsize,
+ self.beta_armijo,
+ active_idx,
+ constraint_gradient,
+ dropped_idx,
)
)
self.alpha_vals.append(self.stepsize)
@@ -144,12 +161,23 @@ def search(
objective_step = self.cost_functional.evaluate()
self.f_vals.append(objective_step)
+ _loggers.debug(
+ f"Line search - Trial stepsize {self.stepsize:.3e} - "
+ f"Function value {objective_step:.3e}"
+ )
+
decrease_measure = self._compute_decrease_measure(search_direction)
if self._satisfies_armijo_condition(
objective_step, current_function_value, decrease_measure
):
+ _loggers.debug("Stepsize satisfies the Armijo decrease condition.")
if self.optimization_variable_abstractions.requires_remeshing():
+ _loggers.debug(
+ "The mesh quality was sufficient for accepting the step, "
+ "but the mesh cannot be used anymore for computing a gradient."
+ "Performing a remeshing operation."
+ )
is_remeshed = (
self.optimization_variable_abstractions.mesh_handler.remesh(
solver
@@ -162,6 +190,9 @@ def search(
break
else:
+ _loggers.debug(
+ "Stepsize does not satisfy the Armijo decrease condition."
+ )
self.stepsize = self._compute_polynomial_stepsize(
current_function_value,
decrease_measure,
diff --git a/cashocs/_optimization/optimal_control/control_variable_abstractions.py b/cashocs/_optimization/optimal_control/control_variable_abstractions.py
index f161a3e9..a7555aed 100644
--- a/cashocs/_optimization/optimal_control/control_variable_abstractions.py
+++ b/cashocs/_optimization/optimal_control/control_variable_abstractions.py
@@ -114,7 +114,13 @@ def revert_variable_update(self) -> None:
self.db.function_db.controls[i].vector().apply("")
def update_optimization_variables(
- self, search_direction: List[fenics.Function], stepsize: float, beta: float
+ self,
+ search_direction: List[fenics.Function],
+ stepsize: float,
+ beta: float,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: np.ndarray | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> float:
"""Updates the optimization variables based on a line search.
@@ -123,6 +129,13 @@ def update_optimization_variables(
stepsize: The current (trial) stepsize.
beta: The parameter for the line search, which "halves" the stepsize if the
test was not successful.
+ active_idx: The list of active indices of the working set. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
+ constraint_gradient: The gradient of the constraints for the mesh quality.
+ Only needed for shape optimization with mesh quality constraints.
+ Default is `None`.
+ dropped_idx: The list of indicies for dropped constraints. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
Returns:
The stepsize which was found to be acceptable.
diff --git a/cashocs/_optimization/optimization_algorithms/gradient_descent.py b/cashocs/_optimization/optimization_algorithms/gradient_descent.py
index 374c54c0..192e2f61 100644
--- a/cashocs/_optimization/optimization_algorithms/gradient_descent.py
+++ b/cashocs/_optimization/optimization_algorithms/gradient_descent.py
@@ -37,8 +37,14 @@ def run(self) -> None:
self.evaluate_cost_functional()
self.compute_search_direction()
+ self.project_search_direction()
self.line_search.perform(
- self, self.search_direction, self.has_curvature_info
+ self,
+ self.search_direction,
+ self.has_curvature_info,
+ self.active_idx,
+ self.constraint_gradient,
+ self.dropped_idx,
)
self.iteration += 1
@@ -46,7 +52,7 @@ def run(self) -> None:
break
def compute_search_direction(self) -> None:
- """Computes the search direction for the gradient descent method."""
+ """Computes the search direction for the (projected) gradient descent method."""
for i in range(len(self.db.function_db.gradient)):
self.search_direction[i].vector().vec().aypx(
0.0, -self.db.function_db.gradient[i].vector().vec()
diff --git a/cashocs/_optimization/optimization_algorithms/l_bfgs.py b/cashocs/_optimization/optimization_algorithms/l_bfgs.py
index 176d718e..d1fa163c 100755
--- a/cashocs/_optimization/optimization_algorithms/l_bfgs.py
+++ b/cashocs/_optimization/optimization_algorithms/l_bfgs.py
@@ -106,8 +106,14 @@ def run(self) -> None:
self.evaluate_cost_functional()
+ self.project_search_direction()
self.line_search.perform(
- self, self.search_direction, self.has_curvature_info
+ self,
+ self.search_direction,
+ self.has_curvature_info,
+ self.active_idx,
+ self.constraint_gradient,
+ self.dropped_idx,
)
self.iteration += 1
diff --git a/cashocs/_optimization/optimization_algorithms/ncg.py b/cashocs/_optimization/optimization_algorithms/ncg.py
index e7423cab..d04437cf 100644
--- a/cashocs/_optimization/optimization_algorithms/ncg.py
+++ b/cashocs/_optimization/optimization_algorithms/ncg.py
@@ -90,8 +90,14 @@ def run(self) -> None:
self.evaluate_cost_functional()
+ self.project_search_direction()
self.line_search.perform(
- self, self.search_direction, self.has_curvature_info
+ self,
+ self.search_direction,
+ self.has_curvature_info,
+ self.active_idx,
+ self.constraint_gradient,
+ self.dropped_idx,
)
self.iteration += 1
diff --git a/cashocs/_optimization/optimization_algorithms/optimization_algorithm.py b/cashocs/_optimization/optimization_algorithms/optimization_algorithm.py
index e4afdfb7..9dd49efe 100644
--- a/cashocs/_optimization/optimization_algorithms/optimization_algorithm.py
+++ b/cashocs/_optimization/optimization_algorithms/optimization_algorithm.py
@@ -61,6 +61,7 @@ def __init__(
self.line_search_broken = False
self.has_curvature_info = False
+ # ToDo: Make this a weakref.proxy
self.optimization_problem = optimization_problem
self.form_handler = optimization_problem.form_handler
self.state_problem: _pde_problems.StateProblem = (
@@ -95,6 +96,10 @@ def __init__(
self.converged = False
self.converged_reason = 0
+ self.active_idx: np.ndarray | None = None
+ self.constraint_gradient: np.ndarray | None = None
+ self.dropped_idx: np.ndarray | None = None
+
if self.db.parameter_db.is_remeshed:
self.rtol = self.db.parameter_db.temp_dict["OptimizationRoutine"]["rtol"]
self.atol = self.db.parameter_db.temp_dict["OptimizationRoutine"]["atol"]
@@ -116,6 +121,8 @@ def __init__(
self.output_manager = optimization_problem.output_manager
self.initialize_solver()
+ self.constraint_manager = optimization_problem.constraint_manager
+
@property
def iteration(self) -> int:
"""The number of iterations performed by the solver."""
@@ -351,3 +358,31 @@ def evaluate_cost_functional(self) -> None:
"""Evaluates the cost functional and performs the output operation."""
self.objective_value = self.cost_functional.evaluate()
self.output()
+
+ def project_search_direction(self) -> None:
+ """Projects the search direction to the tangent space of the active constraints.
+
+ If no mesh quality constraints are active, the search direction will not be
+ changed in any way. Otherwise, self.search_direction will be overwritten.
+
+ """
+ if (
+ self.constraint_manager is None
+ or not self.constraint_manager.has_constraints
+ ):
+ self.active_idx = None
+ self.constraint_gradient = None
+ self.dropped_idx = None
+ else:
+ (
+ p_dof,
+ _,
+ self.active_idx,
+ self.constraint_gradient,
+ self.dropped_idx,
+ ) = self.constraint_manager.compute_projected_search_direction(
+ self.search_direction, self
+ )
+ for i in range(len(self.db.function_db.gradient)):
+ self.search_direction[i].vector().vec().aypx(0.0, p_dof.vector().vec())
+ self.search_direction[i].vector().apply("")
diff --git a/cashocs/_optimization/optimization_problem.py b/cashocs/_optimization/optimization_problem.py
index 0c2f1a81..f57efbd8 100755
--- a/cashocs/_optimization/optimization_problem.py
+++ b/cashocs/_optimization/optimization_problem.py
@@ -51,6 +51,7 @@
from cashocs._optimization import line_search as ls
from cashocs._optimization import optimization_algorithms
from cashocs._optimization import optimization_variable_abstractions as ova
+ from cashocs._optimization.shape_optimization import mesh_constraint_manager
from cashocs._optimization.topology_optimization import (
topology_optimization_algorithm,
)
@@ -274,6 +275,8 @@ def __init__(
self.state_problem,
linear_solver=self.adjoint_linear_solver,
)
+ self.constraint_manager: mesh_constraint_manager.ConstraintManager | None = None
+
self.output_manager = io.OutputManager(self.db)
@abc.abstractmethod
diff --git a/cashocs/_optimization/optimization_variable_abstractions.py b/cashocs/_optimization/optimization_variable_abstractions.py
index e59f2975..4c45978d 100644
--- a/cashocs/_optimization/optimization_variable_abstractions.py
+++ b/cashocs/_optimization/optimization_variable_abstractions.py
@@ -27,6 +27,7 @@
from typing import List, TYPE_CHECKING
import fenics
+import numpy as np
if TYPE_CHECKING:
from cashocs import _typing
@@ -76,7 +77,13 @@ def revert_variable_update(self) -> None:
@abc.abstractmethod
def update_optimization_variables(
- self, search_direction: List[fenics.Function], stepsize: float, beta: float
+ self,
+ search_direction: List[fenics.Function],
+ stepsize: float,
+ beta: float,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: np.ndarray | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> float:
"""Updates the optimization variables based on a line search.
@@ -85,6 +92,13 @@ def update_optimization_variables(
stepsize: The current (trial) stepsize.
beta: The parameter for the line search, which "halves" the stepsize if the
test was not successful.
+ active_idx: The list of active indices of the working set. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
+ constraint_gradient: The gradient of the constraints for the mesh quality.
+ Only needed for shape optimization with mesh quality constraints.
+ Default is `None`.
+ dropped_idx: The list of indicies for dropped constraints. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
Returns:
The stepsize which was found to be acceptable.
diff --git a/cashocs/_optimization/shape_optimization/mesh_constraint_manager.py b/cashocs/_optimization/shape_optimization/mesh_constraint_manager.py
new file mode 100644
index 00000000..6db66272
--- /dev/null
+++ b/cashocs/_optimization/shape_optimization/mesh_constraint_manager.py
@@ -0,0 +1,521 @@
+# Copyright (C) 2020-2024 Sebastian Blauth
+#
+# This file is part of cashocs.
+#
+# cashocs is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# cashocs is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with cashocs. If not, see .
+
+"""Constraints for the mesh / shape in shape optimization."""
+
+from __future__ import annotations
+
+from typing import TYPE_CHECKING
+
+import fenics
+from mpi4py import MPI
+import numpy as np
+from petsc4py import PETSc
+from scipy import sparse
+
+from cashocs import _exceptions
+from cashocs import _loggers
+from cashocs import _utils
+from cashocs._optimization.shape_optimization import mesh_constraints
+import cashocs.io
+
+if TYPE_CHECKING:
+ from cashocs._optimization import optimization_algorithms
+
+
+class ConstraintManager:
+ """This class manages all (selected) mesh quality constraints.
+
+ It is used to treat arbitrary constraints (on the mesh coordinates) in a unified
+ manner.
+ """
+
+ def __init__(
+ self,
+ config: cashocs.io.Config,
+ mesh: fenics.Mesh,
+ boundaries: fenics.MeshFunction,
+ deformation_space: fenics.FunctionSpace,
+ ) -> None:
+ """Initializes the constraint manager.
+
+ Args:
+ config: The configuration of the optimization problem.
+ mesh: The underlying FEM mesh.
+ boundaries: The :py:class`fenics.MeshFunction` used to mark the boundaries
+ of the mesh.
+ deformation_space: A :py:class`fenics.FunctionSpace` of vector CG1 elements
+ for mesh deformations.
+
+ """
+ self.config = config
+ self.mesh = mesh
+ self.boundaries = boundaries
+
+ self.has_constraints = (
+ self.config.getfloat("MeshQualityConstraints", "min_angle") > 0.0
+ ) or (
+ self.config.getfloat(
+ "MeshQualityConstraints", "feasible_angle_reduction_factor"
+ )
+ > 0.0
+ )
+ self.v2d = fenics.vertex_to_dof_map(deformation_space)
+ self.d2v = fenics.dof_to_vertex_map(deformation_space)
+ loc0, loc1 = deformation_space.dofmap().ownership_range()
+ self.d2v_local = self.d2v[: loc1 - loc0]
+
+ fun = fenics.Function(deformation_space)
+ self.local_petsc_size = fun.vector().vec().getSizes()[0]
+ self.comm = self.mesh.mpi_comm()
+
+ self.constraints: list[mesh_constraints.MeshConstraint] = []
+ self.constraint_tolerance: float = self.config.getfloat(
+ "MeshQualityConstraints", "tol"
+ )
+ self.no_constraints = 0
+
+ if self.has_constraints:
+ if self.mesh.geometry().dim() == 2:
+ angle_constraint: mesh_constraints.AngleConstraint = (
+ mesh_constraints.TriangleAngleConstraint(
+ self.mesh, self.config, deformation_space
+ )
+ )
+
+ elif self.mesh.geometry().dim() == 3:
+ angle_constraint = mesh_constraints.SolidAngleConstraint(
+ self.mesh, self.config, deformation_space
+ )
+ else:
+ raise _exceptions.InputError(
+ "ConstraintManager",
+ "mesh",
+ "Can only use mesh quality constraints for 2D and 3D meshes.",
+ )
+
+ self.constraints.append(angle_constraint)
+
+ additional_fixed_idcs = angle_constraint.bad_idcs
+ additional_fixed_coordinates = angle_constraint.bad_coordinates
+
+ self.constraints.append(
+ mesh_constraints.FixedVertexConstraint(
+ self.mesh,
+ self.boundaries,
+ self.config,
+ deformation_space,
+ additional_fixed_idcs=additional_fixed_idcs,
+ additional_fixed_coordinates=additional_fixed_coordinates,
+ )
+ )
+
+ self.inequality_mask = self._compute_inequality_mask()
+ self.no_constraints = len(self.inequality_mask)
+ necessary_constraints = []
+ for constraint in self.constraints:
+ necessary_constraints.append(constraint.is_necessary)
+ self.necessary_constraints = np.concatenate(necessary_constraints)
+
+ if not np.all(self.is_feasible(self.mesh.coordinates().copy().reshape(-1))):
+ raise _exceptions.InputError(
+ "ShapeOptimizationProblem",
+ "mesh",
+ "You must supply a mesh which is feasible w.r.t. the mesh "
+ "quality constraints, or try using a lower minimum angle.",
+ )
+
+ def _compute_inequality_mask(self) -> np.ndarray:
+ """Computes the mask which distinguishes between (in-)equality constaints.
+
+ Returns:
+ A boolean array (a mask) which is `True` when the corresponding constraint
+ is an inequality constraint.
+
+ """
+ mask = []
+ for constraint in self.constraints:
+ if constraint.type == "equality":
+ mask += [False] * constraint.no_constraints
+ elif constraint.type == "inequality":
+ mask += [True] * constraint.no_constraints
+
+ return np.array(mask)
+
+ def evaluate(self, coords_seq: np.ndarray) -> np.ndarray:
+ """Evaluates all (selected) mesh quality constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A numpy array with the values of the constraint functions.
+
+ """
+ result = []
+ for constraint in self.constraints:
+ result.append(constraint.evaluate(coords_seq))
+
+ if len(result) > 0:
+ self.function_values: np.ndarray = np.concatenate(result)
+ else:
+ return np.array([])
+
+ return self.function_values
+
+ def evaluate_active(
+ self, coords_seq: np.ndarray, active_idx: np.ndarray
+ ) -> np.ndarray:
+ """Evaluates only the constraints corresponding to the working set.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+ active_idx: The mask of active indices corresponding to the working set.
+
+ Returns:
+ A numpy array containing only the values of the constraint functions that
+ are in the working set.
+
+ """
+ function_values: np.ndarray = self.evaluate(coords_seq)[active_idx]
+ return function_values
+
+ def _compute_gradient(self, coords_seq: np.ndarray) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the gradient.
+
+ """
+ result = []
+ for constraint in self.constraints:
+ result.append(constraint.compute_gradient(coords_seq))
+
+ if len(result) > 0:
+ self.gradient = sparse.vstack(result)
+ else:
+ return np.array([])
+
+ return self.gradient
+
+ def compute_active_gradient(
+ self, active_idx: np.ndarray, constraint_gradient: sparse.csr_matrix
+ ) -> PETSc.Mat:
+ """Computes the gradient of those constraint functions that are active.
+
+ Args:
+ active_idx: The boolean array corresponding to the current working set.
+ constraint_gradient: The entire (sparse) constraint gradient.
+
+ Returns:
+ A sparse matrix of the constraint gradient w.r.t. the working set.
+
+ """
+ scipy_matrix = constraint_gradient[active_idx]
+
+ petsc_matrix = _utils.linalg.scipy2petsc(
+ scipy_matrix,
+ self.mesh.mpi_comm(),
+ local_size=self.local_petsc_size,
+ )
+ return petsc_matrix
+
+ def compute_active_set(self, coords_seq: np.ndarray) -> np.ndarray:
+ """Computes the working set.
+
+ The working set is the set of constraints which are active at a given point.
+
+ Args:
+ coords_seq: The list of flattened mesh coordinates.
+
+ Returns:
+ A boolean array which is `True` in component `i` if constraint `i` is
+ active.
+
+ """
+ function_values = self.evaluate(coords_seq)
+ result: np.ndarray = np.abs(function_values) <= self.constraint_tolerance
+ return result
+
+ def is_necessary(self, active_idx: np.ndarray | None) -> bool:
+ """Checks, whether constraint treatment is necessary based on the working set.
+
+ This can be `False`, e.g., when only fixed boundary constraints are active (as
+ these are directly treated in the gradient deformation) or no constraints are
+ currently active.
+
+ Args:
+ active_idx: The boolean array representing the working set.
+
+ Returns:
+ A boolean, which is `True` when active treatment of the constraints is
+ necessary and `False` otherwise.
+
+ """
+ if self.has_constraints:
+ necessary_constraints_gathered = self.comm.allgather(
+ self.necessary_constraints
+ )
+ necessary_constraints_global = np.concatenate(
+ necessary_constraints_gathered
+ )
+ active_idx_gathered = self.comm.allgather(active_idx)
+ active_idx_global = np.concatenate(active_idx_gathered)
+
+ result = bool(
+ np.any(np.logical_and(necessary_constraints_global, active_idx_global))
+ )
+ return result
+ else:
+ return False
+
+ def is_feasible(self, coords_seq: np.ndarray) -> np.ndarray:
+ """Checks, whether a given point is feasible w.r.t. all constraints.
+
+ Args:
+ coords_seq: The list of flattened mesh coordinates for the trial point.
+
+ Returns:
+ A boolean array, which is `True` in component `i` if the corresponding
+ constraint is not violated, else `False`.
+
+ """
+ function_values = self.evaluate(coords_seq)
+ function_values_list = self.comm.allgather(function_values)
+ function_values_global = np.concatenate(function_values_list)
+
+ result: np.ndarray = np.less_equal(
+ function_values_global, self.constraint_tolerance
+ )
+ return result
+
+ def compute_projected_search_direction(
+ self,
+ search_direction: list[fenics.Function],
+ solver: optimization_algorithms.OptimizationAlgorithm,
+ ) -> tuple[
+ fenics.Function,
+ bool,
+ np.ndarray | None,
+ sparse.csr_matrix | None,
+ np.ndarray | None,
+ ]:
+ """Projects the search direction to the tangent space of the active constraints.
+
+ Args:
+ search_direction: The current search direction used in the solver.
+ solver: The solver, which is used to solve the optimization problem.
+
+ Returns:
+ A tuple `(p_dof, converged, active_idx, constraint_gradient, dropped_idx)`,
+ where `p_dof` is the projected search direction in dof-based ordering,
+ `active_idx` is the index set of the active constraints (those in the
+ current working set), `constraint_gradient` is the gradient matrix of the
+ constraints, `dropped_idx` is the index set of all dropped constraints.
+
+ """
+ coords_sequential = self.mesh.coordinates().copy().reshape(-1)
+ constraint_gradient = self._compute_gradient(coords_sequential)
+ active_idx = self.compute_active_set(coords_sequential)
+ self._compute_number_of_active_constraints(active_idx)
+
+ if self.is_necessary(active_idx):
+ return self._compute_projected_search_direction(
+ search_direction, solver, active_idx, constraint_gradient
+ )
+ else:
+ p_dof = fenics.Function(search_direction[0].function_space())
+ p_dof.vector().vec().aypx(0.0, search_direction[0].vector().vec())
+ p_dof.vector().apply("")
+ if active_idx is not None:
+ dropped_idx = np.array([False] * len(active_idx))
+ else:
+ dropped_idx = None
+
+ return p_dof, False, active_idx, constraint_gradient, dropped_idx
+
+ def _compute_projected_search_direction(
+ self,
+ search_direction: list[fenics.Function],
+ solver: optimization_algorithms.OptimizationAlgorithm,
+ active_idx: np.ndarray,
+ constraint_gradient: sparse.csr_matrix,
+ ) -> tuple[fenics.Function, bool, np.ndarray, sparse.csr_matrix, np.ndarray]:
+ converged = False
+ has_dropped_constraints = False
+ has_undroppable_constraints = False
+ no_constraints = constraint_gradient.shape[0]
+ dropped_idx_list: list[int] = []
+ undroppable_idx = []
+ lambda_min_rank = 0
+
+ while True:
+ # pylint: disable=invalid-name
+ A = self.compute_active_gradient(active_idx, constraint_gradient)
+ AT = A.copy().transpose() # pylint: disable=invalid-name
+ B = A.matMult(AT) # pylint: disable=invalid-name
+
+ p, lambd = self._project_search_direction_to_tangent_space(
+ search_direction, A, AT, B
+ )
+
+ if has_dropped_constraints:
+ if not self._check_for_feasibility_of_dropped_constraints(
+ p, constraint_gradient, dropped_idx_list
+ ):
+ if self.comm.rank == lambda_min_rank:
+ relevant_idx = dropped_idx_list.pop()
+ active_idx[relevant_idx] = True
+ undroppable_idx.append(relevant_idx)
+ self.comm.barrier()
+ has_undroppable_constraints = True
+ continue
+
+ p_dof = fenics.Function(solver.db.function_db.control_spaces[0])
+ p_dof.vector().set_local(p.getArray())
+ p_dof.vector().apply("")
+ solver.form_handler.apply_shape_bcs(p_dof)
+ p_dof.vector().apply("")
+
+ lambd_padded = np.zeros(no_constraints)
+
+ lambd_padded[active_idx] = lambd
+ lambd_ineq = lambd_padded[self.inequality_mask]
+
+ lambda_min_list = self.comm.allgather(lambd_ineq.min())
+ lambda_min_rank = int(np.argmin(lambda_min_list))
+ lambda_min = np.min(lambda_min_list)
+ gamma = -np.minimum(0.0, lambda_min)
+
+ if (
+ np.sqrt(solver.form_handler.scalar_product([p_dof], [p_dof])) <= gamma
+ and not has_undroppable_constraints
+ ):
+ if self.comm.rank == lambda_min_rank:
+ i_min_list = np.argsort(lambd_ineq)
+ i_min_list_padded = np.where(self.inequality_mask)[0][i_min_list]
+ mask = ~np.isin(i_min_list_padded, undroppable_idx)
+ i_min_padded = i_min_list_padded[mask][0]
+
+ active_idx[i_min_padded] = False
+ dropped_idx_list.append(i_min_padded)
+ print(f"Dropped constraint {i_min_padded}", flush=True)
+
+ has_dropped_constraints = True
+ self.comm.barrier()
+ continue
+ else:
+ break
+
+ if (
+ np.sqrt(solver.form_handler.scalar_product([p_dof], [p_dof]))
+ <= solver.atol + solver.rtol * solver.gradient_norm_initial
+ ):
+ lambda_min = np.min(lambd_ineq)
+
+ if lambda_min >= 0.0:
+ converged = True
+ print("Algorithm converged!")
+ else:
+ pass
+
+ dropped_idx = np.array([False] * len(active_idx))
+ dropped_idx[dropped_idx_list] = True
+
+ return p_dof, converged, active_idx, constraint_gradient, dropped_idx
+
+ def _project_search_direction_to_tangent_space(
+ self,
+ search_direction: list[fenics.Function],
+ A: PETSc.Mat, # pylint: disable=invalid-name
+ AT: PETSc.Mat, # pylint: disable=invalid-name
+ B: PETSc.Mat, # pylint: disable=invalid-name
+ ) -> tuple[PETSc.Vec, PETSc.Vec]:
+ # if self.mode == "complete":
+ # pylint: disable=invalid-name
+ # S = solver.form_handler.scalar_product_matrix[:, :]
+ # S_inv = np.linalg.inv(S) # pylint: disable=invalid-name
+ # lambd = np.linalg.solve(A @ S_inv @ A.T, -A @ self.gradient[0].vector()[:])
+ # p = -(self.gradient[0].vector()[:] + S_inv @ A.T @ lambd)
+ # else:
+
+ b = A.createVecLeft()
+ A.mult(search_direction[0].vector().vec(), b)
+ ksp = PETSc.KSP().create(comm=self.mesh.mpi_comm())
+ options: dict[str, float | int | str | None] = {
+ "ksp_type": "cg",
+ "ksp_max_it": 1000,
+ "ksp_rtol": self.constraint_tolerance / 1e2,
+ "ksp_atol": 1e-30,
+ "pc_type": "hypre",
+ "pc_hypre_type": "boomeramg",
+ # "ksp_monitor_true_residual": None,
+ }
+
+ ksp.setOperators(B)
+ _utils.setup_petsc_options([ksp], [options])
+
+ lambd = B.createVecRight()
+ ksp.solve(b, lambd)
+
+ if ksp.getConvergedReason() < 0:
+ raise _exceptions.NotConvergedError(
+ "Gradient projection", "The gradient projection failed."
+ )
+
+ p = AT.createVecLeft()
+ AT.mult(-lambd, p)
+ p.axpy(1.0, search_direction[0].vector().vec())
+
+ return p, lambd
+
+ def _check_for_feasibility_of_dropped_constraints(
+ self,
+ p: PETSc.Vec,
+ constraint_gradient: sparse.csr_matrix,
+ dropped_idx_list: list[int],
+ ) -> bool:
+ scipy_matrix = constraint_gradient[dropped_idx_list]
+ petsc_matrix = _utils.linalg.scipy2petsc(
+ scipy_matrix,
+ self.comm,
+ local_size=self.local_petsc_size,
+ )
+ res = petsc_matrix.getVecLeft()
+ petsc_matrix.mult(p, res)
+ directional_constraint_derivative_max = res.max()[1]
+ return bool(directional_constraint_derivative_max < 1e-12)
+
+ def _compute_number_of_active_constraints(self, active_idx: np.ndarray) -> None:
+ no_active_equality_constraints_local = sum(active_idx[~self.inequality_mask])
+ no_active_inequality_constraints_local = sum(active_idx[self.inequality_mask])
+
+ no_active_equality_constraints_global = self.comm.allreduce(
+ no_active_equality_constraints_local, op=MPI.SUM
+ )
+ no_active_inequality_constraints_global = self.comm.allreduce(
+ no_active_inequality_constraints_local, op=MPI.SUM
+ )
+
+ _loggers.debug(
+ f"{no_active_equality_constraints_global} equality "
+ f"and {no_active_inequality_constraints_global} inequality constraints "
+ "are currently active."
+ )
diff --git a/cashocs/_optimization/shape_optimization/mesh_constraints.py b/cashocs/_optimization/shape_optimization/mesh_constraints.py
new file mode 100644
index 00000000..85cfa13f
--- /dev/null
+++ b/cashocs/_optimization/shape_optimization/mesh_constraints.py
@@ -0,0 +1,1922 @@
+# Copyright (C) 2020-2024 Sebastian Blauth
+#
+# This file is part of cashocs.
+#
+# cashocs is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# cashocs is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with cashocs. If not, see .
+
+"""Constraints for the mesh / shape in shape optimization."""
+
+from __future__ import annotations
+
+import abc
+
+import fenics
+from mpi4py import MPI
+import numpy as np
+from scipy import sparse
+
+from cashocs import _exceptions
+from cashocs import _loggers
+from cashocs import _utils
+import cashocs.io
+
+cpp_code = """
+#include
+#include
+#include
+namespace py = pybind11;
+
+#include
+
+#include
+#include
+#include
+#include
+
+using namespace dolfin;
+
+void angles_triangle(const Cell& cell, std::vector& angs)
+{
+ const Mesh& mesh = cell.mesh();
+ angs.resize(3);
+ const std::size_t i0 = cell.entities(0)[0];
+ const std::size_t i1 = cell.entities(0)[1];
+ const std::size_t i2 = cell.entities(0)[2];
+
+ const Point p0 = Vertex(mesh, i0).point();
+ const Point p1 = Vertex(mesh, i1).point();
+ const Point p2 = Vertex(mesh, i2).point();
+ Point e0 = p1 - p0;
+ Point e1 = p2 - p0;
+ Point e2 = p2 - p1;
+
+ e0 /= e0.norm();
+ e1 /= e1.norm();
+ e2 /= e2.norm();
+
+ angs[0] = acos(e0.dot(e1));
+ angs[1] = acos(-e0.dot(e2));
+ angs[2] = acos(e1.dot(e2));
+}
+
+void compute_dihedral_angles(const Cell& cell, std::vector& angs)
+{
+ const Mesh& mesh = cell.mesh();
+ angs.resize(6);
+
+ const std::size_t i0 = cell.entities(0)[0];
+ const std::size_t i1 = cell.entities(0)[1];
+ const std::size_t i2 = cell.entities(0)[2];
+ const std::size_t i3 = cell.entities(0)[3];
+
+ const Point p0 = Vertex(mesh, i0).point();
+ const Point p1 = Vertex(mesh, i1).point();
+ const Point p2 = Vertex(mesh, i2).point();
+ const Point p3 = Vertex(mesh, i3).point();
+
+ Point e10 = p1 - p0;
+ Point e20 = p2 - p0;
+ Point e30 = p3 - p0;
+ Point e21 = p2 - p1;
+ Point e31 = p3 - p1;
+
+ Point n031 = e31.cross(e10);
+ Point n021 = e21.cross(e10);
+ Point n231 = e21.cross(e31);
+ Point n230 = e20.cross(e30);
+
+ n031 /= n031.norm();
+ n021 /= n021.norm();
+ n231 /= n231.norm();
+ n230 /= n230.norm();
+
+ angs[0] = acos(n031.dot(n021));
+ angs[1] = acos(-n021.dot(n231));
+ angs[2] = acos(n231.dot(n031));
+ angs[3] = acos(n021.dot(n230));
+ angs[4] = acos(n031.dot(-n230));
+ angs[5] = acos(n230.dot(n231));
+}
+
+py::array_t
+triangle_angles(std::shared_ptr mesh)
+{
+ size_t idx = 0;
+ auto n = mesh->num_cells();
+ py::array_t angles(3*n);
+ auto buf = angles.request();
+ double *ptr = (double *) buf.ptr;
+
+ std::vector angs;
+
+ for (CellIterator cell(*mesh); !cell.end(); ++cell)
+ {
+ angles_triangle(*cell, angs);
+ ptr[3*idx] = angs[0];
+ ptr[3*idx+1] = angs[1];
+ ptr[3*idx+2] = angs[2];
+ idx += 1;
+ }
+ return angles;
+}
+
+py::array_t
+tetrahedron_dihedral_angles(std::shared_ptr mesh)
+{
+ size_t idx = 0;
+ auto n = mesh->num_cells();
+ py::array_t angles(6*n);
+ auto buf = angles.request();
+ double *ptr = (double *) buf.ptr;
+
+ std::vector angs;
+
+ for (CellIterator cell(*mesh); !cell.end(); ++cell)
+ {
+ compute_dihedral_angles(*cell, angs);
+ ptr[6*idx] = angs[0];
+ ptr[6*idx+1] = angs[1];
+ ptr[6*idx+2] = angs[2];
+ ptr[6*idx+3] = angs[3];
+ ptr[6*idx+4] = angs[4];
+ ptr[6*idx+5] = angs[5];
+ idx += 1;
+ }
+ return angles;
+}
+
+py::array_t
+tetrahedron_solid_angles(std::shared_ptr mesh)
+{
+ size_t idx = 0;
+ auto n = mesh->num_cells();
+ py::array_t solid_angles(4*n);
+ auto buf = solid_angles.request();
+ double *ptr = (double *) buf.ptr;
+
+ std::vector d_angs;
+
+ for (CellIterator cell(*mesh); !cell.end(); ++cell)
+ {
+ compute_dihedral_angles(*cell, d_angs);
+ ptr[4*idx+0] = d_angs[0] + d_angs[3] + d_angs[4] - DOLFIN_PI;
+ ptr[4*idx+1] = d_angs[0] + d_angs[1] + d_angs[2] - DOLFIN_PI;
+ ptr[4*idx+2] = d_angs[1] + d_angs[3] + d_angs[5] - DOLFIN_PI;
+ ptr[4*idx+3] = d_angs[2] + d_angs[4] + d_angs[5] - DOLFIN_PI;
+ idx += 1;
+ }
+ return solid_angles;
+}
+
+std::tuple, py::array_t, py::array_t>
+triangle_angle_gradient(std::shared_ptr mesh)
+{
+ size_t idx = 0;
+ auto n = mesh->num_cells();
+
+ py::array_t rows(18*n);
+ auto buf_rows = rows.request();
+ int *ptr_rows = (int *) buf_rows.ptr;
+
+ py::array_t cols(18*n);
+ auto buf_cols = cols.request();
+ int *ptr_cols = (int *) buf_cols.ptr;
+
+ py::array_t vals(18*n);
+ auto buf_vals = vals.request();
+ double *ptr_vals = (double *) buf_vals.ptr;
+
+ for (CellIterator cell(*mesh); !cell.end(); ++cell)
+ {
+ auto ents = cell->entities(0);
+ const std::size_t i0 = ents[0];
+ const std::size_t i1 = ents[1];
+ const std::size_t i2 = ents[2];
+
+ const Point p0 = Vertex(*mesh, i0).point();
+ const Point p1 = Vertex(*mesh, i1).point();
+ const Point p2 = Vertex(*mesh, i2).point();
+ Point e0 = p1 - p0;
+ Point e1 = p2 - p0;
+ Point e2 = p2 - p1;
+
+ Point tpa1 = e0.cross(e0.cross(e1));
+ Point tpa2 = e1.cross(e1.cross(e0));
+ tpa1 /= tpa1.norm();
+ tpa2 /= tpa2.norm();
+
+ Point tpb0 = e0.cross(e0.cross(e2));
+ Point tpb2 = e2.cross(e2.cross(-e0));
+ tpb0 /= tpb0.norm();
+ tpb2 /= tpb2.norm();
+
+ Point tpc0 = e1.cross(e1.cross(-e2));
+ Point tpc1 = e2.cross(e2.cross(-e1));
+ tpc0 /= tpc0.norm();
+ tpc1 /= tpc1.norm();
+
+ Point dad0 = 1.0 / e0.norm() * tpa1 + 1.0 / e1.norm() * tpa2;
+ Point dad1 = -1.0 / e0.norm() * tpa1;
+ Point dad2 = -1.0 / e1.norm() * tpa2;
+
+ Point dbd0 = -1.0 / e0.norm() * tpb0;
+ Point dbd1 = 1.0 / e0.norm() * tpb0 + 1.0 / e2.norm() * tpb2;
+ Point dbd2 = -1.0 / e2.norm() * tpb2;
+
+ Point dcd0 = -1.0 / e1.norm() * tpc0;
+ Point dcd1 = -1.0 / e2.norm() * tpc1;
+ Point dcd2 = 1.0 / e1.norm() * tpc0 + 1.0 / e2.norm() * tpc1;
+
+ ptr_rows[18*idx + 0] = 3 * idx;
+ ptr_rows[18*idx + 1] = 3 * idx;
+ ptr_rows[18*idx + 2] = 3 * idx;
+ ptr_rows[18*idx + 3] = 3 * idx;
+ ptr_rows[18*idx + 4] = 3 * idx;
+ ptr_rows[18*idx + 5] = 3 * idx;
+
+ ptr_cols[18*idx + 0] = 2 * i0 + 0;
+ ptr_cols[18*idx + 1] = 2 * i0 + 1;
+ ptr_cols[18*idx + 2] = 2 * i1 + 0;
+ ptr_cols[18*idx + 3] = 2 * i1 + 1;
+ ptr_cols[18*idx + 4] = 2 * i2 + 0;
+ ptr_cols[18*idx + 5] = 2 * i2 + 1;
+
+ ptr_vals[18*idx + 0] = dad0[0];
+ ptr_vals[18*idx + 1] = dad0[1];
+ ptr_vals[18*idx + 2] = dad1[0];
+ ptr_vals[18*idx + 3] = dad1[1];
+ ptr_vals[18*idx + 4] = dad2[0];
+ ptr_vals[18*idx + 5] = dad2[1];
+
+ ptr_rows[18*idx + 6] = 3 * idx + 1;
+ ptr_rows[18*idx + 7] = 3 * idx + 1;
+ ptr_rows[18*idx + 8] = 3 * idx + 1;
+ ptr_rows[18*idx + 9] = 3 * idx + 1;
+ ptr_rows[18*idx + 10] = 3 * idx + 1;
+ ptr_rows[18*idx + 11] = 3 * idx + 1;
+
+ ptr_cols[18*idx + 6] = 2 * i0 + 0;
+ ptr_cols[18*idx + 7] = 2 * i0 + 1;
+ ptr_cols[18*idx + 8] = 2 * i1 + 0;
+ ptr_cols[18*idx + 9] = 2 * i1 + 1;
+ ptr_cols[18*idx + 10] = 2 * i2 + 0;
+ ptr_cols[18*idx + 11] = 2 * i2 + 1;
+
+ ptr_vals[18*idx + 6] = dbd0[0];
+ ptr_vals[18*idx + 7] = dbd0[1];
+ ptr_vals[18*idx + 8] = dbd1[0];
+ ptr_vals[18*idx + 9] = dbd1[1];
+ ptr_vals[18*idx + 10] = dbd2[0];
+ ptr_vals[18*idx + 11] = dbd2[1];
+
+ ptr_rows[18*idx + 12] = 3 * idx + 2;
+ ptr_rows[18*idx + 13] = 3 * idx + 2;
+ ptr_rows[18*idx + 14] = 3 * idx + 2;
+ ptr_rows[18*idx + 15] = 3 * idx + 2;
+ ptr_rows[18*idx + 16] = 3 * idx + 2;
+ ptr_rows[18*idx + 17] = 3 * idx + 2;
+
+ ptr_cols[18*idx + 12] = 2 * i0 + 0;
+ ptr_cols[18*idx + 13] = 2 * i0 + 1;
+ ptr_cols[18*idx + 14] = 2 * i1 + 0;
+ ptr_cols[18*idx + 15] = 2 * i1 + 1;
+ ptr_cols[18*idx + 16] = 2 * i2 + 0;
+ ptr_cols[18*idx + 17] = 2 * i2 + 1;
+
+ ptr_vals[18*idx + 12] = dcd0[0];
+ ptr_vals[18*idx + 13] = dcd0[1];
+ ptr_vals[18*idx + 14] = dcd1[0];
+ ptr_vals[18*idx + 15] = dcd1[1];
+ ptr_vals[18*idx + 16] = dcd2[0];
+ ptr_vals[18*idx + 17] = dcd2[1];
+
+ idx += 1;
+ }
+ return std::make_tuple(rows, cols, vals);
+}
+
+std::tuple, py::array_t, py::array_t>
+tetrahedron_dihedral_angle_gradient(std::shared_ptr mesh)
+{
+ size_t idx = 0;
+ auto n = mesh->num_cells();
+
+ py::array_t rows(72*n);
+ auto buf_rows = rows.request();
+ int *ptr_rows = (int *) buf_rows.ptr;
+
+ py::array_t cols(72*n);
+ auto buf_cols = cols.request();
+ int *ptr_cols = (int *) buf_cols.ptr;
+
+ py::array_t vals(72*n);
+ auto buf_vals = vals.request();
+ double *ptr_vals = (double *) buf_vals.ptr;
+
+ Eigen::Matrix3d skew_10;
+ Eigen::Matrix3d skew_20;
+ Eigen::Matrix3d skew_30;
+ Eigen::Matrix3d skew_21;
+ Eigen::Matrix3d skew_31;
+ Eigen::Matrix3d skew_32;
+
+ Eigen::RowVector3d dadk;
+ Eigen::RowVector3d dadl;
+ Eigen::RowVector3d dbdk;
+ Eigen::RowVector3d dbdl;
+ Eigen::RowVector3d dcdk;
+ Eigen::RowVector3d dcdl;
+ Eigen::RowVector3d dddk;
+ Eigen::RowVector3d dddl;
+ Eigen::RowVector3d dedk;
+ Eigen::RowVector3d dedl;
+ Eigen::RowVector3d dfdk;
+ Eigen::RowVector3d dfdl;
+
+ for (CellIterator cell(*mesh); !cell.end(); ++cell)
+ {
+ auto ents = cell->entities(0);
+ const std::size_t i0 = ents[0];
+ const std::size_t i1 = ents[1];
+ const std::size_t i2 = ents[2];
+ const std::size_t i3 = ents[3];
+
+ const Point p0 = Vertex(*mesh, i0).point();
+ const Point p1 = Vertex(*mesh, i1).point();
+ const Point p2 = Vertex(*mesh, i2).point();
+ const Point p3 = Vertex(*mesh, i3).point();
+
+ Point e10 = p1 - p0;
+ Point e20 = p2 - p0;
+ Point e30 = p3 - p0;
+ Point e21 = p2 - p1;
+ Point e31 = p3 - p1;
+ Point e32 = p3 - p2;
+
+ skew_10 << 0.0, e10.z(), -e10.y(),
+ -e10.z(), 0.0, e10.x(),
+ e10.y(), -e10.x(), 0.0;
+
+ skew_20 << 0.0, e20.z(), -e20.y(),
+ -e20.z(), 0.0, e20.x(),
+ e20.y(), -e20.x(), 0.0;
+
+ skew_30 << 0.0, e30.z(), -e30.y(),
+ -e30.z(), 0.0, e30.x(),
+ e30.y(), -e30.x(), 0.0;
+
+ skew_21 << 0.0, e21.z(), -e21.y(),
+ -e21.z(), 0.0, e21.x(),
+ e21.y(), -e21.x(), 0.0;
+
+ skew_31 << 0.0, e31.z(), -e31.y(),
+ -e31.z(), 0.0, e31.x(),
+ e31.y(), -e31.x(), 0.0;
+
+ skew_32 << 0.0, e32.z(), -e32.y(),
+ -e32.z(), 0.0, e32.x(),
+ e32.y(), -e32.x(), 0.0;
+
+ Point n031 = e31.cross(e10);
+ Point n021 = e21.cross(e10);
+ Point n231 = e21.cross(e31);
+ Point n230 = e20.cross(e30);
+
+ Point tpa3 = n031.cross(n031.cross(n021));
+ Point tpa2 = n021.cross(n021.cross(n031));
+ tpa3 /= (tpa3.norm() * n031.norm());
+ tpa2 /= (tpa2.norm() * n021.norm());
+ dadk << tpa3.x(), tpa3.y(), tpa3.z();
+ dadl << tpa2.x(), tpa2.y(), tpa2.z();
+
+ Point tpb0 = n021.cross(n021.cross(n231));
+ Point tpb3 = n231.cross(n231.cross(-n021));
+ tpb0 /= (tpb0.norm() * n021.norm());
+ tpb3 /= (tpb3.norm() * n231.norm());
+ dbdk << tpb0.x(), tpb0.y(), tpb0.z();
+ dbdl << tpb3.x(), tpb3.y(), tpb3.z();
+
+ Point tpc2 = n231.cross(n231.cross(-n031));
+ Point tpc0 = n031.cross(n031.cross(-n231));
+ tpc2 /= (tpc2.norm() * n231.norm());
+ tpc0 /= (tpc0.norm() * n031.norm());
+ dcdk << tpc2.x(), tpc2.y(), tpc2.z();
+ dcdl << tpc0.x(), tpc0.y(), tpc0.z();
+
+ Point tpd1 = n021.cross(n021.cross(n230));
+ Point tpd3 = n230.cross(n230.cross(n021));
+ tpd1 /= (tpd1.norm() * n021.norm());
+ tpd3 /= (tpd3.norm() * n230.norm());
+ dddk << tpd1.x(), tpd1.y(), tpd1.z();
+ dddl << tpd3.x(), tpd3.y(), tpd3.z();
+
+ Point tpe1 = n031.cross(n031.cross(-n230));
+ Point tpe2 = n230.cross(n230.cross(n031));
+ tpe1 /= (tpe1.norm() * n031.norm());
+ tpe2 /= (tpe2.norm() * n230.norm());
+ dedk << tpe1.x(), tpe1.y(), tpe1.z();
+ dedl << tpe2.x(), tpe2.y(), tpe2.z();
+
+ Point tpf0 = n230.cross(n230.cross(n231));
+ Point tpf1 = n231.cross(n231.cross(n230));
+ tpf0 /= (tpf0.norm() * n230.norm());
+ tpf1 /= (tpf1.norm() * n231.norm());
+ dfdk << tpf0.x(), tpf0.y(), tpf0.z();
+ dfdl << tpf1.x(), tpf1.y(), tpf1.z();
+
+ auto dad0 = dadk * (-skew_31) + dadl * (-skew_21);
+ auto dad1 = dadk * (skew_10 + skew_31) + dadl * (skew_10 + skew_21);
+ auto dad2 = dadl * (-skew_10);
+ auto dad3 = dadk * (-skew_10);
+
+ auto dbd0 = dbdk * skew_21;
+ auto dbd1 = dbdk * (-skew_21 - skew_10) + dbdl * (-skew_21 + skew_31);
+ auto dbd2 = dbdk * skew_10 + dbdl * (-skew_31);
+ auto dbd3 = dbdl * skew_21;
+
+ auto dcd0 = dcdl * skew_31;
+ auto dcd1 = dcdk * (-skew_31 + skew_21) + dcdl * (-skew_31 - skew_10);
+ auto dcd2 = dcdk * skew_31;
+ auto dcd3 = dcdk * (-skew_21) + dcdl * skew_10;
+
+ auto ddd0 = dddk * (-skew_20 + skew_10) + dddl * (-skew_20 + skew_30);
+ auto ddd1 = dddk * skew_20;
+ auto ddd2 = dddk * (-skew_10) + dddl * (-skew_30);
+ auto ddd3 = dddl * skew_20;
+
+ auto ded0 = dedk * (-skew_30 + skew_10) + dedl * (-skew_30 + skew_20);
+ auto ded1 = dedk * skew_30;
+ auto ded2 = dedl * skew_30;
+ auto ded3 = dedk * (-skew_10) + dedl * (-skew_20);
+
+ auto dfd0 = dfdk * skew_32;
+ auto dfd1 = dfdl * skew_32;
+ auto dfd2 = dfdk * (-skew_32 - skew_20) + dfdl * (-skew_32 - skew_21);
+ auto dfd3 = dfdk * skew_20 + dfdl * skew_21;
+
+ ptr_rows[72*idx + 0] = 6 * idx;
+ ptr_rows[72*idx + 1] = 6 * idx;
+ ptr_rows[72*idx + 2] = 6 * idx;
+ ptr_rows[72*idx + 3] = 6 * idx;
+ ptr_rows[72*idx + 4] = 6 * idx;
+ ptr_rows[72*idx + 5] = 6 * idx;
+ ptr_rows[72*idx + 6] = 6 * idx;
+ ptr_rows[72*idx + 7] = 6 * idx;
+ ptr_rows[72*idx + 8] = 6 * idx;
+ ptr_rows[72*idx + 9] = 6 * idx;
+ ptr_rows[72*idx + 10] = 6 * idx;
+ ptr_rows[72*idx + 11] = 6 * idx;
+
+ ptr_cols[72*idx + 0] = 3 * i0 + 0;
+ ptr_cols[72*idx + 1] = 3 * i0 + 1;
+ ptr_cols[72*idx + 2] = 3 * i0 + 2;
+ ptr_cols[72*idx + 3] = 3 * i1 + 0;
+ ptr_cols[72*idx + 4] = 3 * i1 + 1;
+ ptr_cols[72*idx + 5] = 3 * i1 + 2;
+ ptr_cols[72*idx + 6] = 3 * i2 + 0;
+ ptr_cols[72*idx + 7] = 3 * i2 + 1;
+ ptr_cols[72*idx + 8] = 3 * i2 + 2;
+ ptr_cols[72*idx + 9] = 3 * i3 + 0;
+ ptr_cols[72*idx + 10] = 3 * i3 + 1;
+ ptr_cols[72*idx + 11] = 3 * i3 + 2;
+
+ ptr_vals[72*idx + 0] = dad0[0];
+ ptr_vals[72*idx + 1] = dad0[1];
+ ptr_vals[72*idx + 2] = dad0[2];
+ ptr_vals[72*idx + 3] = dad1[0];
+ ptr_vals[72*idx + 4] = dad1[1];
+ ptr_vals[72*idx + 5] = dad1[2];
+ ptr_vals[72*idx + 6] = dad2[0];
+ ptr_vals[72*idx + 7] = dad2[1];
+ ptr_vals[72*idx + 8] = dad2[2];
+ ptr_vals[72*idx + 9] = dad3[0];
+ ptr_vals[72*idx + 10] = dad3[1];
+ ptr_vals[72*idx + 11] = dad3[2];
+
+
+ ptr_rows[72*idx + 12] = 6 * idx + 1;
+ ptr_rows[72*idx + 13] = 6 * idx + 1;
+ ptr_rows[72*idx + 14] = 6 * idx + 1;
+ ptr_rows[72*idx + 15] = 6 * idx + 1;
+ ptr_rows[72*idx + 16] = 6 * idx + 1;
+ ptr_rows[72*idx + 17] = 6 * idx + 1;
+ ptr_rows[72*idx + 18] = 6 * idx + 1;
+ ptr_rows[72*idx + 19] = 6 * idx + 1;
+ ptr_rows[72*idx + 20] = 6 * idx + 1;
+ ptr_rows[72*idx + 21] = 6 * idx + 1;
+ ptr_rows[72*idx + 22] = 6 * idx + 1;
+ ptr_rows[72*idx + 23] = 6 * idx + 1;
+
+ ptr_cols[72*idx + 12] = 3 * i0 + 0;
+ ptr_cols[72*idx + 13] = 3 * i0 + 1;
+ ptr_cols[72*idx + 14] = 3 * i0 + 2;
+ ptr_cols[72*idx + 15] = 3 * i1 + 0;
+ ptr_cols[72*idx + 16] = 3 * i1 + 1;
+ ptr_cols[72*idx + 17] = 3 * i1 + 2;
+ ptr_cols[72*idx + 18] = 3 * i2 + 0;
+ ptr_cols[72*idx + 19] = 3 * i2 + 1;
+ ptr_cols[72*idx + 20] = 3 * i2 + 2;
+ ptr_cols[72*idx + 21] = 3 * i3 + 0;
+ ptr_cols[72*idx + 22] = 3 * i3 + 1;
+ ptr_cols[72*idx + 23] = 3 * i3 + 2;
+
+ ptr_vals[72*idx + 12] = dbd0[0];
+ ptr_vals[72*idx + 13] = dbd0[1];
+ ptr_vals[72*idx + 14] = dbd0[2];
+ ptr_vals[72*idx + 15] = dbd1[0];
+ ptr_vals[72*idx + 16] = dbd1[1];
+ ptr_vals[72*idx + 17] = dbd1[2];
+ ptr_vals[72*idx + 18] = dbd2[0];
+ ptr_vals[72*idx + 19] = dbd2[1];
+ ptr_vals[72*idx + 20] = dbd2[2];
+ ptr_vals[72*idx + 21] = dbd3[0];
+ ptr_vals[72*idx + 22] = dbd3[1];
+ ptr_vals[72*idx + 23] = dbd3[2];
+
+
+ ptr_rows[72*idx + 24] = 6 * idx + 2;
+ ptr_rows[72*idx + 25] = 6 * idx + 2;
+ ptr_rows[72*idx + 26] = 6 * idx + 2;
+ ptr_rows[72*idx + 27] = 6 * idx + 2;
+ ptr_rows[72*idx + 28] = 6 * idx + 2;
+ ptr_rows[72*idx + 29] = 6 * idx + 2;
+ ptr_rows[72*idx + 30] = 6 * idx + 2;
+ ptr_rows[72*idx + 31] = 6 * idx + 2;
+ ptr_rows[72*idx + 32] = 6 * idx + 2;
+ ptr_rows[72*idx + 33] = 6 * idx + 2;
+ ptr_rows[72*idx + 34] = 6 * idx + 2;
+ ptr_rows[72*idx + 35] = 6 * idx + 2;
+
+ ptr_cols[72*idx + 24] = 3 * i0 + 0;
+ ptr_cols[72*idx + 25] = 3 * i0 + 1;
+ ptr_cols[72*idx + 26] = 3 * i0 + 2;
+ ptr_cols[72*idx + 27] = 3 * i1 + 0;
+ ptr_cols[72*idx + 28] = 3 * i1 + 1;
+ ptr_cols[72*idx + 29] = 3 * i1 + 2;
+ ptr_cols[72*idx + 30] = 3 * i2 + 0;
+ ptr_cols[72*idx + 31] = 3 * i2 + 1;
+ ptr_cols[72*idx + 32] = 3 * i2 + 2;
+ ptr_cols[72*idx + 33] = 3 * i3 + 0;
+ ptr_cols[72*idx + 34] = 3 * i3 + 1;
+ ptr_cols[72*idx + 35] = 3 * i3 + 2;
+
+ ptr_vals[72*idx + 24] = dcd0[0];
+ ptr_vals[72*idx + 25] = dcd0[1];
+ ptr_vals[72*idx + 26] = dcd0[2];
+ ptr_vals[72*idx + 27] = dcd1[0];
+ ptr_vals[72*idx + 28] = dcd1[1];
+ ptr_vals[72*idx + 29] = dcd1[2];
+ ptr_vals[72*idx + 30] = dcd2[0];
+ ptr_vals[72*idx + 31] = dcd2[1];
+ ptr_vals[72*idx + 32] = dcd2[2];
+ ptr_vals[72*idx + 33] = dcd3[0];
+ ptr_vals[72*idx + 34] = dcd3[1];
+ ptr_vals[72*idx + 35] = dcd3[2];
+
+
+ ptr_rows[72*idx + 36] = 6 * idx + 3;
+ ptr_rows[72*idx + 37] = 6 * idx + 3;
+ ptr_rows[72*idx + 38] = 6 * idx + 3;
+ ptr_rows[72*idx + 39] = 6 * idx + 3;
+ ptr_rows[72*idx + 40] = 6 * idx + 3;
+ ptr_rows[72*idx + 41] = 6 * idx + 3;
+ ptr_rows[72*idx + 42] = 6 * idx + 3;
+ ptr_rows[72*idx + 43] = 6 * idx + 3;
+ ptr_rows[72*idx + 44] = 6 * idx + 3;
+ ptr_rows[72*idx + 45] = 6 * idx + 3;
+ ptr_rows[72*idx + 46] = 6 * idx + 3;
+ ptr_rows[72*idx + 47] = 6 * idx + 3;
+
+ ptr_cols[72*idx + 36] = 3 * i0 + 0;
+ ptr_cols[72*idx + 37] = 3 * i0 + 1;
+ ptr_cols[72*idx + 38] = 3 * i0 + 2;
+ ptr_cols[72*idx + 39] = 3 * i1 + 0;
+ ptr_cols[72*idx + 40] = 3 * i1 + 1;
+ ptr_cols[72*idx + 41] = 3 * i1 + 2;
+ ptr_cols[72*idx + 42] = 3 * i2 + 0;
+ ptr_cols[72*idx + 43] = 3 * i2 + 1;
+ ptr_cols[72*idx + 44] = 3 * i2 + 2;
+ ptr_cols[72*idx + 45] = 3 * i3 + 0;
+ ptr_cols[72*idx + 46] = 3 * i3 + 1;
+ ptr_cols[72*idx + 47] = 3 * i3 + 2;
+
+ ptr_vals[72*idx + 36] = ddd0[0];
+ ptr_vals[72*idx + 37] = ddd0[1];
+ ptr_vals[72*idx + 38] = ddd0[2];
+ ptr_vals[72*idx + 39] = ddd1[0];
+ ptr_vals[72*idx + 40] = ddd1[1];
+ ptr_vals[72*idx + 41] = ddd1[2];
+ ptr_vals[72*idx + 42] = ddd2[0];
+ ptr_vals[72*idx + 43] = ddd2[1];
+ ptr_vals[72*idx + 44] = ddd2[2];
+ ptr_vals[72*idx + 45] = ddd3[0];
+ ptr_vals[72*idx + 46] = ddd3[1];
+ ptr_vals[72*idx + 47] = ddd3[2];
+
+
+ ptr_rows[72*idx + 48] = 6 * idx + 4;
+ ptr_rows[72*idx + 49] = 6 * idx + 4;
+ ptr_rows[72*idx + 50] = 6 * idx + 4;
+ ptr_rows[72*idx + 51] = 6 * idx + 4;
+ ptr_rows[72*idx + 52] = 6 * idx + 4;
+ ptr_rows[72*idx + 53] = 6 * idx + 4;
+ ptr_rows[72*idx + 54] = 6 * idx + 4;
+ ptr_rows[72*idx + 55] = 6 * idx + 4;
+ ptr_rows[72*idx + 56] = 6 * idx + 4;
+ ptr_rows[72*idx + 57] = 6 * idx + 4;
+ ptr_rows[72*idx + 58] = 6 * idx + 4;
+ ptr_rows[72*idx + 59] = 6 * idx + 4;
+
+ ptr_cols[72*idx + 48] = 3 * i0 + 0;
+ ptr_cols[72*idx + 49] = 3 * i0 + 1;
+ ptr_cols[72*idx + 50] = 3 * i0 + 2;
+ ptr_cols[72*idx + 51] = 3 * i1 + 0;
+ ptr_cols[72*idx + 52] = 3 * i1 + 1;
+ ptr_cols[72*idx + 53] = 3 * i1 + 2;
+ ptr_cols[72*idx + 54] = 3 * i2 + 0;
+ ptr_cols[72*idx + 55] = 3 * i2 + 1;
+ ptr_cols[72*idx + 56] = 3 * i2 + 2;
+ ptr_cols[72*idx + 57] = 3 * i3 + 0;
+ ptr_cols[72*idx + 58] = 3 * i3 + 1;
+ ptr_cols[72*idx + 59] = 3 * i3 + 2;
+
+ ptr_vals[72*idx + 48] = ded0[0];
+ ptr_vals[72*idx + 49] = ded0[1];
+ ptr_vals[72*idx + 50] = ded0[2];
+ ptr_vals[72*idx + 51] = ded1[0];
+ ptr_vals[72*idx + 52] = ded1[1];
+ ptr_vals[72*idx + 53] = ded1[2];
+ ptr_vals[72*idx + 54] = ded2[0];
+ ptr_vals[72*idx + 55] = ded2[1];
+ ptr_vals[72*idx + 56] = ded2[2];
+ ptr_vals[72*idx + 57] = ded3[0];
+ ptr_vals[72*idx + 58] = ded3[1];
+ ptr_vals[72*idx + 59] = ded3[2];
+
+
+ ptr_rows[72*idx + 60] = 6 * idx + 5;
+ ptr_rows[72*idx + 61] = 6 * idx + 5;
+ ptr_rows[72*idx + 62] = 6 * idx + 5;
+ ptr_rows[72*idx + 63] = 6 * idx + 5;
+ ptr_rows[72*idx + 64] = 6 * idx + 5;
+ ptr_rows[72*idx + 65] = 6 * idx + 5;
+ ptr_rows[72*idx + 66] = 6 * idx + 5;
+ ptr_rows[72*idx + 67] = 6 * idx + 5;
+ ptr_rows[72*idx + 68] = 6 * idx + 5;
+ ptr_rows[72*idx + 69] = 6 * idx + 5;
+ ptr_rows[72*idx + 70] = 6 * idx + 5;
+ ptr_rows[72*idx + 71] = 6 * idx + 5;
+
+ ptr_cols[72*idx + 60] = 3 * i0 + 0;
+ ptr_cols[72*idx + 61] = 3 * i0 + 1;
+ ptr_cols[72*idx + 62] = 3 * i0 + 2;
+ ptr_cols[72*idx + 63] = 3 * i1 + 0;
+ ptr_cols[72*idx + 64] = 3 * i1 + 1;
+ ptr_cols[72*idx + 65] = 3 * i1 + 2;
+ ptr_cols[72*idx + 66] = 3 * i2 + 0;
+ ptr_cols[72*idx + 67] = 3 * i2 + 1;
+ ptr_cols[72*idx + 68] = 3 * i2 + 2;
+ ptr_cols[72*idx + 69] = 3 * i3 + 0;
+ ptr_cols[72*idx + 70] = 3 * i3 + 1;
+ ptr_cols[72*idx + 71] = 3 * i3 + 2;
+
+ ptr_vals[72*idx + 60] = dfd0[0];
+ ptr_vals[72*idx + 61] = dfd0[1];
+ ptr_vals[72*idx + 62] = dfd0[2];
+ ptr_vals[72*idx + 63] = dfd1[0];
+ ptr_vals[72*idx + 64] = dfd1[1];
+ ptr_vals[72*idx + 65] = dfd1[2];
+ ptr_vals[72*idx + 66] = dfd2[0];
+ ptr_vals[72*idx + 67] = dfd2[1];
+ ptr_vals[72*idx + 68] = dfd2[2];
+ ptr_vals[72*idx + 69] = dfd3[0];
+ ptr_vals[72*idx + 70] = dfd3[1];
+ ptr_vals[72*idx + 71] = dfd3[2];
+
+ idx += 1;
+ }
+ return std::make_tuple(rows, cols, vals);
+}
+
+
+
+std::tuple, py::array_t, py::array_t>
+tetrahedron_solid_angle_gradient(std::shared_ptr mesh)
+{
+ size_t idx = 0;
+ auto n = mesh->num_cells();
+
+ py::array_t rows(48*n);
+ auto buf_rows = rows.request();
+ int *ptr_rows = (int *) buf_rows.ptr;
+
+ py::array_t cols(48*n);
+ auto buf_cols = cols.request();
+ int *ptr_cols = (int *) buf_cols.ptr;
+
+ py::array_t vals(48*n);
+ auto buf_vals = vals.request();
+ double *ptr_vals = (double *) buf_vals.ptr;
+
+ Eigen::Matrix3d skew_10;
+ Eigen::Matrix3d skew_20;
+ Eigen::Matrix3d skew_30;
+ Eigen::Matrix3d skew_21;
+ Eigen::Matrix3d skew_31;
+ Eigen::Matrix3d skew_32;
+
+ Eigen::RowVector3d dadk;
+ Eigen::RowVector3d dadl;
+ Eigen::RowVector3d dbdk;
+ Eigen::RowVector3d dbdl;
+ Eigen::RowVector3d dcdk;
+ Eigen::RowVector3d dcdl;
+ Eigen::RowVector3d dddk;
+ Eigen::RowVector3d dddl;
+ Eigen::RowVector3d dedk;
+ Eigen::RowVector3d dedl;
+ Eigen::RowVector3d dfdk;
+ Eigen::RowVector3d dfdl;
+
+ for (CellIterator cell(*mesh); !cell.end(); ++cell)
+ {
+ auto ents = cell->entities(0);
+ const std::size_t i0 = ents[0];
+ const std::size_t i1 = ents[1];
+ const std::size_t i2 = ents[2];
+ const std::size_t i3 = ents[3];
+
+ const Point p0 = Vertex(*mesh, i0).point();
+ const Point p1 = Vertex(*mesh, i1).point();
+ const Point p2 = Vertex(*mesh, i2).point();
+ const Point p3 = Vertex(*mesh, i3).point();
+
+ Point e10 = p1 - p0;
+ Point e20 = p2 - p0;
+ Point e30 = p3 - p0;
+ Point e21 = p2 - p1;
+ Point e31 = p3 - p1;
+ Point e32 = p3 - p2;
+
+ skew_10 << 0.0, e10.z(), -e10.y(),
+ -e10.z(), 0.0, e10.x(),
+ e10.y(), -e10.x(), 0.0;
+
+ skew_20 << 0.0, e20.z(), -e20.y(),
+ -e20.z(), 0.0, e20.x(),
+ e20.y(), -e20.x(), 0.0;
+
+ skew_30 << 0.0, e30.z(), -e30.y(),
+ -e30.z(), 0.0, e30.x(),
+ e30.y(), -e30.x(), 0.0;
+
+ skew_21 << 0.0, e21.z(), -e21.y(),
+ -e21.z(), 0.0, e21.x(),
+ e21.y(), -e21.x(), 0.0;
+
+ skew_31 << 0.0, e31.z(), -e31.y(),
+ -e31.z(), 0.0, e31.x(),
+ e31.y(), -e31.x(), 0.0;
+
+ skew_32 << 0.0, e32.z(), -e32.y(),
+ -e32.z(), 0.0, e32.x(),
+ e32.y(), -e32.x(), 0.0;
+
+ Point n031 = e31.cross(e10);
+ Point n021 = e21.cross(e10);
+ Point n231 = e21.cross(e31);
+ Point n230 = e20.cross(e30);
+
+ Point tpa3 = n031.cross(n031.cross(n021));
+ Point tpa2 = n021.cross(n021.cross(n031));
+ tpa3 /= (tpa3.norm() * n031.norm());
+ tpa2 /= (tpa2.norm() * n021.norm());
+ dadk << tpa3.x(), tpa3.y(), tpa3.z();
+ dadl << tpa2.x(), tpa2.y(), tpa2.z();
+
+ Point tpb0 = n021.cross(n021.cross(n231));
+ Point tpb3 = n231.cross(n231.cross(-n021));
+ tpb0 /= (tpb0.norm() * n021.norm());
+ tpb3 /= (tpb3.norm() * n231.norm());
+ dbdk << tpb0.x(), tpb0.y(), tpb0.z();
+ dbdl << tpb3.x(), tpb3.y(), tpb3.z();
+
+ Point tpc2 = n231.cross(n231.cross(-n031));
+ Point tpc0 = n031.cross(n031.cross(-n231));
+ tpc2 /= (tpc2.norm() * n231.norm());
+ tpc0 /= (tpc0.norm() * n031.norm());
+ dcdk << tpc2.x(), tpc2.y(), tpc2.z();
+ dcdl << tpc0.x(), tpc0.y(), tpc0.z();
+
+ Point tpd1 = n021.cross(n021.cross(n230));
+ Point tpd3 = n230.cross(n230.cross(n021));
+ tpd1 /= (tpd1.norm() * n021.norm());
+ tpd3 /= (tpd3.norm() * n230.norm());
+ dddk << tpd1.x(), tpd1.y(), tpd1.z();
+ dddl << tpd3.x(), tpd3.y(), tpd3.z();
+
+ Point tpe1 = n031.cross(n031.cross(-n230));
+ Point tpe2 = n230.cross(n230.cross(n031));
+ tpe1 /= (tpe1.norm() * n031.norm());
+ tpe2 /= (tpe2.norm() * n230.norm());
+ dedk << tpe1.x(), tpe1.y(), tpe1.z();
+ dedl << tpe2.x(), tpe2.y(), tpe2.z();
+
+ Point tpf0 = n230.cross(n230.cross(n231));
+ Point tpf1 = n231.cross(n231.cross(n230));
+ tpf0 /= (tpf0.norm() * n230.norm());
+ tpf1 /= (tpf1.norm() * n231.norm());
+ dfdk << tpf0.x(), tpf0.y(), tpf0.z();
+ dfdl << tpf1.x(), tpf1.y(), tpf1.z();
+
+ auto dad0 = dadk * (-skew_31) + dadl * (-skew_21);
+ auto dad1 = dadk * (skew_10 + skew_31) + dadl * (skew_10 + skew_21);
+ auto dad2 = dadl * (-skew_10);
+ auto dad3 = dadk * (-skew_10);
+
+ auto dbd0 = dbdk * skew_21;
+ auto dbd1 = dbdk * (-skew_21 - skew_10) + dbdl * (-skew_21 + skew_31);
+ auto dbd2 = dbdk * skew_10 + dbdl * (-skew_31);
+ auto dbd3 = dbdl * skew_21;
+
+ auto dcd0 = dcdl * skew_31;
+ auto dcd1 = dcdk * (-skew_31 + skew_21) + dcdl * (-skew_31 - skew_10);
+ auto dcd2 = dcdk * skew_31;
+ auto dcd3 = dcdk * (-skew_21) + dcdl * skew_10;
+
+ auto ddd0 = dddk * (-skew_20 + skew_10) + dddl * (-skew_20 + skew_30);
+ auto ddd1 = dddk * skew_20;
+ auto ddd2 = dddk * (-skew_10) + dddl * (-skew_30);
+ auto ddd3 = dddl * skew_20;
+
+ auto ded0 = dedk * (-skew_30 + skew_10) + dedl * (-skew_30 + skew_20);
+ auto ded1 = dedk * skew_30;
+ auto ded2 = dedl * skew_30;
+ auto ded3 = dedk * (-skew_10) + dedl * (-skew_20);
+
+ auto dfd0 = dfdk * skew_32;
+ auto dfd1 = dfdl * skew_32;
+ auto dfd2 = dfdk * (-skew_32 - skew_20) + dfdl * (-skew_32 - skew_21);
+ auto dfd3 = dfdk * skew_20 + dfdl * skew_21;
+
+ ptr_rows[48*idx + 0] = 4 * idx;
+ ptr_rows[48*idx + 1] = 4 * idx;
+ ptr_rows[48*idx + 2] = 4 * idx;
+ ptr_rows[48*idx + 3] = 4 * idx;
+ ptr_rows[48*idx + 4] = 4 * idx;
+ ptr_rows[48*idx + 5] = 4 * idx;
+ ptr_rows[48*idx + 6] = 4 * idx;
+ ptr_rows[48*idx + 7] = 4 * idx;
+ ptr_rows[48*idx + 8] = 4 * idx;
+ ptr_rows[48*idx + 9] = 4 * idx;
+ ptr_rows[48*idx + 10] = 4 * idx;
+ ptr_rows[48*idx + 11] = 4 * idx;
+
+ ptr_cols[48*idx + 0] = 3 * i0 + 0;
+ ptr_cols[48*idx + 1] = 3 * i0 + 1;
+ ptr_cols[48*idx + 2] = 3 * i0 + 2;
+ ptr_cols[48*idx + 3] = 3 * i1 + 0;
+ ptr_cols[48*idx + 4] = 3 * i1 + 1;
+ ptr_cols[48*idx + 5] = 3 * i1 + 2;
+ ptr_cols[48*idx + 6] = 3 * i2 + 0;
+ ptr_cols[48*idx + 7] = 3 * i2 + 1;
+ ptr_cols[48*idx + 8] = 3 * i2 + 2;
+ ptr_cols[48*idx + 9] = 3 * i3 + 0;
+ ptr_cols[48*idx + 10] = 3 * i3 + 1;
+ ptr_cols[48*idx + 11] = 3 * i3 + 2;
+
+ ptr_vals[48*idx + 0] = dad0[0] + ddd0[0] + ded0[0];
+ ptr_vals[48*idx + 1] = dad0[1] + ddd0[1] + ded0[1];
+ ptr_vals[48*idx + 2] = dad0[2] + ddd0[2] + ded0[2];
+ ptr_vals[48*idx + 3] = dad1[0] + ddd1[0] + ded1[0];
+ ptr_vals[48*idx + 4] = dad1[1] + ddd1[1] + ded1[1];
+ ptr_vals[48*idx + 5] = dad1[2] + ddd1[2] + ded1[2];
+ ptr_vals[48*idx + 6] = dad2[0] + ddd2[0] + ded2[0];
+ ptr_vals[48*idx + 7] = dad2[1] + ddd2[1] + ded2[1];
+ ptr_vals[48*idx + 8] = dad2[2] + ddd2[2] + ded2[2];
+ ptr_vals[48*idx + 9] = dad3[0] + ddd3[0] + ded3[0];
+ ptr_vals[48*idx + 10] = dad3[1] + ddd3[1] + ded3[1];
+ ptr_vals[48*idx + 11] = dad3[2] + ddd3[2] + ded3[2];
+
+
+ ptr_rows[48*idx + 12] = 4 * idx + 1;
+ ptr_rows[48*idx + 13] = 4 * idx + 1;
+ ptr_rows[48*idx + 14] = 4 * idx + 1;
+ ptr_rows[48*idx + 15] = 4 * idx + 1;
+ ptr_rows[48*idx + 16] = 4 * idx + 1;
+ ptr_rows[48*idx + 17] = 4 * idx + 1;
+ ptr_rows[48*idx + 18] = 4 * idx + 1;
+ ptr_rows[48*idx + 19] = 4 * idx + 1;
+ ptr_rows[48*idx + 20] = 4 * idx + 1;
+ ptr_rows[48*idx + 21] = 4 * idx + 1;
+ ptr_rows[48*idx + 22] = 4 * idx + 1;
+ ptr_rows[48*idx + 23] = 4 * idx + 1;
+
+ ptr_cols[48*idx + 12] = 3 * i0 + 0;
+ ptr_cols[48*idx + 13] = 3 * i0 + 1;
+ ptr_cols[48*idx + 14] = 3 * i0 + 2;
+ ptr_cols[48*idx + 15] = 3 * i1 + 0;
+ ptr_cols[48*idx + 16] = 3 * i1 + 1;
+ ptr_cols[48*idx + 17] = 3 * i1 + 2;
+ ptr_cols[48*idx + 18] = 3 * i2 + 0;
+ ptr_cols[48*idx + 19] = 3 * i2 + 1;
+ ptr_cols[48*idx + 20] = 3 * i2 + 2;
+ ptr_cols[48*idx + 21] = 3 * i3 + 0;
+ ptr_cols[48*idx + 22] = 3 * i3 + 1;
+ ptr_cols[48*idx + 23] = 3 * i3 + 2;
+
+ ptr_vals[48*idx + 12] = dad0[0] + dbd0[0] + dcd0[0];
+ ptr_vals[48*idx + 13] = dad0[1] + dbd0[1] + dcd0[1];
+ ptr_vals[48*idx + 14] = dad0[2] + dbd0[2] + dcd0[2];
+ ptr_vals[48*idx + 15] = dad1[0] + dbd1[0] + dcd1[0];
+ ptr_vals[48*idx + 16] = dad1[1] + dbd1[1] + dcd1[1];
+ ptr_vals[48*idx + 17] = dad1[2] + dbd1[2] + dcd1[2];
+ ptr_vals[48*idx + 18] = dad2[0] + dbd2[0] + dcd2[0];
+ ptr_vals[48*idx + 19] = dad2[1] + dbd2[1] + dcd2[1];
+ ptr_vals[48*idx + 20] = dad2[2] + dbd2[2] + dcd2[2];
+ ptr_vals[48*idx + 21] = dad3[0] + dbd3[0] + dcd3[0];
+ ptr_vals[48*idx + 22] = dad3[1] + dbd3[1] + dcd3[1];
+ ptr_vals[48*idx + 23] = dad3[2] + dbd3[2] + dcd3[2];
+
+
+ ptr_rows[48*idx + 24] = 4 * idx + 2;
+ ptr_rows[48*idx + 25] = 4 * idx + 2;
+ ptr_rows[48*idx + 26] = 4 * idx + 2;
+ ptr_rows[48*idx + 27] = 4 * idx + 2;
+ ptr_rows[48*idx + 28] = 4 * idx + 2;
+ ptr_rows[48*idx + 29] = 4 * idx + 2;
+ ptr_rows[48*idx + 30] = 4 * idx + 2;
+ ptr_rows[48*idx + 31] = 4 * idx + 2;
+ ptr_rows[48*idx + 32] = 4 * idx + 2;
+ ptr_rows[48*idx + 33] = 4 * idx + 2;
+ ptr_rows[48*idx + 34] = 4 * idx + 2;
+ ptr_rows[48*idx + 35] = 4 * idx + 2;
+
+ ptr_cols[48*idx + 24] = 3 * i0 + 0;
+ ptr_cols[48*idx + 25] = 3 * i0 + 1;
+ ptr_cols[48*idx + 26] = 3 * i0 + 2;
+ ptr_cols[48*idx + 27] = 3 * i1 + 0;
+ ptr_cols[48*idx + 28] = 3 * i1 + 1;
+ ptr_cols[48*idx + 29] = 3 * i1 + 2;
+ ptr_cols[48*idx + 30] = 3 * i2 + 0;
+ ptr_cols[48*idx + 31] = 3 * i2 + 1;
+ ptr_cols[48*idx + 32] = 3 * i2 + 2;
+ ptr_cols[48*idx + 33] = 3 * i3 + 0;
+ ptr_cols[48*idx + 34] = 3 * i3 + 1;
+ ptr_cols[48*idx + 35] = 3 * i3 + 2;
+
+ ptr_vals[48*idx + 24] = dbd0[0] + ddd0[0] + dfd0[0];
+ ptr_vals[48*idx + 25] = dbd0[1] + ddd0[1] + dfd0[1];
+ ptr_vals[48*idx + 26] = dbd0[2] + ddd0[2] + dfd0[2];
+ ptr_vals[48*idx + 27] = dbd1[0] + ddd1[0] + dfd1[0];
+ ptr_vals[48*idx + 28] = dbd1[1] + ddd1[1] + dfd1[1];
+ ptr_vals[48*idx + 29] = dbd1[2] + ddd1[2] + dfd1[2];
+ ptr_vals[48*idx + 30] = dbd2[0] + ddd2[0] + dfd2[0];
+ ptr_vals[48*idx + 31] = dbd2[1] + ddd2[1] + dfd2[1];
+ ptr_vals[48*idx + 32] = dbd2[2] + ddd2[2] + dfd2[2];
+ ptr_vals[48*idx + 33] = dbd3[0] + ddd3[0] + dfd3[0];
+ ptr_vals[48*idx + 34] = dbd3[1] + ddd3[1] + dfd3[1];
+ ptr_vals[48*idx + 35] = dbd3[2] + ddd3[2] + dfd3[2];
+
+
+ ptr_rows[48*idx + 36] = 4 * idx + 3;
+ ptr_rows[48*idx + 37] = 4 * idx + 3;
+ ptr_rows[48*idx + 38] = 4 * idx + 3;
+ ptr_rows[48*idx + 39] = 4 * idx + 3;
+ ptr_rows[48*idx + 40] = 4 * idx + 3;
+ ptr_rows[48*idx + 41] = 4 * idx + 3;
+ ptr_rows[48*idx + 42] = 4 * idx + 3;
+ ptr_rows[48*idx + 43] = 4 * idx + 3;
+ ptr_rows[48*idx + 44] = 4 * idx + 3;
+ ptr_rows[48*idx + 45] = 4 * idx + 3;
+ ptr_rows[48*idx + 46] = 4 * idx + 3;
+ ptr_rows[48*idx + 47] = 4 * idx + 3;
+
+ ptr_cols[48*idx + 36] = 3 * i0 + 0;
+ ptr_cols[48*idx + 37] = 3 * i0 + 1;
+ ptr_cols[48*idx + 38] = 3 * i0 + 2;
+ ptr_cols[48*idx + 39] = 3 * i1 + 0;
+ ptr_cols[48*idx + 40] = 3 * i1 + 1;
+ ptr_cols[48*idx + 41] = 3 * i1 + 2;
+ ptr_cols[48*idx + 42] = 3 * i2 + 0;
+ ptr_cols[48*idx + 43] = 3 * i2 + 1;
+ ptr_cols[48*idx + 44] = 3 * i2 + 2;
+ ptr_cols[48*idx + 45] = 3 * i3 + 0;
+ ptr_cols[48*idx + 46] = 3 * i3 + 1;
+ ptr_cols[48*idx + 47] = 3 * i3 + 2;
+
+ ptr_vals[48*idx + 36] = dcd0[0] + ded0[0] + dfd0[0];
+ ptr_vals[48*idx + 37] = dcd0[1] + ded0[1] + dfd0[1];
+ ptr_vals[48*idx + 38] = dcd0[2] + ded0[2] + dfd0[2];
+ ptr_vals[48*idx + 39] = dcd1[0] + ded1[0] + dfd1[0];
+ ptr_vals[48*idx + 40] = dcd1[1] + ded1[1] + dfd1[1];
+ ptr_vals[48*idx + 41] = dcd1[2] + ded1[2] + dfd1[2];
+ ptr_vals[48*idx + 42] = dcd2[0] + ded2[0] + dfd2[0];
+ ptr_vals[48*idx + 43] = dcd2[1] + ded2[1] + dfd2[1];
+ ptr_vals[48*idx + 44] = dcd2[2] + ded2[2] + dfd2[2];
+ ptr_vals[48*idx + 45] = dcd3[0] + ded3[0] + dfd3[0];
+ ptr_vals[48*idx + 46] = dcd3[1] + ded3[1] + dfd3[1];
+ ptr_vals[48*idx + 47] = dcd3[2] + ded3[2] + dfd3[2];
+
+ idx += 1;
+ }
+ return std::make_tuple(rows, cols, vals);
+}
+
+PYBIND11_MODULE(SIGNATURE, m)
+{
+ m.def("triangle_angles", &triangle_angles);
+ m.def("tetrahedron_dihedral_angles", &tetrahedron_dihedral_angles);
+ m.def("tetrahedron_solid_angles", &tetrahedron_solid_angles);
+ m.def("triangle_angle_gradient", &triangle_angle_gradient);
+ m.def("tetrahedron_dihedral_angle_gradient", &tetrahedron_dihedral_angle_gradient);
+ m.def("tetrahedron_solid_angle_gradient", &tetrahedron_solid_angle_gradient);
+}
+"""
+mesh_quality = fenics.compile_cpp_code(cpp_code)
+
+
+class MeshConstraint(abc.ABC):
+ """This class represents a generic constraint on the mesh quality."""
+
+ type: str | None = None
+
+ def __init__(
+ self, mesh: fenics.Mesh, deformation_space: fenics.FunctionSpace
+ ) -> None:
+ """Abstract base class representing an interface for mesh quality constraints.
+
+ Args:
+ mesh: The underlying finite element mesh, which is subjected to the mesh
+ quality constraints.
+ deformation_space: A vector CG1 FEM function space used for defining
+ deformations of the mesh via perturbation of identity.
+
+ """
+ self.mesh = mesh
+ self.dim = self.mesh.geometry().dim()
+
+ self.v2d = fenics.vertex_to_dof_map(deformation_space)
+ self.d2v = fenics.dof_to_vertex_map(deformation_space)
+ loc0, loc1 = deformation_space.dofmap().ownership_range()
+ self.d2v_local = self.d2v[: loc1 - loc0]
+
+ dof_ownership_range = deformation_space.dofmap().ownership_range()
+ self.local_offset = dof_ownership_range[0]
+ self.no_vertices = self.mesh.num_entities_global(0)
+ self.l2g_dofs = deformation_space.dofmap().tabulate_local_to_global_dofs()
+
+ self.global_vertex_indices = self.mesh.topology().global_indices(0)
+ function_space = fenics.FunctionSpace(self.mesh, "CG", 1)
+ loc0, loc1 = function_space.dofmap().ownership_range()
+ d2v = fenics.dof_to_vertex_map(function_space)
+ self.global_vertex_indices_owned = self.global_vertex_indices[
+ d2v[: loc1 - loc0]
+ ]
+
+ self.ghost_offset = self.mesh.topology().ghost_offset(
+ self.mesh.topology().dim()
+ )
+
+ self.no_constraints = 0
+ self.is_necessary: np.ndarray = np.array([False])
+
+ @abc.abstractmethod
+ def evaluate(self, coords_seq: np.ndarray) -> np.ndarray:
+ r"""Evaluates the constaint function at the current iterate.
+
+ This computes :math:`g(x)` where the constraint is given by
+ :math:`g(x) \leq 0` and :math:`x` corresponds to mesh coordinates, i.e.,
+ `coords_seq`.
+
+ Args:
+ coords_seq: The (flattened) list of vertex coordinates of the mesh.
+
+ Returns:
+ A numpy array containing the values of the constraint functions.
+
+ """
+ pass
+
+ @abc.abstractmethod
+ def compute_gradient(self, coords_seq: np.ndarray) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the gradient.
+
+ """
+ pass
+
+
+class FixedVertexConstraint(MeshConstraint):
+ """A discrete mesh constraint for fixed boundaries in shape optimization.
+
+ This constraint is needed to incorporate other mesh constraints for the case that
+ some part of the boundary is fixed during optimization. By default, this is already
+ incorporated into the gradient deformation, so that this constraint alone is
+ not necessary, however, it becomes so when other constraints are considered.
+ The constraint is linear, so that the gradient only has to be computed once.
+ """
+
+ type = "equality"
+
+ def __init__(
+ self,
+ mesh: fenics.Mesh,
+ boundaries: fenics.MeshFunction,
+ config: cashocs.io.Config,
+ deformation_space: fenics.FunctionSpace,
+ additional_fixed_idcs: np.ndarray | None = None,
+ additional_fixed_coordinates: np.ndarray | None = None,
+ ) -> None:
+ """Initializes the fixed boundary mesh constraint.
+
+ Args:
+ mesh: The corresponding finite element mesh.
+ boundaries: The :py:class`fenics.MeshFunction` which is used to mark the
+ boundaries of the mesh.
+ config: The configuration of the optimization problem.
+ deformation_space: The space of vector CG1 elements for mesh deformations.
+ additional_fixed_idcs: Indices, whose repective
+ nodes should be fixed, in addition to the already fixed indices.
+ additional_fixed_coordinates: Vertex coordinates corresponding to
+ `additional_fixed_idcs`.
+
+ """
+ super().__init__(mesh, deformation_space)
+ self.boundaries = boundaries
+ self.config = config
+
+ self.mesh.init(self.mesh.topology().dim() - 1, 0)
+ self.facets = np.array(
+ self.mesh.topology()(self.mesh.topology().dim() - 1, 0)()
+ ).reshape(-1, self.dim)
+
+ shape_bdry_fix = self.config.getlist("ShapeGradient", "shape_bdry_fix")
+ (
+ self.fixed_boundary_idcs,
+ self.fixed_boundary_coordinates,
+ ) = self._compute_fixed_boundary_vertex_indices(shape_bdry_fix)
+
+ shape_bdry_fix_x = self.config.getlist("ShapeGradient", "shape_bdry_fix_x")
+ shape_bdry_fix_y = self.config.getlist("ShapeGradient", "shape_bdry_fix_y")
+ shape_bdry_fix_z = self.config.getlist("ShapeGradient", "shape_bdry_fix_z")
+ (
+ self.partially_fixed_boundary_idcs,
+ self.partially_fixed_boundary_coordinates,
+ ) = self._compute_partially_fixed_boundary_vertex_indices(
+ shape_bdry_fix_x, shape_bdry_fix_y, shape_bdry_fix_z
+ )
+
+ fixed_dimensions = self.config.getlist("ShapeGradient", "fixed_dimensions")
+ (
+ self.fixed_dimension_idcs,
+ self.fixed_dimension_coordinates,
+ ) = self._compute_fixed_dimension_vertex_indices(fixed_dimensions)
+
+ if additional_fixed_idcs is None:
+ additional_fixed_idcs = np.array([], dtype="int64")
+ if additional_fixed_coordinates is None:
+ additional_fixed_coordinates = np.array([])
+
+ self.fixed_idcs = np.concatenate(
+ [
+ self.fixed_boundary_idcs,
+ self.partially_fixed_boundary_idcs,
+ self.fixed_dimension_idcs,
+ additional_fixed_idcs,
+ ]
+ )
+ self.fixed_coordinates = np.concatenate(
+ [
+ self.fixed_boundary_coordinates,
+ self.partially_fixed_boundary_coordinates,
+ self.fixed_dimension_coordinates,
+ additional_fixed_coordinates,
+ ]
+ )
+
+ self.fixed_idcs, unique_mask = np.unique(self.fixed_idcs, return_index=True)
+ self.fixed_coordinates = self.fixed_coordinates[unique_mask]
+
+ self.no_constraints = len(self.fixed_idcs)
+ self.is_necessary = np.array([False] * self.no_constraints)
+ self.fixed_gradient = self._compute_fixed_gradient()
+
+ def _compute_fixed_boundary_vertex_indices(
+ self, shape_bdry_fix: list[int] | int
+ ) -> tuple[np.ndarray, np.ndarray]:
+ """Computes the indices of the mesh vertices on the boundary, which are fixed.
+
+ Args:
+ shape_bdry_fix: An index or list of indices of the boundaries, which are
+ fixed during shape optimization. This is specified in the configuration
+ of the problem.
+
+ Returns:
+ A tuple `fixed_indices, fixed_coordinates`, where `fixed_indices` is an
+ array containing the (flattened) indices of the fixed coordinates and
+ `fixed_coordinates` contains the corresponding values of the fixed vertices.
+
+ """
+ bdry_fix_list = _utils.enlist(shape_bdry_fix)
+
+ temp_fixed_idcs = []
+ for i in bdry_fix_list:
+ idx_i = self.facets[self.boundaries.where_equal(i)]
+ temp_fixed_idcs += idx_i.reshape(-1).tolist()
+
+ temp_fixed_idcs_arr = np.array(temp_fixed_idcs, dtype="int64")
+ fixed_idcs = np.unique(temp_fixed_idcs_arr)
+
+ if len(fixed_idcs) > 0:
+ fixed_idcs_global = self.global_vertex_indices[fixed_idcs]
+ else:
+ fixed_idcs_global = []
+ mask = np.isin(fixed_idcs_global, self.global_vertex_indices_owned)
+ fixed_idcs_local_owned = fixed_idcs[mask]
+
+ if self.dim == 2:
+ fixed_idcs_local = np.array(
+ [
+ self.dim * fixed_idcs_local_owned,
+ self.dim * fixed_idcs_local_owned + 1,
+ ]
+ ).T.reshape(-1)
+ elif self.dim == 3:
+ fixed_idcs_local = np.array(
+ [
+ self.dim * fixed_idcs_local_owned,
+ self.dim * fixed_idcs_local_owned + 1,
+ self.dim * fixed_idcs_local_owned + 2,
+ ]
+ ).T.reshape(-1)
+ else:
+ raise _exceptions.InputError(
+ "FixedVertexConstraint",
+ "mesh",
+ "Can only use mesh quality constraints for 2D and 3D meshes.",
+ )
+
+ if len(fixed_idcs_local) > 0:
+ fixed_coordinates = (
+ self.mesh.coordinates().copy().reshape(-1)[fixed_idcs_local]
+ )
+ else:
+ fixed_coordinates = np.array([])
+
+ return fixed_idcs_local, fixed_coordinates
+
+ def _compute_partially_fixed_boundary_vertex_indices(
+ self,
+ shape_bdry_fix_x: list[int] | int,
+ shape_bdry_fix_y: list[int] | int,
+ shape_bdry_fix_z: list[int] | int,
+ ) -> tuple[np.ndarray, np.ndarray]:
+ """Computes the indices of the partially fixed vertices on the boundary.
+
+ Args:
+ shape_bdry_fix_x: An index or list of indices of the boundaries, whose x
+ coordinates are fixed during shape optimization. This is specified in
+ the configuration of the problem.
+ shape_bdry_fix_y: An index or list of indices of the boundaries, whose y
+ coordinates are fixed during shape optimization. This is specified in
+ the configuration of the problem.
+ shape_bdry_fix_z: An index or list of indices of the boundaries, whose z
+ coordinates are fixed during shape optimization. This is specified in
+ the configuration of the problem.
+
+ Returns:
+ A tuple `partially_fixed_indices, partially_fixed_coordinates`, where
+ `partially_fixed_indices` is an array containing the (flattened) indices of
+ the (partially) fixed coordinates and `partially_fixed_coordinates` contains
+ the corresponding values of the fixed vertices.
+
+ """
+ bdry_fix_x_list = _utils.enlist(shape_bdry_fix_x)
+ bdry_fix_y_list = _utils.enlist(shape_bdry_fix_y)
+ bdry_fix_z_list = _utils.enlist(shape_bdry_fix_z)
+
+ temp_fixed_idcs_x = []
+ temp_fixed_idcs_y = []
+ temp_fixed_idcs_z: list[int] = []
+ for i in bdry_fix_x_list:
+ idx_i = self.facets[self.boundaries.where_equal(i)]
+ temp_fixed_idcs_x += idx_i.reshape(-1).tolist()
+ for i in bdry_fix_y_list:
+ idx_i = self.facets[self.boundaries.where_equal(i)]
+ temp_fixed_idcs_y += idx_i.reshape(-1).tolist()
+ for i in bdry_fix_z_list:
+ idx_i = self.facets[self.boundaries.where_equal(i)]
+ temp_fixed_idcs_z += idx_i.reshape(-1).tolist()
+
+ fixed_idcs_x = np.unique(temp_fixed_idcs_x)
+ fixed_idcs_y = np.unique(temp_fixed_idcs_y)
+ fixed_idcs_z = np.unique(temp_fixed_idcs_z)
+
+ if len(fixed_idcs_x) > 0:
+ fixed_idcs_global_x = self.global_vertex_indices[fixed_idcs_x]
+ else:
+ fixed_idcs_global_x = []
+ if len(fixed_idcs_y) > 0:
+ fixed_idcs_global_y = self.global_vertex_indices[fixed_idcs_y]
+ else:
+ fixed_idcs_global_y = []
+ if len(fixed_idcs_z) > 0:
+ fixed_idcs_global_z = self.global_vertex_indices[fixed_idcs_z]
+ else:
+ fixed_idcs_global_z = []
+
+ mask_x = np.isin(fixed_idcs_global_x, self.global_vertex_indices_owned)
+ mask_y = np.isin(fixed_idcs_global_y, self.global_vertex_indices_owned)
+ mask_z = np.isin(fixed_idcs_global_z, self.global_vertex_indices_owned)
+ fixed_idcs_x_local_owned = fixed_idcs_x[mask_x]
+ fixed_idcs_y_local_owned = fixed_idcs_y[mask_y]
+ fixed_idcs_z_local_owned = fixed_idcs_z[mask_z]
+
+ if self.dim == 2:
+ fixed_idcs_local_x = np.array(
+ [self.dim * fixed_idcs_x_local_owned], dtype="int64"
+ ).T.reshape(-1)
+ fixed_idcs_local_y = np.array(
+ [self.dim * fixed_idcs_y_local_owned + 1], dtype="int64"
+ ).T.reshape(-1)
+
+ partially_fixed_idcs_local = np.concatenate(
+ [fixed_idcs_local_x, fixed_idcs_local_y],
+ )
+
+ elif self.dim == 3:
+ fixed_idcs_local_x = np.array(
+ [self.dim * fixed_idcs_x_local_owned], dtype="int64"
+ ).T.reshape(-1)
+ fixed_idcs_local_y = np.array(
+ [self.dim * fixed_idcs_y_local_owned + 1], dtype="int64"
+ ).T.reshape(-1)
+ fixed_idcs_local_z = np.array(
+ [self.dim * fixed_idcs_z_local_owned + 2], dtype="int64"
+ ).T.reshape(-1)
+
+ partially_fixed_idcs_local = np.concatenate(
+ [fixed_idcs_local_x, fixed_idcs_local_y, fixed_idcs_local_z],
+ )
+ else:
+ raise _exceptions.InputError(
+ "FixedVertexConstraint",
+ "mesh",
+ "Can only use mesh quality constraints for 2D and 3D meshes.",
+ )
+
+ if len(partially_fixed_idcs_local) > 0:
+ partially_fixed_coordinates = (
+ self.mesh.coordinates().copy().reshape(-1)[partially_fixed_idcs_local]
+ )
+ else:
+ partially_fixed_coordinates = np.array([])
+
+ return partially_fixed_idcs_local, partially_fixed_coordinates
+
+ def _compute_fixed_dimension_vertex_indices(
+ self, fixed_dimensions: list[int] | int
+ ) -> tuple[np.ndarray, np.ndarray]:
+ """Computes the indices of the mesh vertices which are fixed.
+
+ These are fixed through the use of the fixed_dimensions configuration parameter,
+ which restricts deformations to some directions.
+
+ Args:
+ fixed_dimensions: The (list of) coordinate indices which are fixed. This
+ is 0 for x, 1 for y, and 2 for z.
+
+ Returns:
+ A tuple `fixed_indices, fixed_coordinates`, where `fixed_indices` is an
+ array containing the (flattened) indices of the fixed coordinates and
+ `fixed_coordinates` contains the corresponding values of the fixed vertices.
+
+ """
+ fixed_dimensions_list = _utils.enlist(fixed_dimensions)
+
+ fixed_idcs = np.arange(self.mesh.num_vertices())
+ fixed_idcs_global = self.global_vertex_indices[fixed_idcs]
+ mask = np.isin(fixed_idcs_global, self.global_vertex_indices_owned)
+ fixed_idcs_local_owned = fixed_idcs[mask]
+
+ fixed_idcs_local = np.array(
+ [self.dim * fixed_idcs_local_owned + i for i in fixed_dimensions_list],
+ dtype="int64",
+ ).T.reshape(-1)
+
+ if len(fixed_idcs_local) > 0:
+ fixed_coordinates = (
+ self.mesh.coordinates().copy().reshape(-1)[fixed_idcs_local]
+ )
+ else:
+ fixed_coordinates = np.array([])
+
+ return fixed_idcs_local, fixed_coordinates
+
+ def evaluate(self, coords_seq: np.ndarray) -> np.ndarray:
+ r"""Evaluates the constaint function at the current iterate.
+
+ This computes :math:`g(x)` where the constraint is given by
+ :math:`g(x) = 0` and :math:`x` corresponds to mesh coordinates, i.e.,
+ `coords_seq`. The constraint returns the mesh coordinates corresponding
+ to the boundaries that shall remain fixed during shape optimization.
+
+ Args:
+ coords_seq: The (flattened) list of vertex coordinates of the mesh.
+
+ Returns:
+ A numpy array containing the values of the constraint functions.
+
+ """
+ if len(self.fixed_idcs) > 0:
+ difference: np.ndarray = (
+ coords_seq[self.fixed_idcs] - self.fixed_coordinates
+ )
+ return difference
+ else:
+ return np.array([])
+
+ def _compute_fixed_gradient(self) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint function.
+
+ As the constraint is linear, the gradient is constant and, so, it is precomputed
+ with this method. Also, the gradient is independent of the actual values of the
+ mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the constraint gradient.
+
+ """
+ if len(self.fixed_idcs) > 0:
+ rows = np.arange(len(self.fixed_idcs))
+
+ cols = self.l2g_dofs[self.v2d[self.fixed_idcs]]
+ vals = np.ones(len(self.fixed_idcs))
+ csr = rows, cols, vals
+ shape = (len(self.fixed_idcs), self.no_vertices * self.dim)
+ gradient = _utils.linalg.sparse2scipy(csr, shape)
+ else:
+ shape = (0, self.no_vertices * self.dim)
+ gradient = _utils.linalg.sparse2scipy(
+ (np.array([]), np.array([]), np.array([])), shape
+ )
+ return gradient
+
+ def compute_gradient(self, coords_seq: np.ndarray) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the gradient.
+
+ """
+ return self.fixed_gradient
+
+
+class AngleConstraint(MeshConstraint):
+ """Base class for constraints on mesh cells based on angles."""
+
+ type = "inequality"
+
+ def __init__(
+ self,
+ mesh: fenics.Mesh,
+ config: cashocs.io.Config,
+ deformation_space: fenics.FunctionSpace,
+ ) -> None:
+ """Initializes the mesh quality constraint for the angles.
+
+ Args:
+ mesh: The corresponding FEM mesh.
+ config: The configuration of the optimization problem.
+ deformation_space: A space of vector CG1 elements for mesh deformations.
+
+ """
+ super().__init__(mesh, deformation_space)
+
+ self.config = config
+
+ self.cells = self.mesh.cells()
+
+ if self.dim == 2:
+ self.no_angles = 3
+ elif self.dim == 3:
+ self.no_angles = 4
+ else:
+ raise _exceptions.InputError(
+ "AngleConstraint",
+ "mesh",
+ "Can only use mesh quality constraints for 2D and 3D meshes.",
+ )
+
+ (
+ self.min_angle,
+ self.bad_idcs,
+ self.bad_coordinates,
+ ) = self._compute_minimum_angle()
+
+ def _compute_minimum_angle(
+ self,
+ ) -> tuple[np.ndarray | float | None, np.ndarray | None, np.ndarray | None]:
+ constant_min_angle = self.config.getfloat("MeshQualityConstraints", "min_angle")
+
+ feasible_angle_reduction_factor = self.config.getfloat(
+ "MeshQualityConstraints", "feasible_angle_reduction_factor"
+ )
+
+ if self.dim == 2:
+ initial_angles = mesh_quality.triangle_angles(self.mesh).reshape(
+ -1, self.no_angles
+ )
+ elif self.dim == 3:
+ initial_angles = mesh_quality.tetrahedron_solid_angles(self.mesh).reshape(
+ -1, self.no_angles
+ )
+ else:
+ raise _exceptions.InputError(
+ "FixedVertexConstraint",
+ "mesh",
+ "Can only use mesh quality constraints for 2D and 3D meshes.",
+ )
+ initial_angles = initial_angles[: self.ghost_offset]
+
+ minimum_initial_angles = np.min(initial_angles, axis=1)
+ bad_idcs, bad_coordinates, self.constraint_filter = self._manage_bad_cells(
+ minimum_initial_angles
+ )
+
+ cellwise_minimum_angle = (
+ feasible_angle_reduction_factor * minimum_initial_angles
+ )
+ cellwise_minimum_angle = np.repeat(cellwise_minimum_angle, self.no_angles)
+
+ if constant_min_angle > 0.0 and feasible_angle_reduction_factor > 0.0:
+ minimum_angle: np.ndarray | float = np.minimum(
+ cellwise_minimum_angle, constant_min_angle
+ )
+ elif constant_min_angle > 0.0 and feasible_angle_reduction_factor == 0.0:
+ minimum_angle = constant_min_angle
+ elif feasible_angle_reduction_factor > 0.0 and constant_min_angle == 0.0:
+ minimum_angle = cellwise_minimum_angle
+ else:
+ raise _exceptions.InputError(
+ "AngleConstraint",
+ "minimum_angle",
+ "Could not compute minimum angle.",
+ )
+
+ constraint_tolerance = self.config.getfloat("MeshQualityConstraints", "tol")
+ minimum_angle = np.maximum(2 * constraint_tolerance, minimum_angle)
+
+ return minimum_angle, bad_idcs, bad_coordinates
+
+ def _manage_bad_cells(
+ self, minimum_initial_angles: np.ndarray
+ ) -> tuple[np.ndarray | None, np.ndarray | None, np.ndarray | None]:
+ constraint_tolerance = self.config.getfloat("MeshQualityConstraints", "tol")
+ bad_cell_idx = np.nonzero(minimum_initial_angles <= 2 * constraint_tolerance)[0]
+
+ constraint_filter = np.zeros(len(minimum_initial_angles), dtype=bool)
+ constraint_filter[bad_cell_idx] = True
+ constraint_filter = np.repeat(constraint_filter, self.no_angles)
+
+ total_bad_cells = self.mesh.mpi_comm().allreduce(len(bad_cell_idx), op=MPI.SUM)
+ if total_bad_cells > 0:
+ _loggers.debug(
+ f"Found {total_bad_cells} bad mesh cells in the initial mesh. "
+ "Fixating these cells for the optimization."
+ )
+
+ if len(bad_cell_idx) > 0:
+ bad_vertex_idcs = self.cells[bad_cell_idx]
+ bad_vertex_idcs = np.unique(bad_vertex_idcs)
+
+ bad_vertex_idcs_global = self.global_vertex_indices[bad_vertex_idcs]
+ mask = np.isin(bad_vertex_idcs_global, self.global_vertex_indices_owned)
+ bad_vertex_idcs_local_owned = bad_vertex_idcs[mask]
+
+ if self.dim == 2:
+ bad_vertex_idcs_local = np.array(
+ [
+ self.dim * bad_vertex_idcs_local_owned,
+ self.dim * bad_vertex_idcs_local_owned + 1,
+ ]
+ ).T.reshape(-1)
+ elif self.dim == 3:
+ bad_vertex_idcs_local = np.array(
+ [
+ self.dim * bad_vertex_idcs_local_owned,
+ self.dim * bad_vertex_idcs_local_owned + 1,
+ self.dim * bad_vertex_idcs_local_owned + 2,
+ ]
+ ).T.reshape(-1)
+ else:
+ raise _exceptions.CashocsException(
+ "Please use a mesh of dimension 2 or 3."
+ )
+
+ bad_coordinates = (
+ self.mesh.coordinates().copy().reshape(-1)[bad_vertex_idcs_local]
+ )
+
+ return bad_vertex_idcs_local, bad_coordinates, constraint_filter
+ else:
+ return None, None, None
+
+
+class TriangleAngleConstraint(AngleConstraint):
+ r"""A mesh quality constraint for the angles of triangles in the mesh.
+
+ This ensures that the all angles :math:`\alpha` of the FEM mesh satisfy the
+ constraint :math:`\alpha \geq \alpha_{min}`, which is equivalently rewritten as
+ :math:`g(x) \leq 0` with :math:`g(x) = \alpha - \alpha_{min}`, where :math:`x` are
+ the mesh coordinates.
+ """
+
+ def __init__(
+ self,
+ mesh: fenics.Mesh,
+ config: cashocs.io.Config,
+ deformation_space: fenics.FunctionSpace,
+ ) -> None:
+ """Initializes the mesh quality constraint for the triangle angles.
+
+ Args:
+ mesh: The corresponding FEM mesh.
+ config: The configuration of the optimization problem.
+ deformation_space: A space of vector CG1 elements for mesh deformations.
+
+ """
+ super().__init__(mesh, config, deformation_space)
+
+ self.no_constraints = 3 * self.ghost_offset
+ self.is_necessary = np.array([True] * self.no_constraints)
+
+ def evaluate(self, coords_seq: np.ndarray) -> np.ndarray:
+ r"""Evaluates the constaint function at the current iterate.
+
+ This computes :math:`g(x)` where the constraint is given by
+ :math:`g(x) <= 0` and :math:`x` corresponds to mesh coordinates, i.e.,
+ `coords_seq`. The constraint returns :math:`\alpha_{min} - \alpha`,
+ where :math:`\alpha` is one angle of a triangle and :math:`\alpha_{min}` is the
+ minimum feasible angle in each triangle.
+
+ Args:
+ coords_seq: The (flattened) list of vertex coordinates of the mesh.
+
+ Returns:
+ A numpy array containing the values of the constraint functions.
+
+ """
+ old_coords = self.mesh.coordinates().copy()
+ self.mesh.coordinates()[:, :] = coords_seq.reshape(-1, self.dim)
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ values: np.ndarray = mesh_quality.triangle_angles(self.mesh)
+ values = values[: 3 * self.ghost_offset]
+
+ if self.constraint_filter is not None:
+ values[self.constraint_filter] = 100.0
+
+ values = self.min_angle - values
+
+ self.mesh.coordinates()[:, :] = old_coords
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ return values
+
+ def compute_gradient(self, coords_seq: np.ndarray) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the gradient.
+
+ """
+ old_coords = self.mesh.coordinates().copy()
+ self.mesh.coordinates()[:, :] = coords_seq.reshape(-1, self.dim)
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ rows, cols, vals = mesh_quality.triangle_angle_gradient(self.mesh)
+ rows = rows[: 18 * self.ghost_offset]
+ cols = cols[: 18 * self.ghost_offset]
+ vals = vals[: 18 * self.ghost_offset]
+
+ self.mesh.coordinates()[:, :] = old_coords
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ cols_local = self.v2d[cols]
+ cols = self.l2g_dofs[cols_local]
+
+ csr = rows, cols, vals
+ shape = (int(3 * self.ghost_offset), self.no_vertices * self.dim)
+ gradient = _utils.linalg.sparse2scipy(csr, shape)
+
+ return gradient
+
+
+class DihedralAngleConstraint(AngleConstraint):
+ r"""A mesh quality constraint for the dihedral angles of tets in the mesh.
+
+ This ensures that the all dihedral angles :math:`\alpha` of the FEM mesh satisfy the
+ constraint :math:`\alpha \geq \alpha_{min}`, which is equivalently rewritten as
+ :math:`g(x) \leq 0` with :math:`g(x) = \alpha - \alpha_{min}`, where :math:`x` are
+ the mesh coordinates.
+ """
+
+ def __init__(
+ self,
+ mesh: fenics.Mesh,
+ config: cashocs.io.Config,
+ deformation_space: fenics.FunctionSpace,
+ ) -> None:
+ """Initializes the mesh quality constraint for the triangle angles.
+
+ Args:
+ mesh: The corresponding FEM mesh.
+ config: The configuration of the optimization problem.
+ deformation_space: A space of vector CG1 elements for mesh deformations.
+
+ """
+ super().__init__(mesh, config, deformation_space)
+
+ self.no_constraints = 6 * self.ghost_offset
+ self.is_necessary = np.array([True] * self.no_constraints)
+
+ def evaluate(self, coords_seq: np.ndarray) -> np.ndarray:
+ r"""Evaluates the constaint function at the current iterate.
+
+ This computes :math:`g(x)` where the constraint is given by
+ :math:`g(x) <= 0` and :math:`x` corresponds to mesh coordinates, i.e.,
+ `coords_seq`. The constraint returns :math:`\alpha_{min} - \alpha`,
+ where :math:`\alpha` is one angle of a triangle and :math:`\alpha_{min}` is the
+ minimum feasible angle in each triangle.
+
+ Args:
+ coords_seq: The (flattened) list of vertex coordinates of the mesh.
+
+ Returns:
+ A numpy array containing the values of the constraint functions.
+
+ """
+ old_coords = self.mesh.coordinates().copy()
+ self.mesh.coordinates()[:, :] = coords_seq.reshape(-1, self.dim)
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ values: np.ndarray = mesh_quality.tetrahedron_angles(self.mesh)
+ values = values[: 6 * self.ghost_offset]
+
+ if self.constraint_filter is not None:
+ values[self.constraint_filter] = 100.0
+
+ values = self.min_angle - values
+
+ self.mesh.coordinates()[:, :] = old_coords
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ return values
+
+ def compute_gradient(self, coords_seq: np.ndarray) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the gradient.
+
+ """
+ old_coords = self.mesh.coordinates().copy()
+ self.mesh.coordinates()[:, :] = coords_seq.reshape(-1, self.dim)
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ rows, cols, vals = mesh_quality.tetrahedron_angle_gradient(self.mesh)
+ rows = rows[: 72 * self.ghost_offset]
+ cols = cols[: 72 * self.ghost_offset]
+ vals = vals[: 72 * self.ghost_offset]
+
+ self.mesh.coordinates()[:, :] = old_coords
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ cols_local = self.v2d[cols]
+ cols = self.l2g_dofs[cols_local]
+
+ csr = rows, cols, vals
+ shape = (int(6 * self.ghost_offset), self.no_vertices * self.dim)
+ gradient = _utils.linalg.sparse2scipy(csr, shape)
+
+ return gradient
+
+
+class SolidAngleConstraint(AngleConstraint):
+ r"""A mesh quality constraint for the solid angles of tets in the mesh.
+
+ This ensures that the all solid angles :math:`\alpha` of the FEM mesh satisfy the
+ constraint :math:`\alpha \geq \alpha_{min}`, which is equivalently rewritten as
+ :math:`g(x) \leq 0` with :math:`g(x) = \alpha - \alpha_{min}`, where :math:`x` are
+ the mesh coordinates.
+ """
+
+ def __init__(
+ self,
+ mesh: fenics.Mesh,
+ config: cashocs.io.Config,
+ deformation_space: fenics.FunctionSpace,
+ ) -> None:
+ """Initializes the mesh quality constraint for the triangle angles.
+
+ Args:
+ mesh: The corresponding FEM mesh.
+ config: The configuration of the optimization problem.
+ deformation_space: A space of vector CG1 elements for mesh deformations.
+
+ """
+ super().__init__(mesh, config, deformation_space)
+
+ self.no_constraints = 4 * self.ghost_offset
+ self.is_necessary = np.array([True] * self.no_constraints)
+
+ def evaluate(self, coords_seq: np.ndarray) -> np.ndarray:
+ r"""Evaluates the constaint function at the current iterate.
+
+ This computes :math:`g(x)` where the constraint is given by
+ :math:`g(x) <= 0` and :math:`x` corresponds to mesh coordinates, i.e.,
+ `coords_seq`. The constraint returns :math:`\alpha_{min} - \alpha`,
+ where :math:`\alpha` is one solid angle of a tetrahedron and
+ :math:`\alpha_{min}` is the minimum feasible solid angle in each tetrahedron.
+
+ Args:
+ coords_seq: The (flattened) list of vertex coordinates of the mesh.
+
+ Returns:
+ A numpy array containing the values of the constraint functions.
+
+ """
+ old_coords = self.mesh.coordinates().copy()
+ self.mesh.coordinates()[:, :] = coords_seq.reshape(-1, self.dim)
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ values: np.ndarray = mesh_quality.tetrahedron_solid_angles(self.mesh)
+ values = values[: 4 * self.ghost_offset]
+
+ if self.constraint_filter is not None:
+ values[self.constraint_filter] = 100.0
+
+ values = self.min_angle - values
+
+ self.mesh.coordinates()[:, :] = old_coords
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ return values
+
+ def compute_gradient(self, coords_seq: np.ndarray) -> sparse.csr_matrix:
+ """Computes the gradient of the constraint functions.
+
+ Args:
+ coords_seq: The flattened list of mesh coordinates.
+
+ Returns:
+ A sparse matrix representation of the gradient.
+
+ """
+ old_coords = self.mesh.coordinates().copy()
+ self.mesh.coordinates()[:, :] = coords_seq.reshape(-1, self.dim)
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ rows, cols, vals = mesh_quality.tetrahedron_solid_angle_gradient(self.mesh)
+ rows = rows[: 48 * self.ghost_offset]
+ cols = cols[: 48 * self.ghost_offset]
+ vals = vals[: 48 * self.ghost_offset]
+
+ self.mesh.coordinates()[:, :] = old_coords
+ self.mesh.bounding_box_tree().build(self.mesh)
+
+ cols_local = self.v2d[cols]
+ cols = self.l2g_dofs[cols_local]
+
+ csr = rows, cols, vals
+ shape = (int(4 * self.ghost_offset), self.no_vertices * self.dim)
+ gradient = _utils.linalg.sparse2scipy(csr, shape)
+
+ return gradient
diff --git a/cashocs/_optimization/shape_optimization/shape_optimization_problem.py b/cashocs/_optimization/shape_optimization/shape_optimization_problem.py
index 9edfd6e1..53614e15 100755
--- a/cashocs/_optimization/shape_optimization/shape_optimization_problem.py
+++ b/cashocs/_optimization/shape_optimization/shape_optimization_problem.py
@@ -44,6 +44,7 @@
from cashocs._optimization import optimization_algorithms
from cashocs._optimization import optimization_problem
from cashocs._optimization import verification
+from cashocs._optimization.shape_optimization import mesh_constraint_manager
from cashocs._optimization.shape_optimization import shape_variable_abstractions
from cashocs.geometry import mesh_testing
@@ -266,8 +267,19 @@ def __init__(
self.db, self.form_handler, self.state_problem
)
+ self.constraint_manager: mesh_constraint_manager.ConstraintManager = (
+ mesh_constraint_manager.ConstraintManager(
+ self.config,
+ self.mesh_handler.mesh,
+ self.boundaries,
+ self.db.function_db.control_spaces[0],
+ )
+ )
+
self.optimization_variable_abstractions = (
- shape_variable_abstractions.ShapeVariableAbstractions(self, self.db)
+ shape_variable_abstractions.ShapeVariableAbstractions(
+ self, self.db, self.constraint_manager
+ )
)
if bool(desired_weights is not None):
diff --git a/cashocs/_optimization/shape_optimization/shape_variable_abstractions.py b/cashocs/_optimization/shape_optimization/shape_variable_abstractions.py
index 34af767c..3d53e11c 100644
--- a/cashocs/_optimization/shape_optimization/shape_variable_abstractions.py
+++ b/cashocs/_optimization/shape_optimization/shape_variable_abstractions.py
@@ -22,14 +22,22 @@
from typing import cast, List, TYPE_CHECKING
import fenics
+from mpi4py import MPI
import numpy as np
+from petsc4py import PETSc
+from scipy import optimize
+from scipy import sparse
+from cashocs import _exceptions
from cashocs import _forms
+from cashocs import _loggers
+from cashocs import _utils
from cashocs._optimization import optimization_variable_abstractions
if TYPE_CHECKING:
from cashocs._database import database
from cashocs._optimization import shape_optimization
+ from cashocs._optimization.shape_optimization import mesh_constraint_manager
class ShapeVariableAbstractions(
@@ -41,17 +49,21 @@ def __init__(
self,
optimization_problem: shape_optimization.ShapeOptimizationProblem,
db: database.Database,
+ constraint_manager: mesh_constraint_manager.ConstraintManager,
) -> None:
"""Initializes self.
Args:
optimization_problem: The corresponding optimization problem.
db: The database of the problem.
+ constraint_manager: The constraint manager for mesh quality constraints.
"""
super().__init__(optimization_problem, db)
self.form_handler = cast(_forms.ShapeFormHandler, self.form_handler)
self.mesh_handler = optimization_problem.mesh_handler
+ self.constraint_manager = constraint_manager
+ self.mode = self.db.config.get("MeshQualityConstraints", "mode")
def compute_decrease_measure(
self, search_direction: List[fenics.Function]
@@ -88,6 +100,50 @@ def revert_variable_update(self) -> None:
self.mesh_handler.revert_transformation()
def update_optimization_variables(
+ self,
+ search_direction: List[fenics.Function],
+ stepsize: float,
+ beta: float,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: np.ndarray | None = None,
+ dropped_idx: np.ndarray | None = None,
+ ) -> float:
+ """Updates the optimization variables based on a line search.
+
+ This variant is used when constraints are present and projects the step back
+ to the surface of the constraints in the active set.
+
+ Args:
+ search_direction: The current search direction.
+ stepsize: The current (trial) stepsize.
+ beta: The parameter for the line search, which "halves" the stepsize if the
+ test was not successful.
+ active_idx: A boolean mask corresponding to the working set.
+ constraint_gradient: The gradient of (all) constraints.
+ dropped_idx: A boolean mask indicating which constraints have been recently
+ dropped from the working set.
+
+ Returns:
+ The stepsize which was found to be acceptable.
+
+ """
+ if (
+ active_idx is not None
+ and constraint_gradient is not None
+ and dropped_idx is not None
+ ):
+ return self._update_constrained_optimization_variables(
+ search_direction,
+ stepsize,
+ beta,
+ active_idx,
+ constraint_gradient,
+ dropped_idx,
+ )
+ else:
+ return self._update_optimization_variables(search_direction, stepsize, beta)
+
+ def _update_optimization_variables(
self, search_direction: List[fenics.Function], stepsize: float, beta: float
) -> float:
"""Updates the optimization variables based on a line search.
@@ -122,6 +178,317 @@ def update_optimization_variables(
return stepsize
+ def _update_constrained_optimization_variables(
+ self,
+ search_direction: List[fenics.Function],
+ stepsize: float,
+ beta: float,
+ active_idx: np.ndarray,
+ constraint_gradient: np.ndarray,
+ dropped_idx: np.ndarray,
+ ) -> float:
+ """Updates the optimization variables based on a line search.
+
+ This variant is used when constraints are present and projects the step back
+ to the surface of the constraints in the active set.
+
+ Args:
+ search_direction: The current search direction.
+ stepsize: The current (trial) stepsize.
+ beta: The parameter for the line search, which "halves" the stepsize if the
+ test was not successful.
+ active_idx: A boolean mask corresponding to the working set.
+ constraint_gradient: The gradient of (all) constraints.
+ dropped_idx: A boolean mask indicating which constraints have been recently
+ dropped from the working set.
+
+ Returns:
+ The stepsize which was found to be acceptable.
+
+ """
+ while True:
+ coords_sequential = self.mesh_handler.mesh.coordinates().copy().reshape(-1)
+ coords_dof = coords_sequential[self.constraint_manager.d2v]
+ search_direction_vertex = (
+ self.mesh_handler.deformation_handler.dof_to_coordinate(
+ search_direction[0]
+ )
+ )
+ search_direction_dof = search_direction_vertex.reshape(-1)[
+ self.constraint_manager.d2v
+ ]
+
+ if len(active_idx) > 0:
+ coords_dof_feasible, stepsize = self.compute_step(
+ coords_dof,
+ search_direction_dof,
+ stepsize,
+ active_idx,
+ constraint_gradient,
+ dropped_idx,
+ )
+
+ dof_deformation_vector = coords_dof_feasible - coords_dof
+ dof_deformation = fenics.Function(self.db.function_db.control_spaces[0])
+ dof_deformation.vector().set_local(dof_deformation_vector)
+ dof_deformation.vector().apply("")
+
+ self.deformation.vector().vec().axpby(
+ 1.0, 0.0, dof_deformation.vector().vec()
+ )
+ self.deformation.vector().apply("")
+ else:
+ self.deformation.vector().vec().axpby(
+ stepsize, 0.0, search_direction[0].vector().vec()
+ )
+ self.deformation.vector().apply("")
+
+ if self.mesh_handler.move_mesh(self.deformation):
+ if (
+ self.mesh_handler.current_mesh_quality
+ < self.mesh_handler.mesh_quality_tol_lower
+ ):
+ stepsize /= beta
+ self.mesh_handler.revert_transformation()
+ continue
+ else:
+ break
+ else:
+ stepsize /= beta
+
+ return stepsize
+
+ def compute_step(
+ self,
+ coords_dof: np.ndarray,
+ search_direction_dof: np.ndarray,
+ stepsize: float,
+ active_idx: np.ndarray,
+ constraint_gradient: sparse.csr_matrix,
+ dropped_idx: np.ndarray,
+ ) -> tuple[np.ndarray, float]:
+ """Computes a feasible mesh movement subject to mesh quality constraints.
+
+ Args:
+ coords_dof: The current coordinates, ordered in a dof-based way.
+ search_direction_dof: The search direction, given also in a dof-based way.
+ stepsize: The trial size of the step.
+ active_idx: A boolean mask used to identify the constraints that are
+ currently in the working set.
+ constraint_gradient: The sparse matrix containing (all) gradients of the
+ constraints.
+ dropped_idx: A boolean mask of indices of constraints, which have been
+ dropped from the working set to generate larger descent.
+
+ Returns:
+ A tuple `feasible_step, feasible_stepsize`, where `feasible_step` is a
+ feasible mesh configuration (based on all constraints) and
+ `feasible_stepsize` is the corresponding stepsize taken.
+
+ """
+ comm = self.mesh_handler.mesh.mpi_comm()
+
+ def func(lambd: float) -> float:
+ _loggers.debug(
+ f"Using a stepsize of {lambd} for computing the distance to the "
+ f"constraint boundary."
+ )
+ projected_step = self.project_to_working_set(
+ coords_dof,
+ search_direction_dof,
+ lambd,
+ active_idx,
+ constraint_gradient,
+ )
+ if projected_step is not None:
+ rval = np.max(
+ self.constraint_manager.evaluate(
+ projected_step[self.constraint_manager.v2d]
+ )[np.logical_and(~active_idx, ~dropped_idx)]
+ )
+ value: float = comm.allreduce(rval, op=MPI.MAX)
+ _loggers.debug(f"Evaluation of func gives value: {value}")
+
+ return value
+ else:
+ return 100.0
+
+ while True:
+ self.constraint_manager.comm.barrier()
+ _loggers.debug(f"Doing a trial step with the stepsize {stepsize:.3e}")
+ trial_step = self.project_to_working_set(
+ coords_dof,
+ search_direction_dof,
+ stepsize,
+ active_idx,
+ constraint_gradient,
+ )
+ self.constraint_manager.comm.barrier()
+ if trial_step is None:
+ stepsize /= 2.0
+ else:
+ _loggers.debug(
+ "Found a stepsize which is feasible for the "
+ "currently active constraints in the working set."
+ )
+ break
+
+ if not np.all(
+ self.constraint_manager.is_feasible(trial_step[self.constraint_manager.v2d])
+ ):
+ feasible_stepsize = optimize.root_scalar(
+ func, bracket=(0.0, stepsize), xtol=1e-10
+ ).root
+
+ _loggers.debug(f"Distance to constraint boundary: {feasible_stepsize:.3e}")
+ feasible_step = self.project_to_working_set(
+ coords_dof,
+ search_direction_dof,
+ feasible_stepsize,
+ active_idx,
+ constraint_gradient,
+ )
+ assert feasible_step is not None # nosec B101
+
+ assert np.all( # nosec B101
+ self.constraint_manager.is_feasible(
+ feasible_step[self.constraint_manager.v2d]
+ )
+ )
+ return feasible_step, feasible_stepsize
+ else:
+ return trial_step, stepsize
+
+ def project_to_working_set(
+ self,
+ coords_dof: np.ndarray,
+ search_direction_dof: np.ndarray,
+ stepsize: float,
+ active_idx: np.ndarray,
+ constraint_gradient: sparse.csr_matrix,
+ ) -> np.ndarray | None:
+ """Projects an (attempted) step back to the working set of active constraints.
+
+ The step is of the form: `coords_dof + stepsize * search_direction_dof`, the
+ working set is defined by `active_idx` and the gradient of (all) constraints is
+ given in `constraint_gradient`.
+
+ Args:
+ coords_dof: The current coordinates, ordered in a dof-based way.
+ search_direction_dof: The search direction, given also in a dof-based way.
+ stepsize: The trial size of the step.
+ active_idx: A boolean mask used to identify the constraints that are
+ currently in the working set.
+ constraint_gradient: The sparse matrix containing (all) gradients of the
+ constraints.
+
+ Returns:
+ The projected step (if the projection was successful) or `None` otherwise.
+
+ """
+ comm = self.mesh_handler.mesh.mpi_comm()
+
+ y_j: np.ndarray = coords_dof + stepsize * search_direction_dof
+ # pylint: disable=invalid-name
+ A = self.constraint_manager.compute_active_gradient(
+ active_idx, constraint_gradient
+ )
+ AT = A.copy().transpose() # pylint: disable=invalid-name
+ B = A.matMult(AT) # pylint: disable=invalid-name
+
+ # if self.mode == "complete":
+ # S = self.form_handler.scalar_product_matrix[ # pylint: disable=invalid-name
+ # :, :
+ # ]
+ # S_inv = np.linalg.inv(S) # pylint: disable=invalid-name
+
+ for its in range(10):
+ trial_active_idx = self.constraint_manager.compute_active_set(
+ y_j[self.constraint_manager.v2d]
+ )[active_idx]
+ satisfies_previous_constraints_local = np.all(trial_active_idx)
+ satisfies_previous_constraints = comm.allgather(
+ satisfies_previous_constraints_local
+ )
+ satisfies_previous_constraints = np.all(satisfies_previous_constraints)
+
+ has_active_constraints_local = np.any(active_idx)
+ has_active_constraints = comm.allgather(has_active_constraints_local)
+ has_active_constraints = np.any(has_active_constraints)
+
+ # no_violated_constraints = np.sum(
+ # ~self.constraint_manager.is_feasible(y_j[self.constraint_manager.v2d])
+ # )
+
+ if has_active_constraints:
+ h = self.constraint_manager.evaluate_active(
+ y_j[self.constraint_manager.v2d], active_idx
+ )
+
+ if len(h) > 0:
+ res_local = np.max(np.abs(h))
+ else:
+ res_local = 0.0
+
+ residual = comm.allreduce(res_local, op=MPI.MAX)
+ _loggers.debug(
+ "Projection to working set. "
+ f"Iteration: {its} Residual: {residual:.3e}"
+ # f" Violated Constraints: {no_violated_constraints}"
+ )
+
+ if not satisfies_previous_constraints:
+ # if self.mode == "complete":
+ # lambd = np.linalg.solve(A @ S_inv @ A.T, h)
+ # y_j = y_j - S_inv @ A.T @ lambd
+ # else:
+ ksp = PETSc.KSP().create(comm=self.constraint_manager.mesh.mpi_comm())
+
+ options: dict[str, int | float | str | None] = {
+ "ksp_type": "cg",
+ "ksp_max_it": 1000,
+ "ksp_rtol": self.constraint_manager.constraint_tolerance / 1e2,
+ "ksp_atol": 1e-30,
+ "pc_type": "hypre",
+ "pc_hypre_type": "boomeramg",
+ # "ksp_monitor_true_residual": None,
+ }
+
+ ksp.setOperators(B)
+ _utils.setup_petsc_options([ksp], [options])
+
+ lambd = B.createVecRight()
+ h_petsc = B.createVecLeft()
+ h_petsc.array_w = h
+ h_petsc.assemble()
+
+ ksp.solve(h_petsc, lambd)
+
+ if ksp.getConvergedReason() < 0:
+ raise _exceptions.NotConvergedError(
+ "Gradient projection", "The gradient projection failed."
+ )
+
+ y_petsc = AT.createVecLeft()
+ AT.mult(lambd, y_petsc)
+
+ update = fenics.Function(self.db.function_db.control_spaces[0])
+ update.vector().vec().aypx(0.0, y_petsc)
+ update.vector().apply("")
+ self.form_handler.apply_shape_bcs(update)
+ update.vector().apply("")
+
+ update_vertex = self.mesh_handler.deformation_handler.dof_to_coordinate(
+ update
+ )
+ update_dof = update_vertex.reshape(-1)[self.constraint_manager.d2v]
+ y_j = y_j - update_dof
+
+ else:
+ return y_j
+
+ return None
+
def compute_a_priori_decreases(
self, search_direction: List[fenics.Function], stepsize: float
) -> int:
diff --git a/cashocs/_optimization/topology_optimization/topology_optimization_problem.py b/cashocs/_optimization/topology_optimization/topology_optimization_problem.py
index 9f90d7aa..1d752d7a 100644
--- a/cashocs/_optimization/topology_optimization/topology_optimization_problem.py
+++ b/cashocs/_optimization/topology_optimization/topology_optimization_problem.py
@@ -202,7 +202,7 @@ def __init__( # pylint: disable=unused-argument
self.topological_derivative_is_identical = self.config.getboolean(
"TopologyOptimization", "topological_derivative_is_identical"
)
- self.re_normalize_levelset = self.config.getboolean(
+ self.re_normalize_levelset: bool = self.config.getboolean(
"TopologyOptimization", "re_normalize_levelset"
)
self.normalize_topological_derivative = self.config.getboolean(
diff --git a/cashocs/_optimization/topology_optimization/topology_variable_abstractions.py b/cashocs/_optimization/topology_optimization/topology_variable_abstractions.py
index 2eb3a91b..38c50b60 100644
--- a/cashocs/_optimization/topology_optimization/topology_variable_abstractions.py
+++ b/cashocs/_optimization/topology_optimization/topology_variable_abstractions.py
@@ -22,6 +22,7 @@
from typing import List, Optional, TYPE_CHECKING
import fenics
+import numpy as np
from cashocs._optimization import optimization_variable_abstractions
@@ -89,7 +90,13 @@ def revert_variable_update(self) -> None:
self.levelset_function.vector().apply("")
def update_optimization_variables(
- self, search_direction: List[fenics.Function], stepsize: float, beta: float
+ self,
+ search_direction: List[fenics.Function],
+ stepsize: float,
+ beta: float,
+ active_idx: np.ndarray | None = None,
+ constraint_gradient: np.ndarray | None = None,
+ dropped_idx: np.ndarray | None = None,
) -> float:
"""Updates the optimization variables based on a line search.
@@ -98,6 +105,13 @@ def update_optimization_variables(
stepsize: The current (trial) stepsize.
beta: The parameter for the line search, which "halves" the stepsize if the
test was not successful.
+ active_idx: The list of active indices of the working set. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
+ constraint_gradient: The gradient of the constraints for the mesh quality.
+ Only needed for shape optimization with mesh quality constraints.
+ Default is `None`.
+ dropped_idx: The list of indicies for dropped constraints. Only needed
+ for shape optimization with mesh quality constraints. Default is `None`.
Returns:
The stepsize which was found to be acceptable.
diff --git a/cashocs/_pde_problems/adjoint_problem.py b/cashocs/_pde_problems/adjoint_problem.py
index cdde0866..ce8cdd33 100755
--- a/cashocs/_pde_problems/adjoint_problem.py
+++ b/cashocs/_pde_problems/adjoint_problem.py
@@ -141,16 +141,11 @@ def solve(self) -> List[fenics.Function]:
rtol=self.picard_rtol,
atol=self.picard_atol,
verbose=self.picard_verbose,
- inner_damped=False,
- inner_inexact=False,
- inner_verbose=False,
inner_max_iter=2,
ksp_options=self.db.parameter_db.adjoint_ksp_options[::-1],
A_tensors=self.A_tensors[::-1],
b_tensors=self.b_tensors[::-1],
- inner_is_linear=True,
preconditioner_forms=self.db.form_db.preconditioner_forms[::-1],
- linear_solver=self.linear_solver,
)
self.has_solution = True
diff --git a/cashocs/_pde_problems/hessian_problems.py b/cashocs/_pde_problems/hessian_problems.py
index 532a1cb9..f5e93f0a 100755
--- a/cashocs/_pde_problems/hessian_problems.py
+++ b/cashocs/_pde_problems/hessian_problems.py
@@ -201,14 +201,10 @@ def hessian_application(
rtol=self.picard_rtol,
atol=self.picard_atol,
verbose=self.picard_verbose,
- inner_damped=False,
- inner_inexact=False,
- inner_verbose=False,
inner_max_iter=2,
ksp_options=self.db.parameter_db.state_ksp_options,
A_tensors=self.state_A_tensors,
b_tensors=self.state_b_tensors,
- inner_is_linear=True,
preconditioner_forms=self.db.form_db.preconditioner_forms,
)
@@ -220,14 +216,10 @@ def hessian_application(
rtol=self.picard_rtol,
atol=self.picard_atol,
verbose=self.picard_verbose,
- inner_damped=False,
- inner_inexact=False,
- inner_verbose=False,
inner_max_iter=2,
ksp_options=self.db.parameter_db.adjoint_ksp_options,
A_tensors=self.adjoint_A_tensors,
b_tensors=self.adjoint_b_tensors,
- inner_is_linear=True,
preconditioner_forms=self.db.form_db.preconditioner_forms,
)
diff --git a/cashocs/_pde_problems/shape_gradient_problem.py b/cashocs/_pde_problems/shape_gradient_problem.py
index 0693db76..e9e00a3b 100755
--- a/cashocs/_pde_problems/shape_gradient_problem.py
+++ b/cashocs/_pde_problems/shape_gradient_problem.py
@@ -42,6 +42,7 @@
if TYPE_CHECKING:
from cashocs import _forms
+ from cashocs import _typing
from cashocs._database import database
from cashocs._pde_problems import adjoint_problem as ap
from cashocs._pde_problems import state_problem as sp
@@ -149,6 +150,7 @@ def solve(self) -> List[fenics.Function]:
fun=self.db.function_db.gradient[0],
ksp_options=self.ksp_options,
)
+ self.form_handler.apply_shape_bcs(self.db.function_db.gradient[0])
self.has_solution = True
@@ -234,15 +236,19 @@ def solve(self) -> None:
self.solution.vector().vec().set(0.0)
self.solution.vector().apply("")
for nonlinear_form in self.form_list:
- nonlinear_solvers.newton_solve(
+ petsc_options: _typing.KspOption = {
+ "snes_type": "newtonls",
+ "snes_linesearch_type": "basic",
+ "snes_ksp_ew": True,
+ }
+ petsc_options.update(self.ksp_options)
+
+ nonlinear_solvers.snes_solve(
nonlinear_form,
self.solution,
self.bcs_shape,
+ petsc_options=petsc_options,
shift=self.shape_derivative,
- damped=False,
- inexact=True,
- verbose=False,
- ksp_options=self.ksp_options,
A_tensor=self.A_tensor,
b_tensor=self.b_tensor,
)
diff --git a/cashocs/_pde_problems/state_problem.py b/cashocs/_pde_problems/state_problem.py
index 19c28e98..d209ffe9 100755
--- a/cashocs/_pde_problems/state_problem.py
+++ b/cashocs/_pde_problems/state_problem.py
@@ -73,6 +73,7 @@ def __init__(
self.bcs_list: List[List[fenics.DirichletBC]] = self.state_form_handler.bcs_list
self.states = self.db.function_db.states
+ self.states_checkpoint = [fun.copy(True) for fun in self.states]
self.picard_rtol = self.config.getfloat("StateSystem", "picard_rtol")
self.picard_atol = self.config.getfloat("StateSystem", "picard_atol")
@@ -84,6 +85,7 @@ def __init__(
self.newton_inexact = self.config.getboolean("StateSystem", "newton_inexact")
self.newton_verbose = self.config.getboolean("StateSystem", "newton_verbose")
self.newton_iter = self.config.getint("StateSystem", "newton_iter")
+ self.backend = self.config.get("StateSystem", "backend")
# pylint: disable=invalid-name
self.A_tensors = [
@@ -127,6 +129,7 @@ def solve(self) -> List[fenics.Function]:
"""
if not self.has_solution:
self.db.callback.call_pre()
+ self._generate_checkpoint()
if (
not self.config.getboolean("StateSystem", "picard_iteration")
or self.db.parameter_db.state_dim == 1
@@ -152,23 +155,37 @@ def solve(self) -> List[fenics.Function]:
for i in range(self.db.parameter_db.state_dim):
if self.initial_guess is not None:
fenics.assign(self.states[i], self.initial_guess[i])
- nonlinear_solvers.newton_solve(
- self.state_form_handler.state_eq_forms[i],
- self.states[i],
- self.bcs_list[i],
- derivative=self.newton_linearizations[i],
- rtol=self.newton_rtol,
- atol=self.newton_atol,
- max_iter=self.newton_iter,
- damped=self.newton_damped,
- inexact=self.newton_inexact,
- verbose=self.newton_verbose,
- ksp_options=self.db.parameter_db.state_ksp_options[i],
- A_tensor=self.A_tensors[i],
- b_tensor=self.b_tensors[i],
- preconditioner_form=self.db.form_db.preconditioner_forms[i],
- linear_solver=self.linear_solver,
- )
+
+ pc_forms = self.db.form_db.preconditioner_forms[i]
+ if self.backend == "petsc":
+ nonlinear_solvers.snes_solve(
+ self.state_form_handler.state_eq_forms[i],
+ self.states[i],
+ self.bcs_list[i],
+ derivative=self.newton_linearizations[i],
+ petsc_options=self.db.parameter_db.state_ksp_options[i],
+ A_tensor=self.A_tensors[i],
+ b_tensor=self.b_tensors[i],
+ preconditioner_form=pc_forms,
+ )
+ else:
+ nonlinear_solvers.newton_solve(
+ self.state_form_handler.state_eq_forms[i],
+ self.states[i],
+ self.bcs_list[i],
+ derivative=self.newton_linearizations[i],
+ rtol=self.newton_rtol,
+ atol=self.newton_atol,
+ max_iter=self.newton_iter,
+ damped=self.newton_damped,
+ inexact=self.newton_inexact,
+ verbose=self.newton_verbose,
+ ksp_options=self.db.parameter_db.state_ksp_options[i],
+ A_tensor=self.A_tensors[i],
+ b_tensor=self.b_tensors[i],
+ preconditioner_form=pc_forms,
+ linear_solver=self.linear_solver,
+ )
else:
nonlinear_solvers.picard_iteration(
@@ -179,16 +196,11 @@ def solve(self) -> List[fenics.Function]:
rtol=self.picard_rtol,
atol=self.picard_atol,
verbose=self.picard_verbose,
- inner_damped=self.newton_damped,
- inner_inexact=self.newton_inexact,
- inner_verbose=self.newton_verbose,
inner_max_iter=self.newton_iter,
ksp_options=self.db.parameter_db.state_ksp_options,
A_tensors=self.A_tensors,
b_tensors=self.b_tensors,
- inner_is_linear=self.config.getboolean("StateSystem", "is_linear"),
preconditioner_forms=self.db.form_db.preconditioner_forms,
- linear_solver=self.linear_solver,
newton_linearizations=self.newton_linearizations,
)
@@ -198,3 +210,25 @@ def solve(self) -> List[fenics.Function]:
self._update_cost_functionals()
return self.states
+
+ def _generate_checkpoint(self) -> None:
+ """Generates a checkpoint of the state variables."""
+ for i in range(len(self.states)):
+ self.states_checkpoint[i].vector().vec().aypx(
+ 0.0, self.states[i].vector().vec()
+ )
+ self.states_checkpoint[i].vector().apply("")
+
+ def revert_to_checkpoint(self) -> None:
+ """Reverts the state variables to a checkpointed value.
+
+ This is useful when the solution of the state problem fails and another attempt
+ is made to solve it. Then, the perturbed solution of Newton's method should not
+ be the initial guess.
+
+ """
+ for i in range(len(self.states)):
+ self.states[i].vector().vec().aypx(
+ 0.0, self.states_checkpoint[i].vector().vec()
+ )
+ self.states[i].vector().apply("")
diff --git a/cashocs/_typing.py b/cashocs/_typing.py
index 7ab383e5..129160aa 100644
--- a/cashocs/_typing.py
+++ b/cashocs/_typing.py
@@ -58,3 +58,5 @@
cost_functional.MinMaxFunctional,
cost_functional.Functional,
]
+
+ShapeOptimizationProblem = shape_optimization.ShapeOptimizationProblem
diff --git a/cashocs/_utils/linalg.py b/cashocs/_utils/linalg.py
index d63be562..a37304dd 100644
--- a/cashocs/_utils/linalg.py
+++ b/cashocs/_utils/linalg.py
@@ -23,8 +23,10 @@
from typing import List, Optional, Tuple, TYPE_CHECKING, Union
import fenics
+from mpi4py import MPI
import numpy as np
from petsc4py import PETSc
+from scipy import sparse
try:
import ufl_legacy as ufl
@@ -36,8 +38,6 @@
from cashocs._utils import forms as forms_module
if TYPE_CHECKING:
- from mpi4py import MPI
-
from cashocs import _typing
iterative_ksp_options: _typing.KspOption = {
@@ -180,7 +180,7 @@ def assemble_petsc_system(
def setup_petsc_options(
- ksps: List[PETSc.KSP], ksp_options: List[_typing.KspOption]
+ objs: List[PETSc.KSP | PETSc.SNES], ksp_options: List[_typing.KspOption]
) -> None:
"""Sets up an (iterative) linear solver.
@@ -188,22 +188,22 @@ def setup_petsc_options(
to the PETSc KSP objects. Here, options[i] is applied to ksps[i].
Args:
- ksps: A list of PETSc KSP objects (linear solvers) to which the (command line)
+ objs: A list of PETSc objects (e.g. linear solvers) to which the (command line)
options are applied to.
- ksp_options: A list of command line options that specify the iterative solver
+ ksp_options: A list of command line options that specify the solver
from PETSc.
"""
fenics.PETScOptions.clear()
opts = PETSc.Options()
- for i in range(len(ksps)):
+ for i in range(len(objs)):
opts.clear()
for key, value in ksp_options[i].items():
opts.setValue(key, value)
- ksps[i].setFromOptions()
+ objs[i].setFromOptions()
def setup_fieldsplit_preconditioner(
@@ -232,17 +232,49 @@ def setup_fieldsplit_preconditioner(
"problem to be solved is not a mixed one.",
)
- pc = ksp.getPC()
- pc.setType(PETSc.PC.Type.FIELDSPLIT)
- idx = []
- name = []
- for i in range(function_space.num_sub_spaces()):
- idx_i = PETSc.IS().createGeneral(function_space.sub(i).dofmap().dofs())
- idx.append(idx_i)
- name.append(f"{i:d}")
- idx_tuples = zip(name, idx)
-
- pc.setFieldSplitIS(*idx_tuples)
+ if not any(key.endswith("_fields") for key in options.keys()):
+ pc = ksp.getPC()
+ pc.setType(PETSc.PC.Type.FIELDSPLIT)
+ idx = []
+ name = []
+ for i in range(function_space.num_sub_spaces()):
+ idx_i = PETSc.IS().createGeneral(
+ function_space.sub(i).dofmap().dofs()
+ )
+ idx.append(idx_i)
+ name.append(f"{i:d}")
+ idx_tuples = zip(name, idx)
+
+ pc.setFieldSplitIS(*idx_tuples)
+ else:
+ dof_total = function_space.dofmap().dofs()
+ offset = np.min(dof_total)
+
+ num_sub_spaces = function_space.num_sub_spaces()
+ dof_list = [
+ np.array(function_space.sub(i).dofmap().dofs())
+ for i in range(num_sub_spaces)
+ ]
+
+ section = PETSc.Section().create()
+ section.setNumFields(num_sub_spaces)
+
+ for i in range(num_sub_spaces):
+ section.setFieldName(i, f"{i:d}")
+ section.setFieldComponents(i, 1)
+ section.setChart(0, len(dof_total))
+ for field_idx, dofs in enumerate(dof_list):
+ for i in dofs:
+ section.setDof(i - offset, 1)
+ section.setFieldDof(i - offset, field_idx, 1)
+ section.setUp()
+
+ dm = PETSc.DMShell().create()
+ dm.setDefaultSection(section)
+ dm.setUp()
+
+ ksp.setDM(dm)
+ ksp.setDMActive(False)
def _initialize_comm(comm: Optional[MPI.Comm] = None) -> MPI.Comm:
@@ -332,6 +364,10 @@ def solve_linear_problem(
) -> PETSc.Vec:
"""Solves a finite dimensional linear problem.
+ An overview over possible command line options for the PETSc KSP object can
+ be found at ``_ and options for the
+ preconditioners can be found at ``_.
+
Args:
A: The PETSc matrix corresponding to the left-hand side of the problem. If
this is None, then the matrix stored in the ksp object is used. Raises
@@ -494,10 +530,7 @@ def solve(
setup_fieldsplit_preconditioner(fun, ksp, options)
setup_petsc_options([ksp], [options])
- if rtol is not None:
- ksp.rtol = rtol
- if atol is not None:
- ksp.atol = atol
+ ksp.setTolerances(rtol=rtol, atol=atol)
ksp.solve(b, x)
@@ -606,3 +639,55 @@ def interpolate(self, u: fenics.Function) -> fenics.Function:
v.vector().apply("")
return v
+
+
+def sparse2scipy(
+ csr: tuple[np.ndarray, np.ndarray, np.ndarray], shape: tuple[int, int] | None = None
+) -> sparse.csr_matrix:
+ """Converts a sparse matrix representation to a sparse scipy matrix.
+
+ Args:
+ csr: The tuple making up the CSR matrix: `rows, cols, vals`.
+ shape: The shape of the sparse matrix.
+
+ Returns:
+ The corresponding sparse scipy csr matrix.
+
+ """
+ rows = csr[0]
+ cols = csr[1]
+ vals = csr[2]
+ matrix = sparse.csr_matrix((vals, (rows, cols)), shape=shape)
+ return matrix
+
+
+def scipy2petsc(
+ scipy_matrix: sparse.csr_matrix,
+ comm: MPI.Comm,
+ local_size: int | None = None,
+) -> PETSc.Mat:
+ """Converts a sparse scipy matrix to a (sparse) PETSc matrix.
+
+ Args:
+ scipy_matrix: The sparse scipy matrix
+ comm: The MPI communicator used for distributing the mesh
+ local_size: The local size (number of rows) of the matrix, different for
+ each process. If this is `None` (the default), then PETSc.DECIDE is used.
+
+ Returns:
+ The corresponding sparse PETSc matrix.
+
+ """
+ shape = scipy_matrix.shape
+
+ no_rows_total = comm.allreduce(shape[0], op=MPI.SUM)
+ if local_size is None:
+ local_size = PETSc.DECIDE
+
+ petsc_matrix = PETSc.Mat().createAIJ(
+ comm=comm,
+ size=((shape[0], no_rows_total), (local_size, shape[1])),
+ csr=(scipy_matrix.indptr, scipy_matrix.indices, scipy_matrix.data),
+ )
+
+ return petsc_matrix
diff --git a/cashocs/geometry/mesh_handler.py b/cashocs/geometry/mesh_handler.py
index 35ed124f..9ee9d595 100644
--- a/cashocs/geometry/mesh_handler.py
+++ b/cashocs/geometry/mesh_handler.py
@@ -169,9 +169,10 @@ def __init__(
self.mesh, self.mesh_quality_type, self.mesh_quality_measure
)
- check_mesh_quality_tolerance(
- self.current_mesh_quality, self.mesh_quality_tol_upper
- )
+ if not self.db.parameter_db.is_remeshed:
+ check_mesh_quality_tolerance(
+ self.current_mesh_quality, self.mesh_quality_tol_upper
+ )
self.options_frobenius: _typing.KspOption = {
"ksp_type": "preonly",
@@ -214,6 +215,9 @@ def __init__(
pathlib.Path(self.config.get("Mesh", "gmsh_file")).resolve().parent
)
+ self._setup_remesh()
+
+ def _setup_remesh(self) -> None:
self.gmsh_file: str = ""
self.remesh_counter = 0
if self.do_remesh and self.db.parameter_db.temp_dict:
diff --git a/cashocs/geometry/mesh_testing.py b/cashocs/geometry/mesh_testing.py
index 48859270..c122bcca 100644
--- a/cashocs/geometry/mesh_testing.py
+++ b/cashocs/geometry/mesh_testing.py
@@ -120,10 +120,15 @@ def __init__(self, mesh: fenics.Mesh) -> None:
self.mesh = mesh
cells = self.mesh.cells()
- flat_cells = cells.flatten().tolist()
+ vertex_ghost_offset = self.mesh.topology().ghost_offset(0)
+ cell_ghost_offset = self.mesh.topology().ghost_offset(
+ self.mesh.topology().dim()
+ )
+
+ flat_cells = cells[:cell_ghost_offset].flatten().tolist()
self.cell_counter: collections.Counter = collections.Counter(flat_cells)
self.occurrences = np.array(
- [self.cell_counter[i] for i in range(self.mesh.num_vertices())]
+ [self.cell_counter[i] for i in range(vertex_ghost_offset)]
)
def test(self) -> bool:
@@ -215,5 +220,7 @@ def compute_collisions(cls, mesh: fenics.Mesh) -> np.ndarray:
cells that vertex ``i`` collides with.
"""
+ vertex_ghost_offset = mesh.topology().ghost_offset(0)
collisions: np.ndarray = cls._cpp_object.compute_collisions(mesh)
+ collisions = collisions[:vertex_ghost_offset]
return collisions
diff --git a/cashocs/geometry/quality.py b/cashocs/geometry/quality.py
index 74572f14..1728f285 100644
--- a/cashocs/geometry/quality.py
+++ b/cashocs/geometry/quality.py
@@ -90,7 +90,6 @@ class MeshQualityCalculator:
#include
#include
#include
- #include
using namespace dolfin;
diff --git a/cashocs/io/config.py b/cashocs/io/config.py
index ec23b7f7..fde8bdf2 100644
--- a/cashocs/io/config.py
+++ b/cashocs/io/config.py
@@ -84,11 +84,6 @@ def __init__(self, config_file: Optional[str] = None) -> None:
self.config_scheme: Dict[str, Dict[str, Dict[str, Any]]] = {
"Mesh": {
- "mesh_file": {
- "type": "str",
- "attributes": ["file"],
- "file_extension": "xdmf",
- },
"gmsh_file": {
"type": "str",
"attributes": ["file"],
@@ -150,6 +145,10 @@ def __init__(self, config_file: Optional[str] = None) -> None:
"picard_verbose": {
"type": "bool",
},
+ "backend": {
+ "type": "str",
+ "possible_options": ["cashocs", "petsc"],
+ },
},
"OptimizationRoutine": {
"algorithm": {
@@ -202,7 +201,6 @@ def __init__(self, config_file: Optional[str] = None) -> None:
"type": "float",
"attributes": ["positive"],
},
- "safeguard_stepsize": {"type": "bool"},
"epsilon_armijo": {
"type": "float",
"attributes": ["positive", "less_than_one"],
@@ -211,18 +209,19 @@ def __init__(self, config_file: Optional[str] = None) -> None:
"type": "float",
"attributes": ["positive", "larger_than_one"],
},
+ "safeguard_stepsize": {"type": "bool"},
"polynomial_model": {
"type": "str",
"possible_options": ["cubic", "quadratic"],
},
- "factor_low": {
+ "factor_high": {
"type": "float",
"attributes": ["less_than_one", "positive"],
+ "larger_than": ("LineSearch", "factor_low"),
},
- "factor_high": {
+ "factor_low": {
"type": "float",
"attributes": ["less_than_one", "positive"],
- "larger_than": ("LineSearch", "factor_low"),
},
"fail_if_not_converged": {
"type": "bool",
@@ -298,6 +297,9 @@ def __init__(self, config_file: Optional[str] = None) -> None:
"shape_bdry_fix_z": {
"type": "list",
},
+ "fixed_dimensions": {
+ "type": "list",
+ },
"use_pull_back": {
"type": "bool",
},
@@ -366,9 +368,6 @@ def __init__(self, config_file: Optional[str] = None) -> None:
"type": "float",
"attributes": ["non_negative", "less_than_one"],
},
- "fixed_dimensions": {
- "type": "list",
- },
"degree_estimation": {
"type": "bool",
},
@@ -477,6 +476,24 @@ def __init__(self, config_file: Optional[str] = None) -> None:
"attributes": ["non_negative"],
},
},
+ "MeshQualityConstraints": {
+ "min_angle": {
+ "type": "float",
+ "attributes": ["non_negative"],
+ },
+ "tol": {
+ "type": "float",
+ "attributes": ["positive"],
+ },
+ "mode": {
+ "type": "str",
+ "possible_options": ["approximate"],
+ },
+ "feasible_angle_reduction_factor": {
+ "type": "float",
+ "attributes": ["less_than_one", "non_negative"],
+ },
+ },
"TopologyOptimization": {
"angle_tol": {
"type": "float",
@@ -558,6 +575,7 @@ def __init__(self, config_file: Optional[str] = None) -> None:
picard_atol = 1e-12
picard_iter = 50
picard_verbose = False
+backend = cashocs
[OptimizationRoutine]
algorithm = none
@@ -588,7 +606,6 @@ def __init__(self, config_file: Optional[str] = None) -> None:
use_p_laplacian = False
p_laplacian_power = 2
p_laplacian_stabilization = 0.0
-degree_estimation = True
use_pull_back = True
use_distance_mu = False
mu_min = 1.0
@@ -606,6 +623,7 @@ def __init__(self, config_file: Optional[str] = None) -> None:
shape_bdry_fix_x = []
shape_bdry_fix_y = []
shape_bdry_fix_z = []
+degree_estimation = True
global_deformation = False
test_for_intersections = True
@@ -656,6 +674,12 @@ def __init__(self, config_file: Optional[str] = None) -> None:
angle_change = inf
remesh_iter = 0
+[MeshQualityConstraints]
+min_angle = 0.0
+feasible_angle_reduction_factor = 0.0
+tol = 1e-2
+mode = approximate
+
[TopologyOptimization]
angle_tol = 1.0
interpolation_scheme = volume
diff --git a/cashocs/io/managers.py b/cashocs/io/managers.py
index 496a2165..2f0785f9 100644
--- a/cashocs/io/managers.py
+++ b/cashocs/io/managers.py
@@ -585,8 +585,16 @@ def _write_xdmf_step(
mesh = function.function_space().mesh()
comm = mesh.mpi_comm()
- if function.function_space().ufl_element().family() == "Real":
- space = fenics.FunctionSpace(mesh, "CG", 1)
+ if function.function_space().ufl_element().family() in [
+ "Real",
+ "NodalEnrichedElement",
+ ]:
+ if len(function.ufl_shape) > 0:
+ space = fenics.VectorFunctionSpace(
+ mesh, "CG", 1, dim=function.ufl_shape[0]
+ )
+ else:
+ space = fenics.FunctionSpace(mesh, "CG", 1)
function = fenics.interpolate(function, space)
function.rename(function_name, function_name)
diff --git a/cashocs/io/mesh.py b/cashocs/io/mesh.py
index 3a556e6f..c25ba7f2 100644
--- a/cashocs/io/mesh.py
+++ b/cashocs/io/mesh.py
@@ -355,14 +355,14 @@ def create_point_representation(
mod_line = ""
if dim == 2:
mod_line = (
- f"{points[idcs[subwrite_counter]][0]:.16f} "
- f"{points[idcs[subwrite_counter]][1]:.16f} 0\n"
+ f"{points[idcs[subwrite_counter]][0]:.16e} "
+ f"{points[idcs[subwrite_counter]][1]:.16e} 0\n"
)
elif dim == 3:
mod_line = (
- f"{points[idcs[subwrite_counter]][0]:.16f} "
- f"{points[idcs[subwrite_counter]][1]:.16f} "
- f"{points[idcs[subwrite_counter]][2]:.16f}\n"
+ f"{points[idcs[subwrite_counter]][0]:.16e} "
+ f"{points[idcs[subwrite_counter]][1]:.16e} "
+ f"{points[idcs[subwrite_counter]][2]:.16e}\n"
)
return mod_line
diff --git a/cashocs/nonlinear_solvers/__init__.py b/cashocs/nonlinear_solvers/__init__.py
index ed8034ca..efc83f23 100644
--- a/cashocs/nonlinear_solvers/__init__.py
+++ b/cashocs/nonlinear_solvers/__init__.py
@@ -24,5 +24,6 @@
from cashocs.nonlinear_solvers.linear_solver import linear_solve
from cashocs.nonlinear_solvers.newton_solver import newton_solve
from cashocs.nonlinear_solvers.picard_solver import picard_iteration
+from cashocs.nonlinear_solvers.snes import snes_solve
-__all__ = ["newton_solve", "picard_iteration", "linear_solve"]
+__all__ = ["newton_solve", "picard_iteration", "linear_solve", "snes_solve"]
diff --git a/cashocs/nonlinear_solvers/picard_solver.py b/cashocs/nonlinear_solvers/picard_solver.py
index 4de55304..fb1e48e6 100644
--- a/cashocs/nonlinear_solvers/picard_solver.py
+++ b/cashocs/nonlinear_solvers/picard_solver.py
@@ -31,7 +31,7 @@
from cashocs import _exceptions
from cashocs import _utils
-from cashocs.nonlinear_solvers import newton_solver
+from cashocs.nonlinear_solvers import snes
if TYPE_CHECKING:
from cashocs import _typing
@@ -80,6 +80,15 @@ def _create_homogenized_bcs(
return bcs_list_hom
+def _enlist_picard(
+ obj: Optional[List[Union[T, None]]], length: int
+) -> List[Union[T, None]]:
+ if obj is None:
+ return [None] * length
+ else:
+ return obj
+
+
def picard_iteration(
form_list: Union[List[ufl.form], ufl.Form],
u_list: Union[List[fenics.Function], fenics.Function],
@@ -88,17 +97,12 @@ def picard_iteration(
rtol: float = 1e-10,
atol: float = 1e-10,
verbose: bool = True,
- inner_damped: bool = True,
- inner_inexact: bool = True,
- inner_verbose: bool = False,
inner_max_iter: int = 25,
ksp_options: Optional[List[_typing.KspOption]] = None,
# pylint: disable=invalid-name
A_tensors: Optional[List[fenics.PETScMatrix]] = None,
b_tensors: Optional[List[fenics.PETScVector]] = None,
- inner_is_linear: bool = False,
preconditioner_forms: Optional[Union[List[ufl.Form], ufl.Form]] = None,
- linear_solver: Optional[_utils.linalg.LinearSolver] = None,
newton_linearizations: Optional[List[ufl.Form]] = None,
) -> None:
"""Solves a system of coupled PDEs via a Picard iteration.
@@ -112,12 +116,6 @@ def picard_iteration(
atol: The absolute tolerance for the Picard iteration, default is 1e-10.
verbose: Boolean flag, if ``True``, output is written to stdout, default is
``True``.
- inner_damped: Boolean flag, if ``True``, the inner problems are solved with a
- damped Newton method, default is ``True``
- inner_inexact: Boolean flag, if ``True``, the inner problems are solved with an
- inexact Newton method, default is ``True``
- inner_verbose: Boolean flag, if ``True``, the inner problems write the history
- to stdout, default is ``False``.
inner_max_iter: Maximum number of iterations for the inner Newton solver;
default is 25.
ksp_options: List of options for the KSP objects.
@@ -125,13 +123,9 @@ def picard_iteration(
equations.
b_tensors: List of vectors for the left-hand sides of the inner (linearized)
equations.
- inner_is_linear: Boolean flag, if this is ``True``, all problems are actually
- linear ones, and only a linear solver is used.
preconditioner_forms: The list of forms for the preconditioner. The default
is `None`, so that the preconditioner matrix is the same as the system
matrix.
- linear_solver: The linear solver (KSP) which is used to solve the linear
- systems arising from the discretized PDE.
newton_linearizations: A list of UFL forms describing which (alternative)
linearizations should be used for the (nonlinear) equations when
solving them (with Newton's method). The default is `None`, so that the
@@ -143,12 +137,9 @@ def picard_iteration(
u_list = _utils.enlist(u_list)
bcs_list = _utils.check_and_enlist_bcs(bcs_list)
bcs_list_hom = _create_homogenized_bcs(bcs_list)
- preconditioner_form_list = _utils.enlist(preconditioner_forms)
- if newton_linearizations is None:
- newton_linearization_list = [None] * len(u_list)
- else:
- newton_linearization_list = newton_linearizations
+ preconditioner_form_list = _enlist_picard(preconditioner_forms, len(u_list))
+ newton_linearization_list = _enlist_picard(newton_linearizations, len(u_list))
comm = u_list[0].function_space().mesh().mpi_comm()
@@ -190,23 +181,18 @@ def picard_iteration(
j, ksp_options, A_tensors, b_tensors
)
- newton_solver.newton_solve(
+ snes.snes_solve(
form_list[j],
u_list[j],
bcs_list[j],
derivative=newton_linearization_list[j],
+ petsc_options=ksp_option,
rtol=eta,
atol=atol * 1e-1,
max_iter=inner_max_iter,
- damped=inner_damped,
- inexact=inner_inexact,
- verbose=inner_verbose,
- ksp_options=ksp_option,
A_tensor=A_tensor,
b_tensor=b_tensor,
- is_linear=inner_is_linear,
preconditioner_form=preconditioner_form_list[j],
- linear_solver=linear_solver,
)
if is_printing:
diff --git a/cashocs/nonlinear_solvers/snes.py b/cashocs/nonlinear_solvers/snes.py
new file mode 100644
index 00000000..cf27b887
--- /dev/null
+++ b/cashocs/nonlinear_solvers/snes.py
@@ -0,0 +1,313 @@
+# Copyright (C) 2020-2024 Sebastian Blauth
+#
+# This file is part of cashocs.
+#
+# cashocs is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# cashocs is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with cashocs. If not, see .
+
+"""Interface for the PETSc SNES solver for nonlinear equations."""
+
+from __future__ import annotations
+
+import copy
+from typing import List, Optional, TYPE_CHECKING, Union
+
+import fenics
+from petsc4py import PETSc
+
+try:
+ import ufl_legacy as ufl
+except ImportError:
+ import ufl
+
+from cashocs import _exceptions
+from cashocs import _utils
+
+if TYPE_CHECKING:
+ from cashocs import _typing
+
+
+default_snes_options: _typing.KspOption = {
+ "snes_type": "newtonls",
+ "snes_atol": 1e-10,
+ "snes_rtol": 1e-10,
+ "snes_max_it": 50,
+}
+
+
+class SNESSolver:
+ """Interface for using PETSc's SNES solver."""
+
+ def __init__(
+ self,
+ nonlinear_form: ufl.Form,
+ u: fenics.Function,
+ bcs: Union[fenics.DirichletBC, List[fenics.DirichletBC]],
+ derivative: Optional[ufl.Form] = None,
+ petsc_options: Optional[_typing.KspOption] = None,
+ shift: Optional[ufl.Form] = None,
+ rtol: Optional[float] = None,
+ atol: Optional[float] = None,
+ max_iter: Optional[int] = None,
+ A_tensor: Optional[fenics.PETScMatrix] = None, # pylint: disable=invalid-name
+ b_tensor: Optional[fenics.PETScVector] = None,
+ preconditioner_form: Optional[ufl.Form] = None,
+ ) -> None:
+ """Initialize the SNES solver.
+
+ Args:
+ nonlinear_form: The variational form of the nonlinear problem to be solved
+ by Newton's method.
+ u: The sought solution / initial guess. It is not assumed that the initial
+ guess satisfies the Dirichlet boundary conditions, they are applied
+ automatically. The method overwrites / updates this Function.
+ bcs: A list of DirichletBCs for the nonlinear variational problem.
+ derivative: The Jacobian of nonlinear_form, used for the Newton method.
+ Default is None, and in this case the Jacobian is computed automatically
+ with AD.
+ petsc_options: The options for PETSc SNES object.
+ shift: A shift term, if the right-hand side of the nonlinear problem is not
+ zero, but shift.
+ rtol: Relative tolerance of the solver. Overrides the specification in the
+ petsc_options.
+ atol: Absolute tolerance of the solver. Overrides the specification in the
+ petsc_options.
+ max_iter: Maximum number of iterations carried out by the method. Overrides
+ the specification in the petsc_options.
+ A_tensor: A fenics.PETScMatrix for storing the left-hand side of the linear
+ sub-problem.
+ b_tensor: A fenics.PETScVector for storing the right-hand side of the linear
+ sub-problem.
+ preconditioner_form: A UFL form which defines the preconditioner matrix.
+
+ """
+ self.nonlinear_form = nonlinear_form
+ self.u = u
+ self.comm = self.u.function_space().mesh().mpi_comm()
+ self.bcs = _utils.enlist(bcs)
+ self.shift = shift
+
+ self.rtol = rtol
+ self.atol = atol
+ self.max_iter = max_iter
+
+ self.is_preassembled = False
+
+ if petsc_options is None:
+ self.petsc_options: _typing.KspOption = copy.deepcopy(default_snes_options)
+ self.petsc_options.update(_utils.linalg.direct_ksp_options)
+ else:
+ self.petsc_options = petsc_options
+
+ if preconditioner_form is not None:
+ if len(preconditioner_form.arguments()) == 1:
+ self.preconditioner_form = fenics.derivative(
+ preconditioner_form, self.u
+ )
+ else:
+ self.preconditioner_form = preconditioner_form
+ else:
+ self.preconditioner_form = None
+
+ temp_derivative = derivative or fenics.derivative(self.nonlinear_form, self.u)
+ self.derivative = _utils.bilinear_boundary_form_modification([temp_derivative])[
+ 0
+ ]
+
+ self.assembler = fenics.SystemAssembler(
+ self.derivative, self.nonlinear_form, self.bcs
+ )
+ self.assembler.keep_diagonal = True
+
+ if A_tensor is not None:
+ self.A_petsc = A_tensor.mat() # pylint: disable=invalid-name
+ else:
+ self.A_petsc = fenics.PETScMatrix(self.comm).mat()
+
+ if b_tensor is not None:
+ self.residual_petsc = b_tensor.vec()
+ else:
+ self.residual_petsc = fenics.PETScVector(self.comm).vec()
+
+ if self.preconditioner_form is not None:
+ self.assembler_pc = fenics.SystemAssembler(
+ self.preconditioner_form, self.nonlinear_form, self.bcs
+ )
+ self.assembler_pc.keep_diagonal = True
+ self.P_petsc = fenics.PETScMatrix( # pylint: disable=invalid-name
+ self.comm
+ ).mat()
+ else:
+ self.P_petsc = None
+
+ self.assembler_shift: Optional[fenics.SystemAssembler] = None
+ self.residual_shift: Optional[fenics.PETScVector] = None
+ if self.shift is not None:
+ self.assembler_shift = fenics.SystemAssembler(
+ self.derivative, self.shift, self.bcs
+ )
+ self.residual_shift = fenics.PETScVector(self.comm)
+
+ def assemble_function(
+ self,
+ snes: PETSc.SNES, # pylint: disable=unused-argument
+ x: PETSc.Vec,
+ f: PETSc.Vec,
+ ) -> None:
+ """Interface for PETSc SNESSetFunction.
+
+ Args:
+ snes: The SNES solver
+ x: The current iterate
+ f: The vector in which the function evaluation is stored.
+
+ """
+ self.u.vector().vec().setArray(x)
+ self.u.vector().apply("")
+ f = fenics.PETScVector(f)
+
+ self.assembler.assemble(f, self.u.vector())
+ if (
+ self.shift is not None
+ and self.assembler_shift is not None
+ and self.residual_shift is not None
+ ):
+ self.assembler_shift.assemble(self.residual_shift, self.u.vector())
+ f[:] -= self.residual_shift[:]
+
+ def assemble_jacobian(
+ self,
+ snes: PETSc.SNES, # pylint: disable=unused-argument
+ x: PETSc.Vec,
+ J: PETSc.Mat, # pylint: disable=invalid-name,
+ P: PETSc.Mat, # pylint: disable=invalid-name
+ ) -> None:
+ """Interface for PETSc SNESSetJacobian.
+
+ Args:
+ snes: The SNES solver.
+ x: The current iterate.
+ J: The matrix storing the Jacobian.
+ P: The matrix storing the preconditioner for the Jacobian.
+
+ """
+ if not self.is_preassembled:
+ self.u.vector().vec().setArray(x)
+ self.u.vector().apply("")
+
+ J = fenics.PETScMatrix(J) # pylint: disable=invalid-name
+ self.assembler.assemble(J)
+ J.ident_zeros()
+
+ if self.preconditioner_form is not None:
+ P = fenics.PETScMatrix(P) # pylint: disable=invalid-name
+ self.assembler_pc.assemble(P)
+ P.ident_zeros()
+ else:
+ self.is_preassembled = False
+
+ def solve(self) -> fenics.Function:
+ """Solves the nonlinear problem with PETSc's SNES."""
+ snes = PETSc.SNES().create()
+
+ snes.setFunction(self.assemble_function, self.residual_petsc)
+ snes.setJacobian(self.assemble_jacobian, self.A_petsc, self.P_petsc)
+
+ ksp = snes.getKSP()
+ _utils.linalg.setup_fieldsplit_preconditioner(self.u, ksp, self.petsc_options)
+
+ if fenics.PETScMatrix(self.A_petsc).empty():
+ self.assemble_jacobian(
+ snes, self.u.vector().vec(), self.A_petsc, self.P_petsc
+ )
+ self.is_preassembled = True
+
+ _utils.setup_petsc_options([snes], [self.petsc_options])
+ snes.setTolerances(rtol=self.rtol, atol=self.atol, max_it=self.max_iter)
+ snes.solve(None, self.u.vector().vec())
+
+ converged_reason = snes.getConvergedReason()
+ if converged_reason < 0:
+ raise _exceptions.PETScSNESError(converged_reason)
+
+ if hasattr(PETSc, "garbage_cleanup"):
+ snes.destroy()
+ PETSc.garbage_cleanup(comm=self.comm)
+ PETSc.garbage_cleanup()
+
+ return self.u
+
+
+def snes_solve(
+ nonlinear_form: ufl.Form,
+ u: fenics.Function,
+ bcs: Union[fenics.DirichletBC, List[fenics.DirichletBC]],
+ derivative: Optional[ufl.Form] = None,
+ petsc_options: Optional[_typing.KspOption] = None,
+ shift: Optional[ufl.Form] = None,
+ rtol: Optional[float] = None,
+ atol: Optional[float] = None,
+ max_iter: Optional[int] = None,
+ A_tensor: Optional[fenics.PETScMatrix] = None, # pylint: disable=invalid-name
+ b_tensor: Optional[fenics.PETScVector] = None,
+ preconditioner_form: Optional[ufl.Form] = None,
+) -> fenics.Function:
+ """Solve a nonlinear PDE problem with PETSc SNES.
+
+ An overview over possible PETSc command line options for the SNES can be found
+ at ``_.
+
+ Args:
+ nonlinear_form: The variational form of the nonlinear problem to be solved
+ by Newton's method.
+ u: The sought solution / initial guess. It is not assumed that the initial
+ guess satisfies the Dirichlet boundary conditions, they are applied
+ automatically. The method overwrites / updates this Function.
+ bcs: A list of DirichletBCs for the nonlinear variational problem.
+ derivative: The Jacobian of nonlinear_form, used for the Newton method.
+ Default is None, and in this case the Jacobian is computed automatically
+ with AD.
+ petsc_options: The options for PETSc SNES object.
+ shift: A shift term, if the right-hand side of the nonlinear problem is not
+ zero, but shift.
+ rtol: Relative tolerance of the solver (default is ``rtol = 1e-10``).
+ atol: Absolute tolerance of the solver (default is ``atol = 1e-10``).
+ max_iter: Maximum number of iterations carried out by the method (default is
+ ``max_iter = 50``).
+ A_tensor: A fenics.PETScMatrix for storing the left-hand side of the linear
+ sub-problem.
+ b_tensor: A fenics.PETScVector for storing the right-hand side of the linear
+ sub-problem.
+ preconditioner_form: A UFL form which defines the preconditioner matrix.
+
+ Returns:
+ The solution in form of a FEniCS Function.
+
+ """
+ solver = SNESSolver(
+ nonlinear_form,
+ u,
+ bcs,
+ derivative=derivative,
+ petsc_options=petsc_options,
+ shift=shift,
+ rtol=rtol,
+ atol=atol,
+ max_iter=max_iter,
+ A_tensor=A_tensor,
+ b_tensor=b_tensor,
+ preconditioner_form=preconditioner_form,
+ )
+
+ solution = solver.solve()
+ return solution
diff --git a/demos/documented/cashocs_as_solver/control_solver/config.ini b/demos/documented/cashocs_as_solver/control_solver/config.ini
index 334c36b2..37d852fc 100755
--- a/demos/documented/cashocs_as_solver/control_solver/config.ini
+++ b/demos/documented/cashocs_as_solver/control_solver/config.ini
@@ -1,53 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-rtol = 1e-3
-atol = 0.0
-max_iter = 100
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
-save_results = True
-save_state = False
-result_dir = ./
+save_results = False
+save_txt = False
\ No newline at end of file
diff --git a/demos/documented/cashocs_as_solver/control_solver/history.json b/demos/documented/cashocs_as_solver/control_solver/history.json
deleted file mode 100755
index 71d0458e..00000000
--- a/demos/documented/cashocs_as_solver/control_solver/history.json
+++ /dev/null
@@ -1 +0,0 @@
-{"cost_function_value": [0.12240249296414983, 0.12236443677831443, 0.04065283206629595, 0.008569132714728856, 0.0007846142266652488, 0.0007841983736892504, 0.0007831010817764615, 0.0007830971199805435, 0.0007827841773009943, 0.0007827272330887028], "gradient_norm": [1.0, 0.9998432897368269, 2.30832977853386, 0.48475760892616865, 0.0026050032048445756, 0.0021487879319433516, 0.0010647103496345242, 0.00682257258141274, 0.0015881049914037476, 0.0007597450079614925], "stepsize": [1.0, 1.0, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], "MeshQuality": [], "initial_gradient_norm": 0.006169211292565742, "state_solves": 11, "adjoint_solves": 10, "iterations": 9}
\ No newline at end of file
diff --git a/demos/documented/cashocs_as_solver/control_solver/history.txt b/demos/documented/cashocs_as_solver/control_solver/history.txt
deleted file mode 100644
index 42e73727..00000000
--- a/demos/documented/cashocs_as_solver/control_solver/history.txt
+++ /dev/null
@@ -1,22 +0,0 @@
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 0, 1.224e-01, 1.000e+00, 6.169e-03,
-
- 1, 1.224e-01, 9.998e-01, 6.168e-03, 1.000e+00
- 2, 4.065e-02, 2.308e+00, 1.424e-02, 1.000e+00
- 3, 8.569e-03, 4.848e-01, 2.991e-03, 5.000e-01
- 4, 7.846e-04, 2.605e-03, 1.607e-05, 1.000e+00
- 5, 7.842e-04, 2.149e-03, 1.326e-05, 1.000e+00
- 6, 7.831e-04, 1.065e-03, 6.568e-06, 1.000e+00
- 7, 7.831e-04, 6.823e-03, 4.209e-05, 1.000e+00
- 8, 7.828e-04, 1.588e-03, 9.797e-06, 1.000e+00
- 9, 7.827e-04, 7.597e-04, 4.687e-06, 1.000e+00
-
-Optimization was successful.
-Statistics:
- total iterations: 9
- final objective value: 7.827e-04
- final gradient norm: 7.597e-04
- total number of state systems solved: 11
- total number of adjoint systems solved: 10
diff --git a/demos/documented/cashocs_as_solver/shape_solver/config.ini b/demos/documented/cashocs_as_solver/shape_solver/config.ini
index bc77a5c2..7a6fbf8e 100755
--- a/demos/documented/cashocs_as_solver/shape_solver/config.ini
+++ b/demos/documented/cashocs_as_solver/shape_solver/config.ini
@@ -1,84 +1,19 @@
-[Mesh]
-#mesh_file = ./mesh/mesh.xdmf
-#gmsh_file = ./mesh/mesh.msh
-#geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
rtol = 5e-3
-atol = 0.0
-max_iter = 50
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
use_pull_back = True
lambda_lame = 1.428571428571429
damping_factor = 0.2
mu_def = 0.35714285714285715
mu_fix = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = condition_number
-type = min
[Output]
verbose = True
save_results = False
-save_state = False
-save_mesh = False
+save_txt = False
diff --git a/demos/documented/misc/xdmf_io/config.ini b/demos/documented/misc/xdmf_io/config.ini
index 24d3a17c..7f450e8d 100755
--- a/demos/documented/misc/xdmf_io/config.ini
+++ b/demos/documented/misc/xdmf_io/config.ini
@@ -1,91 +1,16 @@
-[Mesh]
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
rtol = 5e-3
-atol = 0.0
-max_iter = 50
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
lambda_lame = 1.428571428571429
damping_factor = 0.2
mu_def = 0.35714285714285715
mu_fix = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_curvature = 0.0
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-use_relative_scaling = False
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = condition_number
-type = min
[Output]
verbose = True
@@ -94,6 +19,3 @@ save_txt = False
save_state = True
save_adjoint = True
save_gradient = True
-save_mesh = False
-precision = 3
-time_suffix = False
diff --git a/demos/documented/optimal_control/box_constraints/config.ini b/demos/documented/optimal_control/box_constraints/config.ini
index faf97cac..573d6451 100755
--- a/demos/documented/optimal_control/box_constraints/config.ini
+++ b/demos/documented/optimal_control/box_constraints/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 10
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cr
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-10
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/constraints/config.ini b/demos/documented/optimal_control/constraints/config.ini
index bac3dfbd..082fb6af 100755
--- a/demos/documented/optimal_control/constraints/config.ini
+++ b/demos/documented/optimal_control/constraints/config.ini
@@ -1,58 +1,11 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-rtol = 1e-3
-atol = 0.0
max_iter = 250
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
verbose = False
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/control_boundary_conditions/config.ini b/demos/documented/optimal_control/control_boundary_conditions/config.ini
index 8c7872a4..573d6451 100755
--- a/demos/documented/optimal_control/control_boundary_conditions/config.ini
+++ b/demos/documented/optimal_control/control_boundary_conditions/config.ini
@@ -1,55 +1,9 @@
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-rtol = 1e-3
-atol = 0.0
-max_iter = 100
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
-save_results = True
-save_txt = True
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
+save_results = False
+save_txt = False
diff --git a/demos/documented/optimal_control/control_boundary_conditions/history.json b/demos/documented/optimal_control/control_boundary_conditions/history.json
deleted file mode 100644
index d973e89a..00000000
--- a/demos/documented/optimal_control/control_boundary_conditions/history.json
+++ /dev/null
@@ -1 +0,0 @@
-{"cost_function_value": [0.12300501606628308, 0.12300448858992497, 0.07572158196046494, 0.03170389159967354, 0.031648960640529675, 0.0010917968554650164, 0.001088116113963227, 0.0010879640548438138, 0.0010685739218976426, 0.0010679721843065537, 0.0010665913932377516, 0.0010664006240627731, 0.0010663511929846288, 0.0010658747342230336, 0.001065288954067063, 0.0010647669484440299, 0.0010642996806859966, 0.0010640881199815253, 0.0010635457424854917, 0.0010628538013926884, 0.0010626209919454472, 0.0010625341222233128, 0.0010618611896982305, 0.0010612151291449672, 0.0010611480568097269, 0.0010607737582205238, 0.001060566796397129, 0.0010603946456226615, 0.0010601485247796476, 0.0010593739694870399, 0.001059258077554657, 0.0010590242103768169, 0.0010584701034034088, 0.00105757908051586, 0.001056905653661333, 0.0010568284122044727, 0.0010565011680850743, 0.0010558792421955967, 0.0010552298612748427, 0.0010548074478110916, 0.0010543460535919686, 0.0010540296992555143, 0.0010539643198903697, 0.0010539153683529483, 0.0010537978783262084, 0.0010537604813513322, 0.0010537084170894927, 0.0010536713786845184, 0.0010535910780153453], "gradient_norm": [1.0, 0.9999854403730036, 2.207755943138064, 2.526096619784829, 3.817676670785216, 0.021218033738387376, 0.0030318730000196614, 0.003021211558929574, 0.005028656826254902, 0.01819949859032626, 0.005451311677952323, 0.002082790687500561, 0.002377036896312036, 0.005266516466451236, 0.01015592533538748, 0.005639347828052371, 0.003788329115237423, 0.0036819505237229992, 0.015829300016267724, 0.006217966469669035, 0.003237891738321792, 0.0038718555205111654, 0.007305815699088208, 0.0077652122831730445, 0.0018295138657868693, 0.00234354802531721, 0.0018248981578522334, 0.0015752338532363718, 0.01953930611270368, 0.002750020206167837, 0.0020754770849571945, 0.0021539677995992676, 0.0025713109046200584, 0.015123601349378256, 0.0037243579463525417, 0.002995591772406925, 0.0037857171508175608, 0.006808014218802666, 0.002628728664487449, 0.008066790109588998, 0.00459052325741234, 0.0017434095142568504, 0.0015955911822804225, 0.005247140763676156, 0.00194173399472982, 0.0013250238634070059, 0.0012741562210530353, 0.00261986567455876, 0.0007640938725563539], "stepsize": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.25, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0625, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.125, 1.0, 1.0, 1.0, 1.0, 1.0], "MeshQuality": [], "initial_gradient_norm": 0.0007262783200399558, "state_solves": 60, "adjoint_solves": 49, "iterations": 48}
\ No newline at end of file
diff --git a/demos/documented/optimal_control/control_boundary_conditions/history.txt b/demos/documented/optimal_control/control_boundary_conditions/history.txt
deleted file mode 100644
index bb30394d..00000000
--- a/demos/documented/optimal_control/control_boundary_conditions/history.txt
+++ /dev/null
@@ -1,73 +0,0 @@
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 0, 1.230e-01, 1.000e+00, 7.263e-04,
-
- 1, 1.230e-01, 1.000e+00, 7.263e-04, 1.000e+00
- 2, 7.572e-02, 2.208e+00, 1.603e-03, 1.000e+00
- 3, 3.170e-02, 2.526e+00, 1.835e-03, 1.000e+00
- 4, 3.165e-02, 3.818e+00, 2.773e-03, 1.000e+00
- 5, 1.092e-03, 2.122e-02, 1.541e-05, 1.000e+00
- 6, 1.088e-03, 3.032e-03, 2.202e-06, 1.000e+00
- 7, 1.088e-03, 3.021e-03, 2.194e-06, 1.000e+00
- 8, 1.069e-03, 5.029e-03, 3.652e-06, 1.000e+00
- 9, 1.068e-03, 1.820e-02, 1.322e-05, 2.500e-01
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 10, 1.067e-03, 5.451e-03, 3.959e-06, 1.000e+00
- 11, 1.066e-03, 2.083e-03, 1.513e-06, 1.000e+00
- 12, 1.066e-03, 2.377e-03, 1.726e-06, 1.000e+00
- 13, 1.066e-03, 5.267e-03, 3.825e-06, 1.000e+00
- 14, 1.065e-03, 1.016e-02, 7.376e-06, 1.000e+00
- 15, 1.065e-03, 5.639e-03, 4.096e-06, 1.000e+00
- 16, 1.064e-03, 3.788e-03, 2.751e-06, 1.000e+00
- 17, 1.064e-03, 3.682e-03, 2.674e-06, 1.000e+00
- 18, 1.064e-03, 1.583e-02, 1.150e-05, 5.000e-01
- 19, 1.063e-03, 6.218e-03, 4.516e-06, 1.000e+00
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 20, 1.063e-03, 3.238e-03, 2.352e-06, 1.000e+00
- 21, 1.063e-03, 3.872e-03, 2.812e-06, 1.000e+00
- 22, 1.062e-03, 7.306e-03, 5.306e-06, 1.000e+00
- 23, 1.061e-03, 7.765e-03, 5.640e-06, 1.000e+00
- 24, 1.061e-03, 1.830e-03, 1.329e-06, 6.250e-02
- 25, 1.061e-03, 2.344e-03, 1.702e-06, 1.000e+00
- 26, 1.061e-03, 1.825e-03, 1.325e-06, 1.000e+00
- 27, 1.060e-03, 1.575e-03, 1.144e-06, 1.000e+00
- 28, 1.060e-03, 1.954e-02, 1.419e-05, 1.000e+00
- 29, 1.059e-03, 2.750e-03, 1.997e-06, 1.000e+00
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 30, 1.059e-03, 2.075e-03, 1.507e-06, 1.000e+00
- 31, 1.059e-03, 2.154e-03, 1.564e-06, 1.000e+00
- 32, 1.058e-03, 2.571e-03, 1.867e-06, 1.000e+00
- 33, 1.058e-03, 1.512e-02, 1.098e-05, 5.000e-01
- 34, 1.057e-03, 3.724e-03, 2.705e-06, 1.000e+00
- 35, 1.057e-03, 2.996e-03, 2.176e-06, 1.000e+00
- 36, 1.057e-03, 3.786e-03, 2.749e-06, 1.000e+00
- 37, 1.056e-03, 6.808e-03, 4.945e-06, 1.000e+00
- 38, 1.055e-03, 2.629e-03, 1.909e-06, 1.000e+00
- 39, 1.055e-03, 8.067e-03, 5.859e-06, 1.000e+00
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 40, 1.054e-03, 4.591e-03, 3.334e-06, 1.000e+00
- 41, 1.054e-03, 1.743e-03, 1.266e-06, 1.000e+00
- 42, 1.054e-03, 1.596e-03, 1.159e-06, 1.000e+00
- 43, 1.054e-03, 5.247e-03, 3.811e-06, 1.250e-01
- 44, 1.054e-03, 1.942e-03, 1.410e-06, 1.000e+00
- 45, 1.054e-03, 1.325e-03, 9.623e-07, 1.000e+00
- 46, 1.054e-03, 1.274e-03, 9.254e-07, 1.000e+00
- 47, 1.054e-03, 2.620e-03, 1.903e-06, 1.000e+00
- 48, 1.054e-03, 7.641e-04, 5.549e-07, 1.000e+00
-
-Optimization was successful.
-Statistics:
- total iterations: 48
- final objective value: 1.054e-03
- final gradient norm: 7.641e-04
- total number of state systems solved: 60
- total number of adjoint systems solved: 49
diff --git a/demos/documented/optimal_control/dirichlet_control/config.ini b/demos/documented/optimal_control/dirichlet_control/config.ini
index d66bbae1..573d6451 100755
--- a/demos/documented/optimal_control/dirichlet_control/config.ini
+++ b/demos/documented/optimal_control/dirichlet_control/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/heat_equation/config.ini b/demos/documented/optimal_control/heat_equation/config.ini
index 3d209be5..573d6451 100755
--- a/demos/documented/optimal_control/heat_equation/config.ini
+++ b/demos/documented/optimal_control/heat_equation/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/iterative_solvers/config.ini b/demos/documented/optimal_control/iterative_solvers/config.ini
index 1cb61433..b8116c23 100755
--- a/demos/documented/optimal_control/iterative_solvers/config.ini
+++ b/demos/documented/optimal_control/iterative_solvers/config.ini
@@ -1,58 +1,10 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
rtol = 1e-4
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/monolithic_problems/config.ini b/demos/documented/optimal_control/monolithic_problems/config.ini
index 3d209be5..573d6451 100755
--- a/demos/documented/optimal_control/monolithic_problems/config.ini
+++ b/demos/documented/optimal_control/monolithic_problems/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/multiple_variables/config.ini b/demos/documented/optimal_control/multiple_variables/config.ini
index 3d209be5..573d6451 100755
--- a/demos/documented/optimal_control/multiple_variables/config.ini
+++ b/demos/documented/optimal_control/multiple_variables/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/neumann_control/config.ini b/demos/documented/optimal_control/neumann_control/config.ini
index 3d209be5..573d6451 100755
--- a/demos/documented/optimal_control/neumann_control/config.ini
+++ b/demos/documented/optimal_control/neumann_control/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/nonlinear_pdes/config.ini b/demos/documented/optimal_control/nonlinear_pdes/config.ini
index d23f8149..828cc3b0 100755
--- a/demos/documented/optimal_control/nonlinear_pdes/config.ini
+++ b/demos/documented/optimal_control/nonlinear_pdes/config.ini
@@ -1,58 +1,6 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
-[StateSystem]
-is_linear = False
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
-
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/nonlinear_pdes/demo_nonlinear_pdes.py b/demos/documented/optimal_control/nonlinear_pdes/demo_nonlinear_pdes.py
index 5faccf19..69c39cd9 100755
--- a/demos/documented/optimal_control/nonlinear_pdes/demo_nonlinear_pdes.py
+++ b/demos/documented/optimal_control/nonlinear_pdes/demo_nonlinear_pdes.py
@@ -34,13 +34,14 @@
#
# As this problem has a nonlinear PDE as state constraint, we have to modify the config
# file slightly. In particular, in the Section
-# {ref}`StateSystem ` we have to write
+# {ref}`StateSystem ` we have to use
# :::{code-block} ini
# :caption: config.ini
#
# is_linear = False
# :::
#
+# which is the default value.
# Note, that {ini}`is_linear = False` works for any problem, as linear equations are
# just a special case of nonlinear ones, and the corresponding nonlinear solver
# converges in a single iteration for these. However, in the opposite case, FEniCS will
diff --git a/demos/documented/optimal_control/picard_iteration/config.ini b/demos/documented/optimal_control/picard_iteration/config.ini
index 2e72dbfa..28d79396 100755
--- a/demos/documented/optimal_control/picard_iteration/config.ini
+++ b/demos/documented/optimal_control/picard_iteration/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
-is_linear = False
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
picard_iteration = True
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 25
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/poisson/config.ini b/demos/documented/optimal_control/poisson/config.ini
index 7ac46d31..f10bdb34 100755
--- a/demos/documented/optimal_control/poisson/config.ini
+++ b/demos/documented/optimal_control/poisson/config.ini
@@ -1,59 +1,5 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-rtol = 1e-3
-atol = 0.0
-max_iter = 100
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
-
-[Output]
-verbose = True
-save_results = True
-save_txt = True
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-precision = 3
-time_suffix = False
diff --git a/demos/documented/optimal_control/poisson/demo_poisson.py b/demos/documented/optimal_control/poisson/demo_poisson.py
index 32a3d8af..901409da 100755
--- a/demos/documented/optimal_control/poisson/demo_poisson.py
+++ b/demos/documented/optimal_control/poisson/demo_poisson.py
@@ -83,8 +83,7 @@
#
# Next, we have to load the config file which loads the user's input parameters into the
# script. For a detailed documentation of the config files and the parameters within, we
-# refer to {ref}`config_optimal_control`. Note that the corresponding file is
-# {download}`config.ini `.
+# refer to {ref}`config_optimal_control`.
# The config is then loaded via
config = cashocs.load_config("config.ini")
diff --git a/demos/documented/optimal_control/poisson/history.json b/demos/documented/optimal_control/poisson/history.json
deleted file mode 100644
index 649d72b8..00000000
--- a/demos/documented/optimal_control/poisson/history.json
+++ /dev/null
@@ -1 +0,0 @@
-{"cost_function_value": [0.12240249296414983, 0.12236443677831443, 0.040652832066825975, 0.008569132714501552, 0.0007846142266651456, 0.0007841983736891706, 0.0007831010817764939, 0.0007830971199807883, 0.0007827841773010746, 0.0007827272330887708], "gradient_norm": [1.0, 0.9998432897368269, 2.3083297785492345, 0.4847576089026389, 0.002605003204691906, 0.0021487879318249363, 0.0010647103497016775, 0.006822572583725434, 0.0015881049917775693, 0.0007597450081079757], "stepsize": [1.0, 1.0, 1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], "MeshQuality": [], "initial_gradient_norm": 0.006169211292565742, "state_solves": 11, "adjoint_solves": 10, "iterations": 9}
\ No newline at end of file
diff --git a/demos/documented/optimal_control/poisson/results/history.json b/demos/documented/optimal_control/poisson/results/history.json
new file mode 100644
index 00000000..fe558067
--- /dev/null
+++ b/demos/documented/optimal_control/poisson/results/history.json
@@ -0,0 +1,38 @@
+{
+ "cost_function_value": [
+ 0.12240249296414983,
+ 0.12236443677831443,
+ 0.040652832066825975,
+ 0.008569132714501552,
+ 0.0007846142266651456,
+ 0.0007841983794182448,
+ 0.0007831054455376119,
+ 0.0007827521435794375
+ ],
+ "gradient_norm": [
+ 1.0,
+ 0.9998432897368269,
+ 2.3083297785492345,
+ 0.4847576089026389,
+ 0.002605003204691906,
+ 0.0021488104100337263,
+ 0.0011142631618739258,
+ 0.0006792261532885966
+ ],
+ "stepsize": [
+ 1.0,
+ 1.0,
+ 1.0,
+ 0.5,
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0
+ ],
+ "MeshQuality": [],
+ "angle": [],
+ "initial_gradient_norm": 0.006169211292565742,
+ "state_solves": 9,
+ "adjoint_solves": 8,
+ "iterations": 7
+}
\ No newline at end of file
diff --git a/demos/documented/optimal_control/poisson/history.txt b/demos/documented/optimal_control/poisson/results/history.txt
similarity index 53%
rename from demos/documented/optimal_control/poisson/history.txt
rename to demos/documented/optimal_control/poisson/results/history.txt
index 42e73727..a8a96497 100644
--- a/demos/documented/optimal_control/poisson/history.txt
+++ b/demos/documented/optimal_control/poisson/results/history.txt
@@ -8,15 +8,13 @@ iter, cost function, rel. grad. norm, abs. grad. norm, step size
3, 8.569e-03, 4.848e-01, 2.991e-03, 5.000e-01
4, 7.846e-04, 2.605e-03, 1.607e-05, 1.000e+00
5, 7.842e-04, 2.149e-03, 1.326e-05, 1.000e+00
- 6, 7.831e-04, 1.065e-03, 6.568e-06, 1.000e+00
- 7, 7.831e-04, 6.823e-03, 4.209e-05, 1.000e+00
- 8, 7.828e-04, 1.588e-03, 9.797e-06, 1.000e+00
- 9, 7.827e-04, 7.597e-04, 4.687e-06, 1.000e+00
+ 6, 7.831e-04, 1.114e-03, 6.874e-06, 1.000e+00
+ 7, 7.828e-04, 6.792e-04, 4.190e-06, 1.000e+00
Optimization was successful.
Statistics:
- total iterations: 9
- final objective value: 7.827e-04
- final gradient norm: 7.597e-04
- total number of state systems solved: 11
- total number of adjoint systems solved: 10
+ total iterations: 7
+ final objective value: 7.828e-04
+ final gradient norm: 6.792e-04
+ total number of state systems solved: 9
+ total number of adjoint systems solved: 8
diff --git a/demos/documented/optimal_control/pre_post_callbacks/config.ini b/demos/documented/optimal_control/pre_post_callbacks/config.ini
index 03eb83a9..828cc3b0 100755
--- a/demos/documented/optimal_control/pre_post_callbacks/config.ini
+++ b/demos/documented/optimal_control/pre_post_callbacks/config.ini
@@ -1,58 +1,6 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
-[StateSystem]
-is_linear = False
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
-
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/pre_post_callbacks/demo_pre_post_callbacks.py b/demos/documented/optimal_control/pre_post_callbacks/demo_pre_post_callbacks.py
index 197e9d4d..88133dec 100644
--- a/demos/documented/optimal_control/pre_post_callbacks/demo_pre_post_callbacks.py
+++ b/demos/documented/optimal_control/pre_post_callbacks/demo_pre_post_callbacks.py
@@ -138,7 +138,7 @@ def pre_callback():
- q * div(u) * dx
- inner(c, v) * dx
)
- cashocs.newton_solve(e, up, bcs, verbose=False)
+ cashocs.snes_solve(e, up, bcs)
# where we solve the Navier-Stokes equations with a lower Reynolds number of
diff --git a/demos/documented/optimal_control/scalar_control_tracking/config.ini b/demos/documented/optimal_control/scalar_control_tracking/config.ini
index d1f1f0bd..573d6451 100755
--- a/demos/documented/optimal_control/scalar_control_tracking/config.ini
+++ b/demos/documented/optimal_control/scalar_control_tracking/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-rtol = 1e-3
-atol = 0.0
-max_iter = 100
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
-save_results = True
-save_txt = True
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
+save_results = False
+save_txt = False
diff --git a/demos/documented/optimal_control/scalar_control_tracking/history.json b/demos/documented/optimal_control/scalar_control_tracking/history.json
deleted file mode 100755
index 8e0d9f56..00000000
--- a/demos/documented/optimal_control/scalar_control_tracking/history.json
+++ /dev/null
@@ -1 +0,0 @@
-{"cost_function_value": [0.4983127499227354, 0.4982957186658693, 0.4982612232975325, 0.4981904731149954, 0.4980417060783099, 0.4977131975728245, 0.4969157309068249, 0.4946038139122276, 0.4854338592145077, 0.4264105365531886, 0.006219328715195727, 1.3324508474055567e-06, 1.1309813269240361e-08, 1.6912485472635852e-14], "gradient_norm": [1.0, 1.0050652214918177, 1.015246226489322, 1.0358113942348985, 1.0777616377743529, 1.1649999293229008, 1.3532911546494146, 1.7887610419203719, 2.920916887819883, 6.254170063520282, 2.574049975733761, 0.04000404651128848, 0.0036823000941371997, 4.50326808858134e-06], "stepsize": [1.0, 1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 256.0, 512.0, 0.125, 1.0, 1.0], "MeshQuality": [], "initial_gradient_norm": 0.004121678293258915, "state_solves": 17, "adjoint_solves": 14, "iterations": 13}
\ No newline at end of file
diff --git a/demos/documented/optimal_control/scalar_control_tracking/history.txt b/demos/documented/optimal_control/scalar_control_tracking/history.txt
deleted file mode 100755
index 6962a576..00000000
--- a/demos/documented/optimal_control/scalar_control_tracking/history.txt
+++ /dev/null
@@ -1,29 +0,0 @@
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 0, 4.983e-01, 1.000e+00, 4.122e-03,
-
- 1, 4.983e-01, 1.005e+00, 4.143e-03, 1.000e+00
- 2, 4.983e-01, 1.015e+00, 4.185e-03, 2.000e+00
- 3, 4.982e-01, 1.036e+00, 4.269e-03, 4.000e+00
- 4, 4.980e-01, 1.078e+00, 4.442e-03, 8.000e+00
- 5, 4.977e-01, 1.165e+00, 4.802e-03, 1.600e+01
- 6, 4.969e-01, 1.353e+00, 5.578e-03, 3.200e+01
- 7, 4.946e-01, 1.789e+00, 7.373e-03, 6.400e+01
- 8, 4.854e-01, 2.921e+00, 1.204e-02, 1.280e+02
- 9, 4.264e-01, 6.254e+00, 2.578e-02, 2.560e+02
-
-iter, cost function, rel. grad. norm, abs. grad. norm, step size
-
- 10, 6.219e-03, 2.574e+00, 1.061e-02, 5.120e+02
- 11, 1.332e-06, 4.000e-02, 1.649e-04, 1.250e-01
- 12, 1.131e-08, 3.682e-03, 1.518e-05, 1.000e+00
- 13, 1.691e-14, 4.503e-06, 1.856e-08, 1.000e+00
-
-Optimization was successful.
-Statistics:
- total iterations: 13
- final objective value: 1.691e-14
- final gradient norm: 4.503e-06
- total number of state systems solved: 17
- total number of adjoint systems solved: 14
diff --git a/demos/documented/optimal_control/sparse_control/config.ini b/demos/documented/optimal_control/sparse_control/config.ini
index e4d53c02..5f9f51ad 100755
--- a/demos/documented/optimal_control/sparse_control/config.ini
+++ b/demos/documented/optimal_control/sparse_control/config.ini
@@ -1,58 +1,10 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 100
rtol = 5e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
-save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
+save_txt = False
\ No newline at end of file
diff --git a/demos/documented/optimal_control/state_constraints/config.ini b/demos/documented/optimal_control/state_constraints/config.ini
index a4ebc027..e8f83ab2 100755
--- a/demos/documented/optimal_control/state_constraints/config.ini
+++ b/demos/documented/optimal_control/state_constraints/config.ini
@@ -1,55 +1,14 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-picard_iteration = False
-newton_inexact = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-newton_atol = 1e-13
-newton_rtol = 1e-11
-picard_verbose = False
[OptimizationRoutine]
algorithm = newton
-max_iter = 250
rtol = 1e-4
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[AlgoTNM]
inner_newton = cg
-max_it_inner_newton = 50
inner_newton_rtol = 1e-13
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
diff --git a/demos/documented/optimal_control/stokes/config.ini b/demos/documented/optimal_control/stokes/config.ini
index 3d209be5..37d852fc 100755
--- a/demos/documented/optimal_control/stokes/config.ini
+++ b/demos/documented/optimal_control/stokes/config.ini
@@ -1,58 +1,9 @@
-#[Mesh]
-#mesh_file = ../mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 2
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 50
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[Output]
-verbose = True
save_results = False
-save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-result_dir = ./
-time_suffix = False
+save_txt = False
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/custom_scalar_product/config.ini b/demos/documented/shape_optimization/custom_scalar_product/config.ini
index 91c856d8..3834b196 100755
--- a/demos/documented/shape_optimization/custom_scalar_product/config.ini
+++ b/demos/documented/shape_optimization/custom_scalar_product/config.ini
@@ -1,99 +1,13 @@
-[Mesh]
-#mesh_file = ./mesh/mesh.xdmf
-#gmsh_file = ./mesh/mesh.msh
-#geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
rtol = 5e-3
-atol = 0.0
-max_iter = 50
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
-lambda_lame = 1.428571428571429
-damping_factor = 0.2
-mu_def = 0.35714285714285715
-mu_fix = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = [1]
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = condition_number
-type = min
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
-time_suffix = False
diff --git a/demos/documented/shape_optimization/eikonal_stiffness/config.ini b/demos/documented/shape_optimization/eikonal_stiffness/config.ini
index 56d1be74..8bf9da39 100755
--- a/demos/documented/shape_optimization/eikonal_stiffness/config.ini
+++ b/demos/documented/shape_optimization/eikonal_stiffness/config.ini
@@ -1,87 +1,27 @@
-[Mesh]
-mesh_file = ./mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-picard_iteration = False
-newton_inexact = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-newton_atol = 1e-13
-newton_rtol = 1e-11
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
max_iter = 250
rtol = 5e-4
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1e0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = True
-cg_periodic_its = 25
-cg_relative_restart = False
-cg_restart_tol = 0.9
[ShapeGradient]
shape_bdry_def = [4]
shape_bdry_fix = [1,2,3]
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-lambda_lame = 0.0
-damping_factor = 0.0
-mu_fix = 1.0
-mu_def = 1.0
-use_sqrt_mu = False
-inhomogeneous = False
use_distance_mu = True
dist_min = 0.05
dist_max = 1.25
mu_min = 5e2
mu_max = 1.0
-smooth_mu = false
boundaries_dist = [4]
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
[Regularization]
factor_volume = 1e4
-target_volume = 0.0
use_initial_volume = True
-factor_surface = 0.0
-target_surface = 0.0
-use_initial_surface = True
factor_barycenter = 1e5
-target_barycenter = [0.0, 0.0, 0.0]
use_initial_barycenter = True
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.05
-tol_upper = 0.1
-
[Output]
-verbose = True
save_results = False
save_txt = False
-save_adjoint = False
-save_gradient = False
-save_state = False
-time_suffix = False
diff --git a/demos/documented/shape_optimization/inverse_tomography/config.ini b/demos/documented/shape_optimization/inverse_tomography/config.ini
index a88b0b7e..f229198b 100755
--- a/demos/documented/shape_optimization/inverse_tomography/config.ini
+++ b/demos/documented/shape_optimization/inverse_tomography/config.ini
@@ -1,91 +1,13 @@
-[Mesh]
-mesh_file = ./mesh/mesh.xdmf
-gmsh_file = ./mesh/mesh.msh
-geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = True
-
[StateSystem]
-is_linear = true
-picard_iteration = false
-newton_inexact = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-newton_atol = 1e-13
-newton_rtol = 1e-11
-picard_verbose = false
+is_linear = True
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 50
rtol = 5e-4
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = true
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = true
-
-[AlgoCG]
-cg_method = HZ
-cg_periodic_restart = false
-cg_periodic_its = 5
-cg_relative_restart = false
-cg_restart_tol = 0.5
[ShapeGradient]
-shape_bdry_def = []
shape_bdry_fix = [1, 2, 3, 4]
-lambda_lame = 0.0
-damping_factor = 0.0
-mu_fix = 1.0
-mu_def = 1.0
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 0.0
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 0.0
-use_initial_surface = True
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-measure = skewness
-type = min
-tol_lower = 1e-3
-tol_upper = 1e-2
[Output]
-save_results = false
-save_txt = False
-save_state = false
-save_adjoint = False
-save_gradient = False
-save_mesh = false
-verbose = true
-time_suffix = False
+save_results = False
+save_txt = False
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/config.ini b/demos/documented/shape_optimization/mesh_quality_constraints/config.ini
new file mode 100755
index 00000000..4eb41afa
--- /dev/null
+++ b/demos/documented/shape_optimization/mesh_quality_constraints/config.ini
@@ -0,0 +1,18 @@
+[StateSystem]
+is_linear = True
+
+[OptimizationRoutine]
+algorithm = gd
+rtol = 5e-3
+atol = 0.0
+
+[ShapeGradient]
+shape_bdry_def = [1]
+lambda_lame = 1.428571428571429
+damping_factor = 0.2
+mu_def = 0.35714285714285715
+mu_fix = 0.35714285714285715
+
+[Output]
+save_results = False
+save_txt = False
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/demo_mesh_quality_constraints.py b/demos/documented/shape_optimization/mesh_quality_constraints/demo_mesh_quality_constraints.py
new file mode 100644
index 00000000..857216dd
--- /dev/null
+++ b/demos/documented/shape_optimization/mesh_quality_constraints/demo_mesh_quality_constraints.py
@@ -0,0 +1,303 @@
+# ---
+# jupyter:
+# jupytext:
+# text_representation:
+# extension: .py
+# format_name: light
+# format_version: '1.5'
+# jupytext_version: 1.14.4
+# ---
+
+# ```{eval-rst}
+# .. include:: ../../../global.rst
+# ```
+#
+# (demo_mesh_quality_constraints)=
+# # Mesh Quality Constraints for Shape Optimization
+#
+# # Problem Formulation
+#
+# In this demo, we demonstrate cashocs capability of enforcing a certain mesh quality,
+# which is given by the user. As model problem, we consider the one already considered
+# in {ref}`demo_shape_poisson`, which we briefly recall here
+#
+# $$
+# \begin{align}
+# &\min_\Omega J(u, \Omega) = \int_\Omega u \text{ d}x \\
+# &\text{subject to} \qquad
+# \begin{alignedat}[t]{2}
+# -\Delta u &= f \quad &&\text{ in } \Omega,\\
+# u &= 0 \quad &&\text{ on } \Gamma.
+# \end{alignedat}
+# \end{align}
+# $$
+#
+# For the initial domain, we use the unit disc
+# $\Omega = \{ x \in \mathbb{R}^2 \,\mid\, \lvert\lvert x \rvert\rvert_2 < 1 \}$ and the
+# right-hand side $f$ is given by
+#
+# $$
+# f(x) = 2.5 \left( x_1 + 0.4 - x_2^2 \right)^2 + x_1^2 + x_2^2 - 1.
+# $$
+#
+# # Mesh Quality Constraints
+#
+# Our software cashocs has the option to enforce a certain mesh quality during the
+# shape optimization. This is done by adding additional equality and inequality
+# constraints, which act on the discretized geometry, i.e., the finite element mesh.
+# These constraints are of the form
+#
+# $$
+# \alpha \geq c \quad \text{ for all } \alpha \in \Omega_h,
+# $$
+#
+# where $\alpha$ is some angle (in the case of a 2D triangular mesh) or solid
+# angle (for a 3D tetrahedral mesh) and $c$ is a lower bound for this angle. Note that
+# this constraint is posed for all angles $\alpha$ in the mesh (which is denoted by
+# $\Omega_h$).
+#
+# :::{note}
+# Note that many mesh quality criteria are either explicitly or implictly dependent on
+# the (solid) angle of the mesh elements. For examples, we refer the reader to
+# {py:mod}`cashocs.geometry.quality`. As a concrete example, consider the so-called
+# skewness of the mesh, which is given by
+#
+# $$
+# 1 - \max\left( \frac{\alpha - \alpha^*}{\pi - \alpha^*},
+# \frac{\alpha^* - \alpha}{\alpha^* - 0} \right).
+# $$
+#
+# It is easy to see, that this is maximal (i.e. has the value 1) for $\alpha = \alpha^*$
+# and that the mesh quality deteriorates (i.e. it goes to 0) for either $\alpha \to 0$
+# or $\alpha \to \pi$.
+#
+# With the help of the above constraint, the skewness of some triangular mesh is bounded
+# by
+#
+# $$
+# \min\left( \frac{2c}{\pi - \alpha^*}, \frac{c}{\alpha^*} \right),
+# $$
+#
+# due to the fact that the above constraint implies that $\alpha \leq \pi - 2c$ for a
+# triangular mesh (the sum of all triangular angles is $\pi$). A similar observation
+# also holds true for a tetrahedral mesh (there, the sum of the solid angles is
+# bounded between 0 and $2\pi$).
+#
+# For this reason, the above constraints enforce the quality in the mesh in the sense
+# that no element can become degenerate during the optimization if the constraints are
+# satisfied.
+# :::
+#
+# :::{note}
+# Note that for some meshes it might not be sensible to define the lower threshold for
+# the (solid) angle globally, i.e., use a single value of $c$ for all cells, for
+# example when using stretched elements for resolving boundary layers. Therefore,
+# cashocs can either use a globally defined threshold $c > 0$ or a value of $c$ which
+# is different for each cell in the mesh and depends on the angles in the initial mesh.
+# In the latter case, the user can specify a factor $\varphi \in (0,1)$ and $c$ in
+# element $k$ is chosen as $c_k = \phi \min_i \alpha_i$, i.e., it is chosen as $\varphi$
+# times the minimum angle of the element. This choice still preserves the mesh quality
+# as it ensures that the elements can not deteriorate.
+# :::
+#
+# Of course, the constraints can only be satisfied up to a numerical tolerance, so
+# that this tolerance also needs to be specified by the user. It is suggested that users
+# try the default tolerance of 1e-2 first. For some problems, a larger tolerance, e.g.,
+# 1e-1 might yield faster results, but sometimes it might be necessary to use a tighter
+# tolerance.
+#
+# ## Implementation
+#
+# The complete python code can be found in the file
+# {download}`demo_mesh_quality_constraints.py
+# `,
+# and the corresponding config can be found in {download}`config.ini
+# `.
+#
+# ### Solving the Problem without Mesh Quality Constraints
+#
+# Let us first consider solving the above problem without any mesh quality to see what
+# happens. To do so, we follow {ref}`demo_shape_poisson`, with some minor modifications.
+
+# +
+from fenics import *
+import numpy as np
+
+import cashocs
+
+print("### Optimization without Mesh Quality Constraints ###")
+cashocs.set_log_level(cashocs.LogLevel.INFO)
+config = cashocs.load_config("./config.ini")
+
+mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh("./mesh/mesh.xdmf")
+
+initial_mesh_quality = cashocs.compute_mesh_quality(mesh)
+
+V = FunctionSpace(mesh, "CG", 1)
+u = Function(V)
+p = Function(V)
+
+x = SpatialCoordinate(mesh)
+f = 2.5 * pow(x[0] + 0.4 - pow(x[1], 2), 2) + pow(x[0], 2) + pow(x[1], 2) - 1
+
+e = inner(grad(u), grad(p)) * dx - f * p * dx
+bcs = DirichletBC(V, Constant(0), boundaries, 1)
+
+J = cashocs.IntegralFunctional(u * dx)
+
+sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config=config)
+sop.solve()
+
+optimized_mesh_quality = cashocs.compute_mesh_quality(mesh)
+print(f"Quality of the initial mesh: {initial_mesh_quality:.3e}")
+print(f"Quality of the optimized mesh: {optimized_mesh_quality:.3e}")
+
+# -
+
+# This code is the same as before, the only difference is that the mesh quality for the
+# initial and optimized meshes is computed and printed to the console. The output is
+# given by
+# :::{code-block} console
+# Quality of the initial mesh: 6.391e-01
+# Quality of the optimized mesh: 4.831e-01
+# :::
+#
+# Hence, we observe that the mesh quality goes down quite a bit. Of course, the quality
+# of the optimized mesh is still acceptable, nevertheless we use this as an example
+# to show how cashocs can preserve the mesh quality.
+#
+# ### Solving the Problem with Mesh Quality Constraints
+#
+# For using the mesh quality constraints, the user only has to change the configuration
+# file. To make this more obvious, we load the config file into the python script and
+# modify the corresponding values directly there. Hence, our setup is very similar to
+# before, i.e.,
+
+# +
+from fenics import *
+
+import cashocs
+
+print("### Optimization with Mesh Quality Constraints ###")
+cashocs.set_log_level(cashocs.LogLevel.INFO)
+config = cashocs.load_config("./config.ini")
+
+mesh, subdomains, boundaries, dx, ds, dS = cashocs.import_mesh("./mesh/mesh.xdmf")
+
+initial_mesh_quality = cashocs.compute_mesh_quality(mesh)
+
+V = FunctionSpace(mesh, "CG", 1)
+u = Function(V)
+p = Function(V)
+
+x = SpatialCoordinate(mesh)
+f = 2.5 * pow(x[0] + 0.4 - pow(x[1], 2), 2) + pow(x[0], 2) + pow(x[1], 2) - 1
+
+e = inner(grad(u), grad(p)) * dx - f * p * dx
+bcs = DirichletBC(V, Constant(0), boundaries, 1)
+
+J = cashocs.IntegralFunctional(u * dx)
+# -
+
+# To specify the mesh quality constraints, we now modify the corresponding parameters
+# in the configuration with the following line. We only have specify the minimum angle
+# of the elements (in radian) which is done with
+
+min_angle = 2 * np.pi * 35.0 / 360.0
+# min_angle = 35.0
+config.set("MeshQualityConstraints", "min_angle", f"{min_angle}")
+
+# A minimum angle of 35°, as specified above, leads to a minimum skewness of the mesh of
+# `0.5833` and since we consider a tolerance of `1e-2`, this means that we can
+# expect a minimum skewness of `0.5733` for the mesh.
+#
+# :::{note}
+# The min_angle must be specified in radian or steradian (for 3D problems), respectively.
+#
+# :::{warning}
+# Mesh quality constraints are implemented for all available methods for shape
+# optimization, i.e., the gradient descent, nonlinear CG, and BFGS methods. However, the
+# theory only works for the gradient descent method at the moment. Numerical examples
+# suggest, that the method also works well with the NCG and BFGS methods, but there
+# is no guarantee that this works, so use this with some care only.
+# :::
+#
+# ::::{note}
+# As we are solving the problem numerically, the constraints can only be satisfied up to
+# a certain numerical tolerance. This can be specified with the line
+#
+# :::{code-block} python
+# config.set("MeshQualityConstraints", "tol", "1e-2")
+# :::
+#
+# A value of `1e-2` is the default and should work reasonably well for most problems. If
+# the constraint handling takes too much time, a higher tolerance of `1e-1` might be
+# useful for some problems. On the other hand, for problems requiring more strict
+# handling of the constraints, a lower tolerance, such as `1e-3`, could be beneficial.
+# ::::
+#
+# ::::{note}
+# If one has a non-uniform mesh, e.g., for resolving boundary layers, then
+# the user can, as explained above, define a factor $\varphi \in (0,1)$ which the angles
+# of some element can become smaller. This can be done with the configuration parameter
+# :::{code-block} python
+# cfg.set("MeshQualityConstraints", "feasible_angle_reduction_factor", "0.5")
+# :::
+#
+# This means that all (solid) angles of the mesh can become half (or a factor of
+# $\varphi$ in general) of the minimum angle of the respective element.
+#
+# If both a {ini}`feasible_angle_reduction_factor` and {ini}`min_angle` are specified,
+# then the minimum of both (on a per-element basis) is used to ensure that the initial
+# mesh is feasible w.r.t. the constraints.
+# ::::
+#
+# Finally, we can solve this problem with the lines
+#
+
+sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config=config)
+sop.solve()
+
+# To compare the solution with the mesh quality constraints, we also compute the
+# mesh quality of the optimized mesh with the lines
+
+optimized_mesh_quality = cashocs.compute_mesh_quality(mesh)
+print(f"Quality of the initial mesh: {initial_mesh_quality:.3e}")
+print(f"Quality of the optimized mesh: {optimized_mesh_quality:.3e}")
+
+# and we get the following output
+#
+# :::{code-block} console
+# Quality of the initial mesh: 6.391e-01
+# Quality of the optimized mesh: 5.751e-01
+# :::
+#
+# i.e. the mesh quality constraints have been successful in enforcing a higher mesh
+# quality. In particular, we observe that the minimum allowed skewness of `0.5733` is,
+# in fact, (numerically) achieved for the optimized mesh.
+#
+# Finally, we visualize the result with the following code
+
+# +
+import matplotlib.pyplot as plt
+
+plt.figure(figsize=(10, 5))
+
+ax_mesh = plt.subplot(1, 2, 1)
+fig_mesh = plot(mesh)
+plt.title("Discretization of the optimized geometry")
+
+ax_u = plt.subplot(1, 2, 2)
+ax_u.set_xlim(ax_mesh.get_xlim())
+ax_u.set_ylim(ax_mesh.get_ylim())
+fig_u = plot(u)
+plt.colorbar(fig_u, fraction=0.046, pad=0.04)
+plt.title("State variable u")
+
+plt.tight_layout()
+# plt.savefig("./img_mesh_quality_constraints.png", dpi=150, bbox_inches="tight")
+# -
+
+# and the result should look like this
+# ![](/../../demos/documented/shape_optimization/mesh_quality_constraints/img_mesh_quality_constraints.png)
+#
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/img_mesh_quality_constraints.png b/demos/documented/shape_optimization/mesh_quality_constraints/img_mesh_quality_constraints.png
new file mode 100644
index 00000000..a87420c8
Binary files /dev/null and b/demos/documented/shape_optimization/mesh_quality_constraints/img_mesh_quality_constraints.png differ
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.geo b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.geo
new file mode 100755
index 00000000..49afd1e4
--- /dev/null
+++ b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.geo
@@ -0,0 +1,10 @@
+lc = 7.5e-2;
+
+SetFactory("OpenCASCADE");
+Disk(1) = {0, 0, 0, 1, 1};
+
+Mesh.MeshSizeMax = lc;
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diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.h5 b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.h5
new file mode 100644
index 00000000..51ffdea8
Binary files /dev/null and b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.h5 differ
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.msh b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.msh
new file mode 100644
index 00000000..eb20a313
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+$EndElements
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.xdmf b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.xdmf
new file mode 100644
index 00000000..d66f1f0f
--- /dev/null
+++ b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh.xdmf
@@ -0,0 +1 @@
+mesh.h5:/data0mesh.h5:/data1
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_boundaries.h5 b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_boundaries.h5
new file mode 100644
index 00000000..b84eaef1
Binary files /dev/null and b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_boundaries.h5 differ
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_boundaries.xdmf b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_boundaries.xdmf
new file mode 100644
index 00000000..44a63bd2
--- /dev/null
+++ b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_boundaries.xdmf
@@ -0,0 +1 @@
+mesh_boundaries.h5:/data0mesh_boundaries.h5:/data1mesh_boundaries.h5:/data2
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_subdomains.h5 b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_subdomains.h5
new file mode 100644
index 00000000..3672e899
Binary files /dev/null and b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_subdomains.h5 differ
diff --git a/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_subdomains.xdmf b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_subdomains.xdmf
new file mode 100644
index 00000000..f89bf0d0
--- /dev/null
+++ b/demos/documented/shape_optimization/mesh_quality_constraints/mesh/mesh_subdomains.xdmf
@@ -0,0 +1 @@
+mesh_subdomains.h5:/data0mesh_subdomains.h5:/data1mesh_subdomains.h5:/data2
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/p_laplacian/config.ini b/demos/documented/shape_optimization/p_laplacian/config.ini
index 52cddf2e..559cd5c2 100755
--- a/demos/documented/shape_optimization/p_laplacian/config.ini
+++ b/demos/documented/shape_optimization/p_laplacian/config.ini
@@ -1,101 +1,16 @@
-[Mesh]
-#mesh_file = ./mesh/mesh.xdmf
-#gmsh_file = ./mesh/mesh.msh
-#geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = gd
rtol = 1e-2
-atol = 0.0
-max_iter = 50
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
-lambda_lame = 0.0
damping_factor = 1e-2
-mu_def = 1.0
-mu_fix = 1.0
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
use_p_laplacian = True
p_laplacian_power = 10
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_curvature = 0.0
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-use_relative_scaling = False
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = condition_number
-type = min
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
-time_suffix = False
diff --git a/demos/documented/shape_optimization/regularization/config.ini b/demos/documented/shape_optimization/regularization/config.ini
index a0ec6c2e..8e60dcc0 100755
--- a/demos/documented/shape_optimization/regularization/config.ini
+++ b/demos/documented/shape_optimization/regularization/config.ini
@@ -1,99 +1,20 @@
-[Mesh]
-#mesh_file = ./mesh/mesh.xdmf
-#gmsh_file = ./mesh/mesh.msh
-#geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_atol = 1e-13
-newton_rtol = 1e-11
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-newton_iter = 50
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 50
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-lambda_lame = 1.428571428571429
-damping_factor = 0.2
-mu_fix = 0.35714285714285715
-mu_def = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
+damping_factor = 0.5
[Regularization]
factor_volume = 1.0
target_volume = 1.5
-use_initial_volume = False
factor_surface = 1.0
target_surface = 4.5
-use_initial_surface = False
factor_curvature = 1e-4
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = False
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.01
-tol_upper = 0.02
-measure = skewness
-type = min
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
-time_suffix = False
diff --git a/demos/documented/shape_optimization/regularization/demo_regularization.py b/demos/documented/shape_optimization/regularization/demo_regularization.py
index 78ff79f4..1a7b32f9 100755
--- a/demos/documented/shape_optimization/regularization/demo_regularization.py
+++ b/demos/documented/shape_optimization/regularization/demo_regularization.py
@@ -95,7 +95,7 @@
u * dx + Constant(alpha_vol) * dx + Constant(alpha_surf) * ds
)
-# The remaining two parts are specified via {download}`config.ini
+# The remaining parts are specified via {download}`config.ini
# `, where
# the following lines are relevant
#
@@ -104,10 +104,8 @@
# [Regularization]
# factor_volume = 1.0
# target_volume = 1.5
-# use_initial_volume = False
# factor_surface = 1.0
# target_surface = 4.5
-# use_initial_surface = False
# factor_curvature = 1e-4
# ```
#
diff --git a/demos/documented/shape_optimization/remeshing/config.ini b/demos/documented/shape_optimization/remeshing/config.ini
index bf389e27..5b353d4d 100755
--- a/demos/documented/shape_optimization/remeshing/config.ini
+++ b/demos/documented/shape_optimization/remeshing/config.ini
@@ -1,5 +1,4 @@
[Mesh]
-mesh_file = ./mesh/mesh.xdmf
gmsh_file = ./mesh/mesh.msh
geo_file = ./mesh/mesh.geo
remesh = True
@@ -7,86 +6,22 @@ show_gmsh_output = True
[StateSystem]
is_linear = True
-newton_inexact = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-newton_atol = 1e-13
-newton_rtol = 1e-11
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 50
-rtol = 1e-3
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
lambda_lame = 1.428571428571429
damping_factor = 0.2
mu_fix = 0.35714285714285715
mu_def = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
[MeshQuality]
-angle_change = inf
-volume_change = inf
tol_lower = 0.1
tol_upper = 0.25
measure = condition_number
-type = min
[Output]
-verbose = True
-save_results = True
-save_txt = True
-save_state = True
-save_adjoint = False
-save_gradient = False
-save_mesh = True
-time_suffix = False
+save_results = False
+save_txt = False
diff --git a/demos/documented/shape_optimization/remeshing/results/history.json b/demos/documented/shape_optimization/remeshing/results/history.json
deleted file mode 100644
index 7746a7b6..00000000
--- a/demos/documented/shape_optimization/remeshing/results/history.json
+++ /dev/null
@@ -1 +0,0 @@
-{"cost_function_value": [-0.010710701247112275, -0.058833215400487214, -0.06555925947427521, -0.09209476824962189, -0.09335348356358737, -0.09341891467063694, -0.09350254217987962, -0.09368835809752675, -0.09370320332650307, -0.09372497186197695, -0.09374325189602112, -0.09375140904682254, -0.09375389922815995, -0.09376064629560443, -0.09376323516455523, -0.09376427731820364, -0.0937648865091959, -0.09376545201103059, -0.09376566205889032], "gradient_norm": [1.0, 0.2908995832389938, 0.24583807649965103, 0.050102216974149474, 0.017142126685834928, 0.024009019093443794, 0.02028564316878872, 0.006391807579206077, 0.015887139655809124, 0.007905165182555176, 0.003867886381716813, 0.004013642483696643, 0.009219819988085841, 0.0038584517036234184, 0.0017346684989415946, 0.0016745674448175336, 0.00250363267525518, 0.0010353491101071637, 0.0008477975446633024], "stepsize": [1.0, 0.25, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.25, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0], "MeshQuality": [0.3126345571836947, 0.3133864049012093, 0.31430214571040815, 0.2611476650195171, 0.41794937861823783, 0.417487448679133, 0.4171328838784906, 0.41398017299475065, 0.41198074703258725, 0.411271195858114, 0.4102325444325339, 0.4099873986065528, 0.4113278724575023, 0.41170751385728893, 0.41287476615445623, 0.4140052231474779, 0.4151629209757527, 0.4151553914951008, 0.41507435904605644], "initial_gradient_norm": 0.6341622263073908, "state_solves": 24, "adjoint_solves": 19, "iterations": 18}
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/remeshing/results/history.txt b/demos/documented/shape_optimization/remeshing/results/history.txt
deleted file mode 100644
index 077bc0e7..00000000
--- a/demos/documented/shape_optimization/remeshing/results/history.txt
+++ /dev/null
@@ -1,9 +0,0 @@
-
-iter, cost function, rel. grad. norm, abs. grad. norm, mesh qlty, step size
-
- 0, -1.071e-02, 1.000e+00, 6.342e-01, 3.126e-01,
-
- 1, -5.883e-02, 2.909e-01, 1.845e-01, 3.134e-01, 2.500e-01
- 2, -6.556e-02, 2.458e-01, 1.559e-01, 3.143e-01, 1.000e+00
- 3, -9.209e-02, 5.010e-02, 3.177e-02, 2.611e-01, 1.000e+00
- 4, -9.335e-02, 1.714e-02, 1.087e-02, 4.179e-01, 1.000e+00
diff --git a/demos/documented/shape_optimization/remeshing/results/optimized_mesh.msh b/demos/documented/shape_optimization/remeshing/results/optimized_mesh.msh
deleted file mode 100644
index f6b50233..00000000
--- a/demos/documented/shape_optimization/remeshing/results/optimized_mesh.msh
+++ /dev/null
@@ -1,14998 +0,0 @@
-$MeshFormat
-4.1 0 8
-$EndMeshFormat
-$Entities
-5 4 1 0
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-1 -1.051929108541821 -1.086606209600702 0 0.6321319636334792 1.086438409202127 0 1 1 4 1 2 3 4
-$EndEntities
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-$EndElements
diff --git a/demos/documented/shape_optimization/scaling/config.ini b/demos/documented/shape_optimization/scaling/config.ini
index 57b5ac42..b52db2d5 100755
--- a/demos/documented/shape_optimization/scaling/config.ini
+++ b/demos/documented/shape_optimization/scaling/config.ini
@@ -1,89 +1,14 @@
-[Mesh]
-#mesh_file = ./mesh/mesh.xdmf
-#gmsh_file = ./mesh/mesh.msh
-#geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-rtol = 5e-3
-atol = 0.0
-max_iter = 50
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 3
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
-lambda_lame = 1.428571428571429
-damping_factor = 0.2
-mu_def = 0.35714285714285715
-mu_fix = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_curvature = 0.0
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = condition_number
-type = min
+damping_factor = 0.5
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
diff --git a/demos/documented/shape_optimization/shape_poisson/config.ini b/demos/documented/shape_optimization/shape_poisson/config.ini
index 9b2b5e85..5ae98560 100755
--- a/demos/documented/shape_optimization/shape_poisson/config.ini
+++ b/demos/documented/shape_optimization/shape_poisson/config.ini
@@ -1,102 +1,18 @@
-[Mesh]
-#mesh_file = ./mesh/mesh.xdmf
-#gmsh_file = ./mesh/mesh.msh
-#geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
rtol = 5e-3
-atol = 0.0
-max_iter = 50
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1.0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
[AlgoLBFGS]
bfgs_memory_size = 3
use_bfgs_scaling = True
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
[ShapeGradient]
shape_bdry_def = [1]
-shape_bdry_fix = []
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
-lambda_lame = 1.428571428571429
-damping_factor = 0.2
-mu_def = 0.35714285714285715
-mu_fix = 0.35714285714285715
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_curvature = 0.0
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-use_relative_scaling = False
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = condition_number
-type = min
+damping_factor = 0.5
[Output]
-verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
-precision = 3
-time_suffix = False
diff --git a/demos/documented/shape_optimization/shape_stokes/config.ini b/demos/documented/shape_optimization/shape_stokes/config.ini
index 8092e112..d4f5a0d7 100755
--- a/demos/documented/shape_optimization/shape_stokes/config.ini
+++ b/demos/documented/shape_optimization/shape_stokes/config.ini
@@ -1,87 +1,22 @@
-[Mesh]
-mesh_file = ./mesh/mesh.xdmf
-
[StateSystem]
is_linear = True
-newton_inexact = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-newton_atol = 1e-13
-newton_rtol = 1e-11
-picard_verbose = False
[OptimizationRoutine]
algorithm = lbfgs
-max_iter = 250
rtol = 5e-4
-atol = 0.0
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1e0
-safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = True
-cg_periodic_its = 25
-cg_relative_restart = False
-cg_restart_tol = 0.9
[ShapeGradient]
shape_bdry_def = [4]
shape_bdry_fix = [1,2,3]
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-lambda_lame = 0.0
-damping_factor = 0.0
mu_fix = 1
mu_def = 5e2
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
[Regularization]
factor_volume = 1e4
-target_volume = 0.0
use_initial_volume = True
-factor_surface = 0.0
-target_surface = 0.0
-use_initial_surface = True
factor_barycenter = 1e5
-target_barycenter = [0.0, 0.0, 0.0]
use_initial_barycenter = True
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.05
-tol_upper = 0.1
-
[Output]
-verbose = True
save_results = False
save_txt = False
-save_adjoint = False
-save_gradient = False
-save_state = False
-time_suffix = False
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/config.ini b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/config.ini
index 11397aa7..29c73057 100755
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/config.ini
+++ b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/config.ini
@@ -1,95 +1,19 @@
-[Mesh]
-remesh = False
-show_gmsh_output = False
-
-[StateSystem]
-is_linear = False
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
-
[OptimizationRoutine]
algorithm = lbfgs
rtol = 1e-2
-atol = 0.0
-max_iter = 250
-soft_exit = False
[LineSearch]
initial_stepsize = 1e2
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
-shape_bdry_def = []
shape_bdry_fix = [1,2,3,4]
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
-lambda_lame = 0.0
damping_factor = 0.1
-mu_def = 1.0
-mu_fix = 1.0
-use_sqrt_mu = False
-inhomogeneous = False
-use_distance_mu = False
-dist_min = 0.05
-dist_max = 1.25
-mu_min = 5e2
-mu_max = 1.0
-smooth_mu = false
-boundaries_dist = []
-use_p_laplacian = False
-p_laplacian_power = 2
-p_laplacian_stabilization = 0.0
-
-[Regularization]
-factor_volume = 0.0
-target_volume = 3.14
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 1.0
-use_initial_surface = True
-factor_curvature = 0.0
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = True
-use_relative_scaling = False
[MeshQuality]
angle_change = 0.3
volume_change = 2.0
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = skewness
-type = min
[Output]
verbose = False
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
-time_suffix = False
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/demo_space_mapping_semilinear_transmission.py b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/demo_space_mapping_semilinear_transmission.py
index f135df17..a0f6eb80 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/demo_space_mapping_semilinear_transmission.py
+++ b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/demo_space_mapping_semilinear_transmission.py
@@ -170,7 +170,7 @@ def create_desired_state(alpha_1, alpha_2, beta, f_1, f_2):
- Constant(f_2) * v * dx(2)
)
bcs = cashocs.create_dirichlet_bcs(V, Constant(0.0), boundaries, [1, 2, 3, 4])
- cashocs.newton_solve(F, u, bcs, verbose=False)
+ cashocs.snes_solve(F, u, bcs)
return u
@@ -255,7 +255,7 @@ def solve_and_evaluate(self) -> None:
- Constant(self.f_2) * v * dx(2)
)
bcs = cashocs.create_dirichlet_bcs(V, Constant(0.0), boundaries, [1, 2, 3, 4])
- cashocs.newton_solve(F, u, bcs, verbose=False)
+ cashocs.snes_solve(F, u, bcs)
LagrangeInterpolator.interpolate(u_des, self.u_des_fixed)
@@ -312,7 +312,7 @@ def solve_and_evaluate(self) -> None:
# - Constant(self.f_2) * v * dx(2)
# )
# bcs = cashocs.create_dirichlet_bcs(V, Constant(0.0), boundaries, [1, 2, 3, 4])
-# cashocs.newton_solve(F, u, bcs, verbose=False)
+# cashocs.snes_solve(F, u, bcs)
# :::
#
# After solving the fine model PDE constraint, we re-interpolate the desired state to
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh.h5 b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh.h5
index 55f86722..eb02b108 100644
Binary files a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh.h5 and b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh.h5 differ
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_1.msh b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_1.msh
index 6ae103b4..b5569f03 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_1.msh
+++ b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_1.msh
@@ -27,28 +27,28 @@ $Nodes
18 5398 1 5398
0 1 0 1
1
-0.0000000000000000 0.0000000000000000 0
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0 6 0 1
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0 7 0 1
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1 1 0 66
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diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_2.msh b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_2.msh
index 6814fe61..3650e2d9 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_2.msh
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diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_3.msh b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_3.msh
index cb19a849..87369655 100644
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index 771d1266..6054cc22 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_4.msh
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diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_5.msh b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_5.msh
index 8fe72a4d..0ecd042d 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_5.msh
+++ b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_5.msh
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diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_6.msh b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_6.msh
index 3b9147cd..a5b271d7 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_6.msh
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$EndNodes
$Elements
6 10794 1 10794
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_boundaries.h5 b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_boundaries.h5
index 6210079a..c70f7987 100644
Binary files a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_boundaries.h5 and b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_boundaries.h5 differ
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_subdomains.h5 b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_subdomains.h5
index 81c4f677..d36c612b 100644
Binary files a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_subdomains.h5 and b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/mesh/fine/mesh_subdomains.h5 differ
diff --git a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/sm_history.json b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/sm_history.json
index 04ddfa1a..2b30b109 100644
--- a/demos/documented/shape_optimization/space_mapping_semilinear_transmission/sm_history.json
+++ b/demos/documented/shape_optimization/space_mapping_semilinear_transmission/sm_history.json
@@ -1 +1,34 @@
-{"cost_function_value": [8.435764674972805e-05, 6.321406373133801e-06, 3.757248246419054e-07, 6.492747314444208e-08, 2.550228199419987e-08, 1.0455135609844983e-08], "eps": [0.27146898441562106, 0.09123719674130686, 0.04209945367946616, 0.02632393957495021, 0.011912935969793356, 0.0042929331548266034], "stepsize": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0], "MeshQuality": [0.34418629809714807, 0.38658324849707726, 0.38460354314010514, 0.37743786779446986, 0.3721885038607101, 0.36652185899846157]}
\ No newline at end of file
+{
+ "cost_function_value": [
+ 8.43576467497285e-05,
+ 6.321406373138715e-06,
+ 3.757248246405087e-07,
+ 6.492747314444575e-08,
+ 2.5502281994099945e-08,
+ 1.045513561000219e-08
+ ],
+ "eps": [
+ 0.2714689844155716,
+ 0.09123719674129165,
+ 0.04209945367935356,
+ 0.02632393957488272,
+ 0.011912935969791951,
+ 0.00429293315489518
+ ],
+ "stepsize": [
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0
+ ],
+ "MeshQuality": [
+ 0.3441862980971556,
+ 0.38658324849707115,
+ 0.38460354314010936,
+ 0.37743786779448596,
+ 0.37218850386072166,
+ 0.3665218589984678
+ ]
+}
\ No newline at end of file
diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/config.ini b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/config.ini
index 1b8f2e22..59855807 100755
--- a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/config.ini
+++ b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/config.ini
@@ -1,86 +1,16 @@
-[Mesh]
-mesh_file = ./mesh/mesh.xdmf
-gmsh_file = ./mesh/mesh.msh
-geo_file = ./mesh/mesh.geo
-remesh = False
-show_gmsh_output = False
-
[StateSystem]
-is_linear = False
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
+is_linear = True
[OptimizationRoutine]
algorithm = bfgs
rtol = 1e-2
-atol = 0.0
-max_iter = 50
-soft_exit = False
-
-[LineSearch]
-initial_stepsize = 1e-0
-epsilon_armijo = 1e-4
-beta_armijo = 2
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = DY
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
[ShapeGradient]
shape_bdry_def = [2, 3]
shape_bdry_fix = [1, 4, 5]
-shape_bdry_fix_x = []
-shape_bdry_fix_y = []
-shape_bdry_fix_z = []
-use_pull_back = True
-lambda_lame = 0.0
-damping_factor = 0.0
-mu_def = 1.0
-mu_fix = 1.0
-use_sqrt_mu = False
inhomogeneous = True
-[Regularization]
-factor_volume = 0.0
-target_volume = 0.0
-use_initial_volume = True
-factor_surface = 0.0
-target_surface = 0.0
-use_initial_surface = False
-factor_curvature = 0.0
-factor_barycenter = 0.0
-target_barycenter = [0.0, 0.0, 0.0]
-use_initial_barycenter = False
-use_relative_scaling = False
-
-[MeshQuality]
-angle_change = inf
-volume_change = inf
-tol_lower = 0.0
-tol_upper = 1e-15
-measure = skewness
-type = min
-
[Output]
verbose = False
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-save_mesh = False
diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/demo_space_mapping_uniform_flow_distribution.py b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/demo_space_mapping_uniform_flow_distribution.py
index 257620b7..0f249246 100644
--- a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/demo_space_mapping_uniform_flow_distribution.py
+++ b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/demo_space_mapping_uniform_flow_distribution.py
@@ -285,7 +285,7 @@ def solve_and_evaluate(self):
bc_pressure = DirichletBC(V.sub(1), Constant(0.0), boundaries, 5)
bcs = [bc_in] + bcs_wall + [bc_out] + [bc_pressure]
- cashocs.newton_solve(F, up, bcs, verbose=False)
+ cashocs.snes_solve(F, up, bcs)
self.u, p = up.split(True)
file = File(f"./pvd/u_{self.iter}.pvd")
@@ -416,9 +416,9 @@ def solve_and_evaluate(self):
# bcs = [bc_in
# :::
#
-# The problem is then solved with {py:func}``
+# The problem is then solved with {py:func}``
# :::{code-block} python
-# cashocs.newton_solve(F, up, bcs, verbose=False)
+# cashocs.snes_solve(F, up, bcs)
# :::
#
# Finally, after having solved the problem, we first save the solution for later
diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.h5 b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.h5
index e92aa105..ed0d3d46 100644
Binary files a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.h5 and b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.h5 differ
diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.msh b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.msh
index ae8fff15..94681898 100644
--- a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.msh
+++ b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine.msh
@@ -4,72 +4,72 @@ $EndMeshFormat
$Entities
23 25 4 0
1 0 0 0 0
-2 5.376997370226176 0.005887593849028 0 0
+2 5.376996272711287 0.00588744009439099 0 0
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index e4154a09..aca1bcb1 100644
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diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine_boundaries.h5 b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine_boundaries.h5
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diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine_subdomains.h5 b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/fine_subdomains.h5
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diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/mesh_1.msh b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/mesh_1.msh
index ccf40bb9..11ae04cc 100644
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index e84dd412..b24bb8f4 100644
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index 90cb616d..4cf40c42 100644
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diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/mesh_4.msh b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/mesh_4.msh
index 9eedac5a..38b2205e 100644
--- a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/mesh/fine/mesh_4.msh
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index 55432883..be7fd083 100644
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index e65ed898..b854df0a 100644
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+1.8173240772510892e+00 -1.2487534658953861e+00 0
$EndNodes
$Elements
29 14432 1 14432
diff --git a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/sm_history.json b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/sm_history.json
index 5433943e..f767ca54 100644
--- a/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/sm_history.json
+++ b/demos/documented/shape_optimization/space_mapping_uniform_flow_distribution/sm_history.json
@@ -1 +1,34 @@
-{"cost_function_value": [0.01844722599823243, 0.00296873348143958, 1.4032785561840204e-05, 7.260544997837202e-08, 3.326967484440141e-10, 7.023523016083452e-12], "eps": [1.1799821078642916, 0.5402821415702382, 0.041319297271306316, 0.002511332273905528, 0.0001705077050190124, 1.7101313450600688e-05], "stepsize": [1.0, 1.0, 1.0, 1.0, 1.0, 1.0], "MeshQuality": [0.4620241540461052, 0.4853416537320775, 0.47521250698821693, 0.4699161459671043, 0.4702939412320447, 0.47031734718459794]}
\ No newline at end of file
+{
+ "cost_function_value": [
+ 0.018446680546406656,
+ 0.002968854234065752,
+ 1.4044251007537854e-05,
+ 7.436794541939878e-08,
+ 3.3125779878852174e-10,
+ 8.482194687660224e-12
+ ],
+ "eps": [
+ 1.179960634946022,
+ 0.5402985640019651,
+ 0.04134590331701034,
+ 0.0025498084692193185,
+ 0.0001745737550440082,
+ 3.498288550331805e-05
+ ],
+ "stepsize": [
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0,
+ 1.0
+ ],
+ "MeshQuality": [
+ 0.46202415404612307,
+ 0.48534105296851593,
+ 0.4752113308318474,
+ 0.46991474242477005,
+ 0.47029941170390377,
+ 0.4703210833311442
+ ]
+}
\ No newline at end of file
diff --git a/demos/documented/topology_optimization/cantilever/config.ini b/demos/documented/topology_optimization/cantilever/config.ini
index 7a2e3902..a2d33de8 100644
--- a/demos/documented/topology_optimization/cantilever/config.ini
+++ b/demos/documented/topology_optimization/cantilever/config.ini
@@ -1,56 +1,18 @@
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = bfgs
-rtol = 1e-10
-atol = 0.0
-max_iter = 1000
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
[LineSearch]
-;method = polynomial
initial_stepsize = 1e-3
safeguard_stepsize = False
epsilon_armijo = 1e-20
-beta_armijo = 2.0
[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
bfgs_periodic_restart = 3
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
-
[Output]
verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-time_suffix = False
diff --git a/demos/documented/topology_optimization/pipe_bend/config.ini b/demos/documented/topology_optimization/pipe_bend/config.ini
index b3f7a36b..d1d7424e 100644
--- a/demos/documented/topology_optimization/pipe_bend/config.ini
+++ b/demos/documented/topology_optimization/pipe_bend/config.ini
@@ -1,49 +1,11 @@
[StateSystem]
is_linear = True
-newton_rtol = 1e-8
-newton_atol = 1e-13
-newton_iter = 20
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = bfgs
-rtol = 1e-10
-atol = 0.0
-max_iter = 1000
-gradient_method = direct
-gradient_tol = 1e-9
-soft_exit = True
[LineSearch]
-initial_stepsize = 1.0
safeguard_stepsize = False
-epsilon_armijo = 1e-4
-beta_armijo = 2
-;method = polynomial
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
[TopologyOptimization]
topological_derivative_is_identical = True
@@ -52,7 +14,3 @@ topological_derivative_is_identical = True
verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-time_suffix = False
diff --git a/demos/documented/topology_optimization/poisson_clover/config.ini b/demos/documented/topology_optimization/poisson_clover/config.ini
index 41280b69..9a7644c7 100755
--- a/demos/documented/topology_optimization/poisson_clover/config.ini
+++ b/demos/documented/topology_optimization/poisson_clover/config.ini
@@ -1,50 +1,10 @@
[StateSystem]
is_linear = True
-newton_rtol = 1e-11
-newton_atol = 1e-13
-newton_iter = 50
-newton_damped = True
-newton_inexact = False
-newton_verbose = False
-picard_iteration = False
-picard_rtol = 1e-10
-picard_atol = 1e-12
-picard_iter = 10
-picard_verbose = False
[OptimizationRoutine]
algorithm = bfgs
-rtol = 1e-10
-atol = 0.0
-max_iter = 10
-gradient_method = direct
-gradient_tol = 1e-9
soft_exit = True
-[LineSearch]
-initial_stepsize = 1.0
-#safeguard_stepsize = True
-epsilon_armijo = 1e-4
-beta_armijo = 2
-;method = polynomial
-
-[AlgoLBFGS]
-bfgs_memory_size = 5
-use_bfgs_scaling = True
-
-[AlgoCG]
-cg_method = PR
-cg_periodic_restart = False
-cg_periodic_its = 5
-cg_relative_restart = False
-cg_restart_tol = 0.5
-
-[AlgoTNM]
-inner_newton = cg
-max_it_inner_newton = 100
-inner_newton_rtol = 1e-15
-inner_newton_atol = 0.0
-
[TopologyOptimization]
topological_derivative_is_identical = True
@@ -52,8 +12,4 @@ topological_derivative_is_identical = True
verbose = True
save_results = False
save_txt = False
-save_state = False
-save_adjoint = False
-save_gradient = False
-time_suffix = False
diff --git a/demos/undocumented/solvers/fieldsplit_nesting.py b/demos/undocumented/solvers/fieldsplit_nesting.py
new file mode 100644
index 00000000..e9e7de0b
--- /dev/null
+++ b/demos/undocumented/solvers/fieldsplit_nesting.py
@@ -0,0 +1,59 @@
+from fenics import *
+
+import cashocs
+
+mesh, subdomains, boundaries, dx, ds, dS = cashocs.regular_mesh(16)
+v_elem = VectorElement("CG", mesh.ufl_cell(), 2)
+p_elem = FiniteElement("CG", mesh.ufl_cell(), 1)
+V = FunctionSpace(mesh, MixedElement(v_elem, p_elem, p_elem))
+# order of the MixedElement determines (single) prefixes for PETSc solver
+# velocity block gets 0, pressure 1, and temperature 2
+
+upT = Function(V)
+u, p, T = split(upT)
+v, q, S = TestFunctions(V)
+
+mu = 1.0 / (T + 1)
+
+F = (
+ mu * inner(grad(u), grad(v)) * dx
+ + dot(grad(u) * u, v) * dx
+ - p * div(v) * dx
+ - q * div(u) * dx
+ + dot(grad(T), grad(S)) * dx
+ + dot(u, grad(T)) * S * dx
+ - Constant(100.0) * S * dx
+)
+u_in = Expression(("4.0 * x[1] * (1.0 - x[1])", "0.0"), degree=2)
+bcs = cashocs.create_dirichlet_bcs(V.sub(0), u_in, boundaries, 1)
+bcs += cashocs.create_dirichlet_bcs(V.sub(0), Constant((0.0, 0.0)), boundaries, [3, 4])
+bcs += cashocs.create_dirichlet_bcs(V.sub(2), Constant(1.0), boundaries, [1, 3, 4])
+
+petsc_options = {
+ "snes_type": "newtonls",
+ "snes_monitor": None,
+ "snes_max_it": 7,
+ "ksp_type": "fgmres",
+ "ksp_rtol": 1e-1,
+ "pc_type": "fieldsplit",
+ "pc_fieldsplit_type": "multiplicative",
+ "pc_fieldsplit_0_fields": "0,1", # will get prefix fieldsplit_0_
+ "pc_fieldsplit_1_fields": "2", # will get prefix fieldsplit_2_
+ "fieldsplit_0_ksp_type": "fgmres",
+ "fieldsplit_0_ksp_rtol": 1e-1,
+ "fieldsplit_0_pc_type": "fieldsplit", # sub fields get global (mixed) index
+ "fieldsplit_0_pc_fieldsplit_type": "schur",
+ "fieldsplit_0_pc_fieldsplit_schur_precondition": "selfp",
+ "fieldsplit_0_fieldsplit_0_ksp_type": "preonly",
+ "fieldsplit_0_fieldsplit_0_pc_type": "lu",
+ "fieldsplit_0_fieldsplit_1_ksp_type": "gmres",
+ "fieldsplit_0_fieldsplit_1_ksp_rtol": 1e-1,
+ "fieldsplit_0_fieldsplit_1_pc_type": "hypre",
+ "fieldsplit_0_fieldsplit_1_ksp_converged_reason": None,
+ "fieldsplit_2_ksp_type": "gmres",
+ "fieldsplit_2_ksp_rtol": 1e-1,
+ "fieldsplit_2_pc_type": "hypre",
+}
+
+cashocs.snes_solve(F, upT, bcs, petsc_options=petsc_options, max_iter=8)
+u, p, T = upT.split(True)
diff --git a/docs/requirements.txt b/docs/requirements.txt
index a9608a6d..578ed669 100644
--- a/docs/requirements.txt
+++ b/docs/requirements.txt
@@ -1,18 +1,21 @@
-numpy>=1.22.2 # not directly required, pinned by Snyk to avoid a vulnerability
+numpy>=1.22.2
matplotlib
scipy
-Sphinx==7.2.6
+Sphinx==7.3.7
sphinx-argparse==0.4.0
sphinx-copybutton==0.5.2
meshio==5.3.5
-docutils==0.20.1
-pydata-sphinx-theme==0.15.2
-sphinx-design==0.5.0
-setuptools>=65.5.1 # not directly required, pinned by Snyk to avoid a vulnerability
-pygments>=2.7.4 # not directly required, pinned by Snyk to avoid a vulnerability
+docutils==0.21.2
+pydata-sphinx-theme==0.15.4
+sphinx-design==0.6.0
+setuptools>=65.5.1
+pygments>=2.7.4
typing_extensions
-myst-parser==2.0.0
-jupytext==1.16.1
+myst-parser==3.0.1
+jupytext==1.16.3
sphinx-favicon==1.0.1
-pillow>=10.0.1 # not directly required, pinned by Snyk to avoid a vulnerability
-fonttools>=4.43.0 # not directly required, pinned by Snyk to avoid a vulnerability
+matplotlib
+pillow>=10.0.1
+fonttools>=4.43.0
+requests>=2.32.0
+zipp>=3.19.1
diff --git a/docs/source/about/citing.rst b/docs/source/about/citing.rst
index 99f80475..f407fb31 100644
--- a/docs/source/about/citing.rst
+++ b/docs/source/about/citing.rst
@@ -1,3 +1,159 @@
-.. include:: ../../../README.rst
- :start-after: readme_start_citing
- :end-before: readme_end_citing
+Citing
+======
+
+If you use cashocs for your research, please cite the following papers
+
+.. tab-set::
+
+ .. tab-item:: Plain Text
+
+ .. code-block:: text
+
+ cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software
+ Sebastian Blauth
+ SoftwareX, Volume 13, 2021
+ https://doi.org/10.1016/j.softx.2020.100646
+
+ .. tab-item:: BibTeX
+
+ .. code-block:: bibtex
+
+ @Article{Blauth2021cashocs,
+ author = {Sebastian Blauth},
+ journal = {SoftwareX},
+ title = {{cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software}},
+ year = {2021},
+ issn = {2352-7110},
+ pages = {100646},
+ volume = {13},
+ doi = {https://doi.org/10.1016/j.softx.2020.100646},
+ keywords = {PDE constrained optimization, Adjoint approach, Shape optimization, Optimal control},
+ }
+
+as well as
+
+.. tab-set::
+
+ .. tab-item:: Plain Text
+
+ .. code-block:: text
+
+ Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software
+ Sebastian Blauth
+ SoftwareX, Volume 24, 2023
+ https://doi.org/10.1016/j.softx.2023.101577
+
+ .. tab-item:: BibTeX
+
+ .. code-block:: bibtex
+
+ @Article{Blauth2023Version,
+ author = {Sebastian Blauth},
+ journal = {SoftwareX},
+ title = {{Version 2.0 - cashocs: A Computational, Adjoint-Based Shape Optimization and Optimal Control Software}},
+ year = {2023},
+ issn = {2352-7110},
+ pages = {101577},
+ volume = {24},
+ doi = {https://doi.org/10.1016/j.softx.2023.101577},
+ keywords = {PDE constrained optimization, Shape optimization, Topology optimization, Space mapping},
+ }
+
+
+Additionally, if you are using the nonlinear conjugate gradient methods for shape optimization implemented in cashocs, please cite the following paper
+
+.. tab-set::
+
+ .. tab-item:: Plain Text
+
+ .. code-block:: text
+
+ Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov--Poincaré-Type Metrics
+ Sebastian Blauth
+ SIAM Journal on Optimization, Volume 31, Issue 3, 2021
+ https://doi.org/10.1137/20M1367738
+
+ .. tab-item:: BibTeX
+
+ .. code-block:: BibTeX
+
+ @Article{Blauth2021Nonlinear,
+ author = {Sebastian Blauth},
+ journal = {SIAM J. Optim.},
+ title = {{Nonlinear Conjugate Gradient Methods for PDE Constrained Shape Optimization Based on Steklov-Poincaré-Type Metrics}},
+ year = {2021},
+ number = {3},
+ pages = {1658--1689},
+ volume = {31},
+ doi = {10.1137/20M1367738},
+ fjournal = {SIAM Journal on Optimization},
+ }
+
+
+
+If you are using the space mapping methods for shape optimization, please cite the paper
+
+.. tab-set::
+
+ .. tab-item:: Plain Text
+
+ .. code-block:: text
+
+ Space Mapping for PDE Constrained Shape Optimization
+ Sebastian Blauth
+ SIAM Journal on Optimization, Volume 33, Issue 3, 2023
+ https://doi.org/10.1137/22M1515665
+
+ .. tab-item:: BibTeX
+
+ .. code-block:: bibtex
+
+ @Article{Blauth2023Space,
+ author = {Blauth, Sebastian},
+ journal = {SIAM J. Optim.},
+ title = {{Space Mapping for PDE Constrained Shape Optimization}},
+ year = {2023},
+ issn = {1052-6234,1095-7189},
+ number = {3},
+ pages = {1707--1733},
+ volume = {33},
+ doi = {10.1137/22M1515665},
+ fjournal = {SIAM Journal on Optimization},
+ mrclass = {49Q10 (35Q93 49M41 65K05)},
+ mrnumber = {4622415},
+ }
+
+
+
+and if you are using the topology optimization methods implemented in cashocs, please cite the paper
+
+.. tab-set::
+
+ .. tab-item:: Plain Text
+
+ .. code-block:: text
+
+ Quasi-Newton Methods for Topology Optimization Using a Level-Set Method
+ Sebastian Blauth and Kevin Sturm
+ Structural and Multidisciplinary Optimization, Volume 66, 2023
+ https://doi.org/10.1007/s00158-023-03653-2
+
+ .. tab-item:: BibTeX
+
+ .. code-block:: bibtex
+
+ @Article{Blauth2023Quasi,
+ author = {Blauth, Sebastian and Sturm, Kevin},
+ journal = {Struct. Multidiscip. Optim.},
+ title = {{Quasi-Newton methods for topology optimization using a level-set method}},
+ year = {2023},
+ issn = {1615-147X,1615-1488},
+ number = {9},
+ pages = {203},
+ volume = {66},
+ doi = {10.1007/s00158-023-03653-2},
+ fjournal = {Structural and Multidisciplinary Optimization},
+ mrclass = {99-06},
+ mrnumber = {4635978},
+ }
+
diff --git a/docs/source/conf.py b/docs/source/conf.py
index 95f8dd09..dd417688 100755
--- a/docs/source/conf.py
+++ b/docs/source/conf.py
@@ -28,7 +28,7 @@
author = "Sebastian Blauth"
# The full version, including alpha/beta/rc tags
-release = "2.1.4"
+release = "2.2.0-dev"
# -- General configuration ---------------------------------------------------
diff --git a/docs/source/user/demos/optimal_control/doc_config.rst b/docs/source/user/demos/optimal_control/doc_config.rst
index a6bd6d3a..8c86f452 100755
--- a/docs/source/user/demos/optimal_control/doc_config.rst
+++ b/docs/source/user/demos/optimal_control/doc_config.rst
@@ -6,8 +6,6 @@ Documentation of the Config Files for Optimal Control Problems
Let us take a look at how the config files are structured for optimal control
problems.
-The corresponding config file is :download:`config.ini
-`.
First of all, the config is divided into the sections: :ref:`Mesh
`, :ref:`StateSystem `,
@@ -162,6 +160,20 @@ Picard iteration, and is set as follows
Its default value is :ini:`False`.
+The parameter :ini:`backend` specifies which solver backend should be used for solving nonlinear systems.
+Its default value is given by
+
+.. code-block:: ini
+
+ backend = cashocs
+
+Possible options are :ini:`backend = cashocs` and :ini:`backend = petsc`. In the former case, a
+damped, inexact Newton method which is affine co-variant is used. Its parameters are specified in the
+configuration above. In the latter case, PETSc's SNES interface for solving nonlinear equations
+is used which can be configured with the `ksp_options` supplied by the user to the
+:py:class:`cashocs.OptimizationProblem`. An overview over possible PETSc command line options
+can be found at ``_.
+
@@ -646,6 +658,8 @@ in the following.
- maximum iterations for Picard iteration
* - :ini:`picard_verbose = False`
- :ini:`picard_verbose = True` enables verbose output of Picard iteration
+ * - :ini:`backend = cashocs`
+ - specifies the backend for solving nonlinear equations, can be either :ini:`cashocs` or :ini:`petsc`
[OptimizationRoutine]
*********************
@@ -661,7 +675,7 @@ in the following.
- relative tolerance for the optimization algorithm
* - :ini:`atol = 0.0`
- absolute tolerance for the optimization algorithm
- * - :ini:`maximum iterations = 100`
+ * - :ini:`max_iter = 100`
- maximum iterations for the optimization algorithm
* - :ini:`gradient_method = direct`
- specifies the solver for computing the gradient, can be either :ini:`gradient_method = direct` or :ini:`gradient_method = iterative`
diff --git a/docs/source/user/demos/shape_optimization/doc_config.rst b/docs/source/user/demos/shape_optimization/doc_config.rst
index 80bf2bbc..5a7752eb 100755
--- a/docs/source/user/demos/shape_optimization/doc_config.rst
+++ b/docs/source/user/demos/shape_optimization/doc_config.rst
@@ -4,9 +4,7 @@ Documentation of the Config Files for Shape Optimization Problems
=================================================================
Let us take a detailed look at the config files for shape optimization problems and
-discusss the corresponding parameters. The corresponding
-config file used for this discussion is :download:`config.ini `,
-which is the config file used for :ref:`demo_shape_poisson`.
+discusss the corresponding parameters.
For shape optimization problems, the config file is a lot larger compared to the :ref:`config files
for optimal control `.
@@ -218,6 +216,20 @@ boolean flag
which is set to :ini:`picard_verbose = False` by default.
+The parameter :ini:`backend` specifies which solver backend should be used for solving nonlinear systems.
+Its default value is given by
+
+.. code-block:: ini
+
+ backend = cashocs
+
+Possible options are :ini:`backend = cashocs` and :ini:`backend = petsc`. In the former case, a
+damped, inexact Newton method which is affine co-variant is used. Its parameters are specified in the
+configuration above. In the latter case, PETSc's SNES interface for solving nonlinear equations
+is used which can be configured with the `ksp_options` supplied by the user to the
+:py:class:`cashocs.OptimizationProblem`. An overview over possible PETSc command line options
+can be found at ``_.
+
.. _config_shape_optimization_routine:
@@ -580,6 +592,14 @@ boundaries should not be deformable in x-direction, but can be deformed in the y
and z-directions. Of course you can constrain a boundary to be only variable in a
single direction by adding the markers to the remaining lists.
+Furthermore, we have the parameter :ini:`fixed_dimensions`, which enables us to restrict the shape gradient to specific dimensions. It is set via
+
+.. code-block:: ini
+
+ fixed_dimensions = []
+
+In case :ini:`fixed_dimensions = []`, there is no restriction on the shape gradient. However, if :ini:`fixed_dimensions = [i]`, then the i-th component of the shape gradient is set to 0, so that we have no deformation in the i-th coordinate direction. For example, if :ini:`fixed_dimensions = [0, 2]`, we only have a deformation in the :math:`y`-component of the mesh. The default is :ini:`fixed_dimensions = []`.
+
The next parameter is specified via
.. code-block:: ini
@@ -746,14 +766,30 @@ Finally, there is the possibility to use a stabilized weak form for the :math:`p
The default value of this parameter is :ini:`p_laplacian_stabilization = 0.0`. Note, that the parameter should be chosen comparatively small, i.e., significantly smaller than 1.
+Moreover, we have the parameter :ini:`degree_estimation` which is specified via
-Furthermore, we have the parameter :ini:`fixed_dimensions`, which enables us to restrict the shape gradient to specific dimensions. It is set via
+.. code-block:: ini
+
+ degree_estimation = True
+
+This parameter enables cashocs' default estimation of the quadrature degree for the shape derivative. If this is set to `False`, an error related to FEniCS may occur - so this should be always enabled.
+
+Next, we have the parameter :ini:`global_deformation` which is set via the line
.. code-block:: ini
- fixed_dimensions = []
+ global_deformation = False
+
+If this is set to `True`, cashocs computes the deformation from the initial to the optimized mesh (even when remeshing has been performed). This can, however, lead to some unexpected errors with PETSc, so this should be used with care.
+
+We have the parameter :ini:`test_for_intersections`, which is specified via
+
+.. code-block:: ini
+
+ test_for_intersections = True
+
+If this parameter is set to `True`, cashocs will check the deformed meshes for (self) intersections, which would generate non-physical geometries and reject them - so that all generated designs are physically meaningful. This should not be set to `False`.
-In case :ini:`fixed_dimensions = []`, there is no restriction on the shape gradient. However, if :ini:`fixed_dimensions = [i]`, then the i-th component of the shape gradient is set to 0, so that we have no deformation in the i-th coordinate direction. For example, if :ini:`fixed_dimensions = [0, 2]`, we only have a deformation in the :math:`y`-component of the mesh. The default is :ini:`fixed_dimensions = []`.
.. _config_shape_regularization:
@@ -991,6 +1027,48 @@ Finally, we have the parameter :ini:`remesh_iter` in which the user can specify
where :ini:`remesh_iter = 0` means that no automatic remeshing is performed (this is the default), and :ini:`remesh_iter = n` means that remeshing is performed after each `n` iterations. Note that to use this parameter and avoid unexpected results, it might be beneficial to the the lower and upper mesh quality tolerances to a low value, so that the "quality based remeshing" does not interfere with the "iteration based remeshing", but both can be used in combination.
+.. _config_shape_mesh_quality_constraints:
+
+Section MeshQualityConstraints
+------------------------------
+
+The parameter :ini:`min_angle` is used to define the threshold angle, i.e. the minimum (solid) angle which is feasible for the mesh. The default is given by
+
+.. code-block:: ini
+
+ min_angle = 0.0
+
+which ensures that the constraints are not active by default. Note that the initial mesh has to be feasible for the method to work, so if the minimum angle in the mesh is smaller than the :ini:`min_angle` specified in the configuration, cashocs will raise an exception. Note that the angle is specified in radian and **not** degree.
+
+To circumvent this problem for meshes with small angles (which could be used, e.g., to resolve boundary layers, the next parameter :ini:`feasible_angle_reduction_factor` is used. This parameter specifies, how much smaller the (solid) angles of the mesh are allowed to become relative to the value in the initial mesh. That means a value of :ini:`feasible_angle_reduction_factor = 0.25` ensures that no (solid) angle in a mesh element will become smaller than one quarter of the smallest angle of the element in the initial mesh. The default is given by
+
+.. code-block:: ini
+
+ feasible_angle_reduction_factor = 0.0
+
+which ensures that the constraints are not active by default.
+
+.. note::
+
+ If both the :ini:`feasible_angle_reduction_factor` and :ini:`min_angle` are given, cashocs uses the element-wise minimum of the two. In particular, this means that a strategy of using :ini:`feasible_angle_reduction_factor = 0.9999` and some value for :ini:`min_angle` can be used to constrain the (solid) angle to a specific value, wherever this is possible (and leave the angles that are below this threshold as they are).
+
+The parameter :ini:`tol` is used to define a tolerance for which constraints are treated as active or not. As we treat the constraints numerically, they can only be satisfied up to a certain tolerance, which the user can specify here. The default value of
+
+.. code-block:: ini
+
+ tol = 1e-2
+
+should work well in most situations. In some situations, the optimization could be faster with a tolerance of :ini:`tol = 1e-1` (but should never be larger) or more accurate when using, e.g., :ini:`tol = 1e-3` (lower values should most of the time not be necessary).
+
+The parameter :ini:`mode` can only be set to
+
+.. code-block:: ini
+
+ mode = approximate
+
+at the moment, which is also the default value. In the future, other options might be possible.
+
+
.. _config_shape_output:
Section Output
@@ -1152,6 +1230,9 @@ in the following.
- maximum iterations for Picard iteration
* - :ini:`picard_verbose = False`
- :ini:`picard_verbose = True` enables verbose output of Picard iteration
+ * - :ini:`backend = cashocs`
+ - specifies the backend for solving nonlinear equations, can be either :ini:`cashocs` or :ini:`petsc`
+
[OptimizationRoutine]
@@ -1303,6 +1384,12 @@ in the following.
- The parameter :math:`p` of the :math:`p`-Laplacian
* - :ini:`p_laplacian_stabilization = 0.0`
- The stabilization parameter for the :math:`p`-Laplacian problem. No stabilization is used when this is :ini:`p_laplacian_stabilization = 0.0`.
+ * - :ini:`global_deformation = False`
+ - Computes the global deformation from initial to optimized mesh. This can lead to unexpected errors, use with care.
+ * - :ini:`degree_estimation = True`
+ - Estimate the required degree for quadrature of the shape derivative. This should be `True`, otherwise unexpected errors can happen.
+ * - :ini:`test_for_intersections = True`
+ - If enabled, the mesh is tested for intersections which would create non-physical meshes. This should always be enabled, otherwise the obtained results might be incorrect.
[Regularization]
@@ -1361,9 +1448,26 @@ in the following.
- determines which quality measure is used
* - :ini:`type = min`
- determines if minimal or average quality is considered
+ * - :ini:`remesh_iter`
+ - When set to a value > 0, remeshing is performed every :ini:`remesh_iter` iterations.
+[MeshQualityConstraints]
+************************
+.. list-table::
+ :header-rows: 1
+
+ * - Parameter = Default value
+ - Remarks
+ * - :ini:`min_angle = 0.0`
+ - The minimum feasible triangle / solid angle of the mesh cells in radian. This is constant for all cells. If this is positive, the constraints are used. If this is 0, no constraints are used.
+ * - :ini:`tol = 1e-2`
+ - The tolerance for the mesh quality constraints. If `abs(g(x)) < tol`, then the constraint is considered active
+ * - :ini:`mode = approximate`
+ - The mode for calculating the (shape) derivatives of the constraint functions. At the moment, only "approximate" is supported.
+ * - :ini:`feasible_angle_reduction_factor = 0.0`
+ - A factor in the interval [0,1) which sets the feasible reduction of the triangle / solid angles. This means, that each cell is only allowed to have angles larger than this times the initial minimum angle.
[Output]
********
diff --git a/docs/source/user/demos/shape_optimization/index.rst b/docs/source/user/demos/shape_optimization/index.rst
index 05b8b152..1eecfea0 100644
--- a/docs/source/user/demos/shape_optimization/index.rst
+++ b/docs/source/user/demos/shape_optimization/index.rst
@@ -20,3 +20,4 @@ be treated with cashocs.
demo_p_laplacian.md
demo_space_mapping_semilinear_transmission.md
demo_space_mapping_uniform_flow_distribution.md
+ demo_mesh_quality_constraints.md
diff --git a/pyproject.toml b/pyproject.toml
index 1cd65174..c349916a 100755
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -7,7 +7,7 @@ build-backend = "setuptools.build_meta"
[project]
name = "cashocs"
-version = "2.1.4"
+version = "2.2.0-dev"
description = "Computational Adjoint-Based Shape Optimization and Optimal Control Software"
readme = "README.rst"
requires-python = ">=3.8"
@@ -45,6 +45,7 @@ classifiers = [
dependencies = [
"meshio >= 4.1.0",
"numpy",
+ "scipy",
"typing_extensions",
"matplotlib",
]
@@ -137,5 +138,6 @@ module = [
"meshio",
"h5py",
"matplotlib.*",
+ "scipy.*",
]
ignore_missing_imports = true
diff --git a/tests/config_remesh.ini b/tests/config_remesh.ini
index aa5164eb..be76b05f 100755
--- a/tests/config_remesh.ini
+++ b/tests/config_remesh.ini
@@ -1,5 +1,4 @@
[Mesh]
-mesh_file = ./mesh/mesh.xdmf
gmsh_file = ./mesh/mesh.msh
geo_file = ./mesh/mesh.geo
remesh = True
diff --git a/tests/test_fieldsplit.py b/tests/test_fieldsplit.py
new file mode 100644
index 00000000..795ae2d8
--- /dev/null
+++ b/tests/test_fieldsplit.py
@@ -0,0 +1,157 @@
+# Copyright (C) 2020-2024 Sebastian Blauth
+#
+# This file is part of cashocs.
+#
+# cashocs is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# cashocs is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with cashocs. If not, see .
+
+"""Tests for the linear solvers.
+
+"""
+
+from fenics import *
+import numpy as np
+
+import cashocs
+
+
+def test_fieldsplit_pc():
+ mesh, subdomains, boundaries, dx, ds, dS = cashocs.regular_mesh(8)
+ v_elem = VectorElement("CG", mesh.ufl_cell(), 2)
+ p_elem = FiniteElement("CG", mesh.ufl_cell(), 1)
+ V = FunctionSpace(mesh, MixedElement(v_elem, p_elem))
+
+ up = Function(V)
+ u, p = split(up)
+ v, q = TestFunctions(V)
+
+ F = inner(grad(u), grad(v)) * dx - p * div(v) * dx - q * div(u) * dx
+ bcs = cashocs.create_dirichlet_bcs(V.sub(0), Constant((1.0, 0.0)), boundaries, 1)
+ bcs += cashocs.create_dirichlet_bcs(
+ V.sub(0), Constant((0.0, 0.0)), boundaries, [3, 4]
+ )
+
+ ksp_options = {
+ "ksp_type": "fgmres",
+ "ksp_rtol": 1e-5,
+ "ksp_max_it": 1,
+ "ksp_monitor_true_residual": None,
+ "pc_type": "fieldsplit",
+ "pc_fieldsplit_type": "schur",
+ "pc_fieldsplit_schur_precondition": "selfp",
+ "fieldsplit_0_ksp_type": "preonly",
+ "fieldsplit_0_pc_type": "lu",
+ "fieldsplit_1_ksp_type": "gmres",
+ "fieldsplit_1_ksp_rtol": 1e-6,
+ "fieldsplit_1_ksp_max_it": 25,
+ "fieldsplit_1_pc_type": "hypre",
+ "fieldsplit_1_ksp_converged_reason": None,
+ }
+
+ cashocs.linear_solve(F, up, bcs, ksp_options=ksp_options)
+ assert True
+
+
+def test_fieldsplit_pc_section():
+ mesh, subdomains, boundaries, dx, ds, dS = cashocs.regular_mesh(8)
+ v_elem = VectorElement("CG", mesh.ufl_cell(), 2)
+ p_elem = FiniteElement("CG", mesh.ufl_cell(), 1)
+ V = FunctionSpace(mesh, MixedElement(p_elem, v_elem))
+
+ pu = Function(V)
+ p, u = split(pu)
+ q, v = TestFunctions(V)
+
+ F = inner(grad(u), grad(v)) * dx - p * div(v) * dx - q * div(u) * dx
+ bcs = cashocs.create_dirichlet_bcs(V.sub(1), Constant((1.0, 0.0)), boundaries, 1)
+ bcs += cashocs.create_dirichlet_bcs(
+ V.sub(1), Constant((0.0, 0.0)), boundaries, [3, 4]
+ )
+
+ ksp_options = {
+ "ksp_type": "fgmres",
+ "ksp_rtol": 1e-5,
+ "ksp_max_it": 1,
+ "pc_type": "fieldsplit",
+ "pc_fieldsplit_type": "schur",
+ "pc_fieldsplit_schur_precondition": "selfp",
+ "pc_fieldsplit_0_fields": "1",
+ "pc_fieldsplit_1_fields": "0",
+ "fieldsplit_0_ksp_type": "gmres",
+ "fieldsplit_0_pc_type": "hypre",
+ "fieldsplit_0_ksp_rtol": 1e-6,
+ "fieldsplit_0_ksp_max_it": 25,
+ "fieldsplit_0_ksp_converged_reason": None,
+ "fieldsplit_1_ksp_type": "preonly",
+ "fieldsplit_1_pc_type": "lu",
+ }
+
+ cashocs.linear_solve(F, pu, bcs, ksp_options=ksp_options)
+ assert True
+
+
+def test_fieldsplit_snes_nested():
+ mesh, subdomains, boundaries, dx, ds, dS = cashocs.regular_mesh(8)
+ v_elem = VectorElement("CG", mesh.ufl_cell(), 2)
+ p_elem = FiniteElement("CG", mesh.ufl_cell(), 1)
+ V = FunctionSpace(mesh, MixedElement(v_elem, p_elem, p_elem))
+
+ upT = Function(V)
+ u, p, T = split(upT)
+ v, q, S = TestFunctions(V)
+
+ mu = 1.0 / (T + 1)
+
+ F = (
+ mu * inner(grad(u), grad(v)) * dx
+ + dot(grad(u) * u, v) * dx
+ - p * div(v) * dx
+ - q * div(u) * dx
+ + dot(grad(T), grad(S)) * dx
+ + dot(u, grad(T)) * S * dx
+ - Constant(1.0) * S * dx
+ )
+ bcs = cashocs.create_dirichlet_bcs(V.sub(0), Constant((1.0, 0.0)), boundaries, 1)
+ bcs += cashocs.create_dirichlet_bcs(
+ V.sub(0), Constant((0.0, 0.0)), boundaries, [3, 4]
+ )
+ bcs += cashocs.create_dirichlet_bcs(V.sub(2), Constant(1.0), boundaries, [1, 3, 4])
+
+ petsc_options = {
+ "snes_type": "newtonls",
+ "snes_monitor": None,
+ "snes_max_it": 7,
+ "ksp_type": "fgmres",
+ "ksp_rtol": 1e-1,
+ "pc_type": "fieldsplit",
+ "pc_fieldsplit_type": "multiplicative",
+ "pc_fieldsplit_0_fields": "0,1",
+ "pc_fieldsplit_1_fields": "2",
+ "fieldsplit_0_ksp_type": "fgmres",
+ "fieldsplit_0_ksp_rtol": 1e-1,
+ "fieldsplit_0_pc_type": "fieldsplit",
+ "fieldsplit_0_pc_fieldsplit_type": "schur",
+ "fieldsplit_0_pc_fieldsplit_schur_precondition": "selfp",
+ "fieldsplit_0_fieldsplit_0_ksp_type": "preonly",
+ "fieldsplit_0_fieldsplit_0_pc_type": "lu",
+ "fieldsplit_0_fieldsplit_1_ksp_type": "gmres",
+ "fieldsplit_0_fieldsplit_1_ksp_rtol": 1e-1,
+ "fieldsplit_0_fieldsplit_1_pc_type": "hypre",
+ "fieldsplit_0_fieldsplit_1_ksp_converged_reason": None,
+ "fieldsplit_2_ksp_type": "gmres",
+ "fieldsplit_2_ksp_rtol": 1e-1,
+ "fieldsplit_2_pc_type": "hypre",
+ }
+
+ cashocs.snes_solve(F, upT, bcs, petsc_options=petsc_options, max_iter=8)
+ assert True
diff --git a/tests/test_mesh_quality_constraints.py b/tests/test_mesh_quality_constraints.py
new file mode 100644
index 00000000..8d3a4edd
--- /dev/null
+++ b/tests/test_mesh_quality_constraints.py
@@ -0,0 +1,143 @@
+# Copyright (C) 2020-2023 Sebastian Blauth
+#
+# This file is part of cashocs.
+#
+# cashocs is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# cashocs is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with cashocs. If not, see .
+
+from __future__ import annotations
+
+import pathlib
+
+from fenics import *
+import numpy as np
+import pytest
+
+import cashocs
+from cashocs._optimization.shape_optimization.mesh_constraint_manager import (
+ ConstraintManager,
+)
+
+dir_path = str(pathlib.Path(__file__).parent)
+
+
+def compute_convergence_rates(
+ epsilons: list[float], residuals: list[float], verbose: bool = True
+) -> list[float]:
+ """Computes the convergence rate of the Taylor test.
+
+ Args:
+ epsilons: The step sizes.
+ residuals: The corresponding residuals.
+ verbose: Prints the result to the console, if ``True``. Default is ``True``.
+
+ Returns:
+ The computed convergence rates
+
+ """
+ rates: list[float] = []
+ for i in range(1, len(epsilons)):
+ rate: float = np.log(residuals[i] / residuals[i - 1]) / np.log(
+ epsilons[i] / epsilons[i - 1]
+ )
+ rates.append(rate)
+
+ print(f"Taylor test convergence rate: {rates}", flush=True)
+
+ return rates
+
+
+@pytest.mark.skipif(
+ MPI.size(MPI.comm_world) > 1,
+ reason="This test cannot be run in parallel.",
+)
+def test_triangle_mesh_constraints():
+ cfg = cashocs.io.config.Config()
+ min_angle = 2 * np.pi * 30.0 / 360.0
+ cfg.set("MeshQualityConstraints", "min_angle", f"{min_angle}")
+ cfg.set("MeshQualityConstraints", "tol", "1e-2")
+ cfg.set("ShapeGradient", "shape_bdry_fix", "[]")
+ cfg.set("ShapeGradient", "shape_bdry_def", "[1,2,3,4]")
+
+ mesh, subdomains, boundaries, dx, ds, dS = cashocs.regular_mesh(8)
+ bbtree = mesh.bounding_box_tree()
+ rng = np.random.RandomState(300696)
+ VCG = VectorFunctionSpace(mesh, "CG", 1)
+
+ defo = 0.01 * rng.standard_normal(mesh.coordinates().shape)
+ mesh.coordinates()[:, :] += defo
+ bbtree.build(mesh)
+
+ cm = ConstraintManager(cfg, mesh, boundaries, VCG)
+ x = mesh.coordinates().copy().reshape(-1)
+
+ residuals = []
+ epsilons = [1e-4 / 2**i for i in range(6)]
+ h = rng.standard_normal(x.shape)
+ f_k = cm.evaluate(x)
+ gradient = cm._compute_gradient(x)
+ directional_derivative = gradient @ h
+
+ for eps in epsilons:
+ x_mod = x + eps * h[cm.v2d]
+ f_mod = cm.evaluate(x_mod)
+
+ res = abs(f_mod - f_k - eps * directional_derivative)
+ residuals.append(res)
+
+ rates = np.array(compute_convergence_rates(epsilons, residuals)).T
+ mask = np.nonzero(residuals[0] > 1e-8)
+ assert np.min(rates[mask]) > 1.8
+
+
+@pytest.mark.skipif(
+ MPI.size(MPI.comm_world) > 1,
+ reason="This test cannot be run in parallel.",
+)
+def test_solid_angle_mesh_constraints():
+ cfg = cashocs.io.config.Config()
+ cfg.set("MeshQualityConstraints", "min_angle", "0.175")
+ cfg.set("MeshQualityConstraints", "tol", "1e-2")
+ cfg.set("ShapeGradient", "shape_bdry_fix", "[]")
+ cfg.set("ShapeGradient", "shape_bdry_def", "[1,2,3,4,5,6]")
+
+ mesh, subdomains, boundaries, dx, ds, dS = cashocs.regular_mesh(4, length_z=1.0)
+ bbtree = mesh.bounding_box_tree()
+ rng = np.random.RandomState(300696)
+ VCG = VectorFunctionSpace(mesh, "CG", 1)
+
+ defo = 0.01 * rng.standard_normal(mesh.coordinates().shape)
+ mesh.coordinates()[:, :] += defo
+ bbtree.build(mesh)
+
+ cm = ConstraintManager(cfg, mesh, boundaries, VCG)
+ x = mesh.coordinates().copy().reshape(-1)
+
+ residuals = []
+ epsilons = [1e-4 / 2**i for i in range(4)]
+ h = rng.standard_normal(x.shape)
+ f_k = cm.evaluate(x)
+ gradient = cm._compute_gradient(x)
+ directional_derivative = gradient @ h
+
+ for eps in epsilons:
+ x_mod = x + eps * h[cm.v2d]
+ f_mod = cm.evaluate(x_mod)
+
+ res = abs(f_mod - f_k - eps * directional_derivative)
+ residuals.append(res)
+
+ rates = np.array(compute_convergence_rates(epsilons, residuals)).T
+
+ mask = np.nonzero(residuals[0] > 1e-8)
+ assert np.min(rates[mask]) > 1.8
diff --git a/tests/test_nonlinear_solvers.py b/tests/test_nonlinear_solvers.py
index 74c1fcb8..255ed7ad 100755
--- a/tests/test_nonlinear_solvers.py
+++ b/tests/test_nonlinear_solvers.py
@@ -23,6 +23,8 @@
import numpy as np
import cashocs
+import cashocs._utils
+import cashocs._utils.linalg
def test_newton_solver():
@@ -61,6 +63,40 @@ def test_newton_solver():
assert np.allclose(u.vector()[:], u_fen.vector()[:])
+def test_snes_solver():
+ mesh, _, boundaries, dx, ds, _ = cashocs.regular_mesh(5)
+ V = FunctionSpace(mesh, "CG", 1)
+
+ u = Function(V)
+ u_fen = Function(V)
+ v = TestFunction(V)
+
+ F = (
+ inner(grad(u), grad(v)) * dx
+ + Constant(1e2) * pow(u, 3) * v * dx
+ - Constant(1) * v * dx
+ )
+ bcs = cashocs.create_dirichlet_bcs(V, Constant(0), boundaries, [1, 2, 3, 4])
+
+ solve(F == 0, u, bcs)
+ u_fen.vector().vec().aypx(0.0, u.vector().vec())
+ u_fen.vector().apply("")
+ u.vector().vec().set(0.0)
+ u.vector().apply("")
+
+ petsc_options = {
+ "snes_type": "newtonls",
+ "snes_monitor": None,
+ "snes_atol": 1e-10,
+ "snes_rtol": 1e-9,
+ }
+ petsc_options.update(cashocs._utils.linalg.direct_ksp_options)
+
+ cashocs.snes_solve(F, u, bcs, petsc_options=petsc_options)
+
+ assert np.allclose(u.vector()[:], u_fen.vector()[:])
+
+
def test_newton_linearization(config_sop):
config_sop.set("StateSystem", "is_linear", "False")
config_sop.set("StateSystem", "newton_verbose", "True")
diff --git a/tests/test_remeshing.py b/tests/test_remeshing.py
index a5712292..7892a164 100755
--- a/tests/test_remeshing.py
+++ b/tests/test_remeshing.py
@@ -55,7 +55,6 @@ def test_verification_remeshing():
def mesh_parametrization(mesh_file):
config = cashocs.load_config(f"{dir_path}/config_remesh.ini")
- config.set("Mesh", "mesh_file", dir_path + "/mesh/remesh/mesh.xdmf")
config.set("Mesh", "gmsh_file", dir_path + "/mesh/remesh/mesh.msh")
config.set("Mesh", "geo_file", dir_path + "/mesh/remesh/mesh.geo")
@@ -105,7 +104,6 @@ def test_remeshing():
def mesh_parametrization(mesh_file):
config = cashocs.load_config(f"{dir_path}/config_remesh.ini")
- config.set("Mesh", "mesh_file", dir_path + "/mesh/remesh/mesh.xdmf")
config.set("Mesh", "gmsh_file", dir_path + "/mesh/remesh/mesh.msh")
config.set("Mesh", "geo_file", dir_path + "/mesh/remesh/mesh.geo")
config.set("Output", "result_dir", dir_path + "/temp/")
@@ -168,7 +166,6 @@ def test_remesh_scaling():
def mesh_parametrization(mesh_file):
config = cashocs.load_config(f"{dir_path}/config_remesh.ini")
- config.set("Mesh", "mesh_file", dir_path + "/mesh/remesh/mesh.xdmf")
config.set("Mesh", "gmsh_file", dir_path + "/mesh/remesh/mesh.msh")
config.set("Mesh", "geo_file", dir_path + "/mesh/remesh/mesh.geo")
@@ -208,7 +205,6 @@ def test_remeshing_disabled():
mesh_file = f"{dir_path}/mesh/remesh/mesh.xdmf"
config = cashocs.load_config(f"{dir_path}/config_remesh.ini")
- config.set("Mesh", "mesh_file", dir_path + "/mesh/remesh/mesh.xdmf")
config.set("Mesh", "gmsh_file", dir_path + "/mesh/remesh/mesh.msh")
config.set("Mesh", "geo_file", dir_path + "/mesh/remesh/mesh.geo")
config.set("Mesh", "remesh", "False")
diff --git a/tests/test_shape_optimization.py b/tests/test_shape_optimization.py
index d7fcf2df..7045c766 100755
--- a/tests/test_shape_optimization.py
+++ b/tests/test_shape_optimization.py
@@ -335,58 +335,64 @@ def test_shape_gd():
assert sop.solver.relative_norm < sop.solver.rtol
-def test_shape_cg_fr():
+@pytest.mark.parametrize(
+ "algorithm, expected_iterations",
+ [("gd", 26), ("ncg", 23), ("bfgs", 28)],
+)
+def test_mesh_quality_constraints_min_angle(algorithm, expected_iterations):
config = cashocs.load_config(dir_path + "/config_sop.ini")
- config.set("AlgoCG", "cg_method", "FR")
+ min_angle = 2 * np.pi * 35.0 / 360.0
+ config.set("MeshQualityConstraints", "min_angle", f"{min_angle}")
+ config.set("MeshQualityConstraints", "tol", "1e-2")
mesh.coordinates()[:, :] = initial_coordinates
mesh.bounding_box_tree().build(mesh)
sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config)
- sop.solve(algorithm="ncg", rtol=1e-2, atol=0.0, max_iter=21)
+ sop.solve(algorithm=algorithm, rtol=1e-2, atol=0.0, max_iter=expected_iterations)
assert sop.solver.relative_norm < sop.solver.rtol
-
-def test_shape_cg_pr():
- config = cashocs.load_config(dir_path + "/config_sop.ini")
- config.set("AlgoCG", "cg_method", "PR")
-
- mesh.coordinates()[:, :] = initial_coordinates
- mesh.bounding_box_tree().build(mesh)
- sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config)
- sop.solve(algorithm="ncg", rtol=1e-2, atol=0.0, max_iter=16)
- assert sop.solver.relative_norm < sop.solver.rtol
+ mesh_quality = cashocs.compute_mesh_quality(
+ mesh, quality_type="min", quality_measure="skewness"
+ )
+ assert mesh_quality > 0.5733
-def test_shape_cg_hs():
+@pytest.mark.parametrize(
+ "algorithm, expected_iterations",
+ [("gd", 46), ("ncg", 51), ("bfgs", 56)],
+)
+def test_mesh_quality_constraints_reduction_factor(algorithm, expected_iterations):
config = cashocs.load_config(dir_path + "/config_sop.ini")
- config.set("AlgoCG", "cg_method", "HS")
+ config.set("MeshQualityConstraints", "tol", "1e-2")
+ config.set("MeshQualityConstraints", "feasible_angle_reduction_factor", "0.66")
+ config.set("AlgoCG", "cg_method", "PR")
+ # config.set("AlgoCG", "cg_periodic_restart", "True")
+ # config.set("AlgoCG", "cg_periodic_its", "10")
mesh.coordinates()[:, :] = initial_coordinates
mesh.bounding_box_tree().build(mesh)
sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config)
- sop.solve(algorithm="ncg", rtol=1e-2, atol=0.0, max_iter=18)
+ sop.solve(algorithm=algorithm, rtol=1e-2, atol=0.0, max_iter=expected_iterations)
assert sop.solver.relative_norm < sop.solver.rtol
-
-def test_shape_cg_dy():
- config = cashocs.load_config(dir_path + "/config_sop.ini")
- config.set("AlgoCG", "cg_method", "DY")
-
- mesh.coordinates()[:, :] = initial_coordinates
- mesh.bounding_box_tree().build(mesh)
- sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config)
- sop.solve(algorithm="ncg", rtol=1e-2, atol=0.0, max_iter=18)
- assert sop.solver.relative_norm < sop.solver.rtol
+ mesh_quality = cashocs.compute_mesh_quality(
+ mesh, quality_type="min", quality_measure="skewness"
+ )
+ assert mesh_quality > 0.434
-def test_shape_cg_hz():
+@pytest.mark.parametrize(
+ "method, expected_iterations",
+ [("FR", 21), ("PR", 16), ("HS", 18), ("DY", 18), ("HZ", 18)],
+)
+def test_shape_cg(method, expected_iterations):
config = cashocs.load_config(dir_path + "/config_sop.ini")
- config.set("AlgoCG", "cg_method", "HZ")
+ config.set("AlgoCG", "cg_method", method)
mesh.coordinates()[:, :] = initial_coordinates
mesh.bounding_box_tree().build(mesh)
sop = cashocs.ShapeOptimizationProblem(e, bcs, J, u, p, boundaries, config)
- sop.solve(algorithm="ncg", rtol=1e-2, atol=0.0, max_iter=18)
+ sop.solve(algorithm="ncg", rtol=1e-2, atol=0.0, max_iter=expected_iterations)
assert sop.solver.relative_norm < sop.solver.rtol
diff --git a/tests/test_shape_optimization_space_mapping.py b/tests/test_shape_optimization_space_mapping.py
index 63499f83..89006345 100644
--- a/tests/test_shape_optimization_space_mapping.py
+++ b/tests/test_shape_optimization_space_mapping.py
@@ -97,7 +97,7 @@ def solve_and_evaluate(self):
bc_pressure = DirichletBC(V.sub(1), Constant(0.0), boundaries, 5)
bcs = [bc_in] + bcs_wall + [bc_out] + [bc_pressure]
- cashocs.newton_solve(F, up, bcs, verbose=False)
+ cashocs.snes_solve(F, up, bcs)
J = cashocs.IntegralFunctional(
Constant(0.5) * dot(u - u_des, u - u_des) * ds(5)