Merge branch 'b_bar_LIE_M' into 'master'

B bar method for M#LIE See merge request ogs/ogs!5084
ufz · Sep 4, 2024 · 66e0c38 · 66e0c38
2 parents 7b03929 + c0d8121
commit 66e0c38
Show file tree

Hide file tree

Showing 48 changed files with 1,801 additions and 22 deletions.
diff --git a/...ion/ProjectFile/prj/processes/process/SMALL_DEFORMATION_WITH_LIE/t_use_b_bar.md b/...ion/ProjectFile/prj/processes/process/SMALL_DEFORMATION_WITH_LIE/t_use_b_bar.md
@@ -0,0 +1 @@
+\copydoc ProcessLib::LIE::SmallDeformation::SmallDeformationProcessData::use_b_bar
diff --git a/ProcessLib/LIE/SmallDeformation/CreateSmallDeformationProcess.cpp b/ProcessLib/LIE/SmallDeformation/CreateSmallDeformationProcess.cpp
@@ -181,10 +181,13 @@ std::unique_ptr<Process> createSmallDeformationProcess(
  config.getConfigParameter<double>(
  "reference_temperature", std::numeric_limits<double>::quiet_NaN());
 
+ //! \ogs_file_param{prj__processes__process__SMALL_DEFORMATION_WITH_LIE__use_b_bar}
+ auto const use_b_bar = config.getConfigParameter<bool>("use_b_bar", false);
+
  SmallDeformationProcessData<DisplacementDim> process_data{
- materialIDs(mesh), std::move(solid_constitutive_relations),
+ materialIDs(mesh),  std::move(solid_constitutive_relations),
  std::move(fracture_model), std::move(fracture_properties),
- reference_temperature};
+ reference_temperature, use_b_bar};
 
  SecondaryVariableCollection secondary_variables;
 

diff --git a/ProcessLib/LIE/SmallDeformation/LocalAssembler/IntegrationPointDataMatrix.h b/ProcessLib/LIE/SmallDeformation/LocalAssembler/IntegrationPointDataMatrix.h
@@ -44,8 +44,8 @@ struct IntegrationPointDataMatrix final
  typename BMatricesType::KelvinMatrixType _C;
  double integration_weight;
 
- typename ShapeMatricesType::NodalRowVectorType N;
- typename ShapeMatricesType::GlobalDimNodalMatrixType dNdx;
+ typename ShapeMatricesType::NodalRowVectorType N_u;
+ typename ShapeMatricesType::GlobalDimNodalMatrixType dNdx_u;
 
  void pushBackState()
  {

diff --git a/ProcessLib/LIE/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrix-impl.h b/ProcessLib/LIE/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrix-impl.h
@@ -67,8 +67,8 @@ SmallDeformationLocalAssemblerMatrix<ShapeFunction, DisplacementDim>::
  _ip_data.emplace_back(solid_material);
  auto& ip_data = _ip_data[ip];
  auto const& sm = shape_matrices[ip];
- ip_data.N = sm.N;
- ip_data.dNdx = sm.dNdx;
+ ip_data.N_u = sm.N;
+ ip_data.dNdx_u = sm.dNdx;
  ip_data.integration_weight =
  _integration_method.getWeightedPoint(ip).getWeight() *
  sm.integralMeasure * sm.detJ;
@@ -115,21 +115,23 @@ void SmallDeformationLocalAssemblerMatrix<ShapeFunction, DisplacementDim>::
  ParameterLib::SpatialPosition x_position;
  x_position.setElementID(_element.getID());
 
+ auto const B_dil_bar = getDilatationalBBarMatrix();
+
  for (unsigned ip = 0; ip < n_integration_points; ip++)
  {
  x_position.setIntegrationPoint(ip);
  auto const& w = _ip_data[ip].integration_weight;
 
- auto const& N = _ip_data[ip].N;
- auto const& dNdx = _ip_data[ip].dNdx;
+ auto const& N = _ip_data[ip].N_u;
+ auto const& dNdx = _ip_data[ip].dNdx_u;
  auto const x_coord =
  NumLib::interpolateXCoordinate<ShapeFunction, ShapeMatricesType>(
  _element, N);
- auto const B =
-   LinearBMatrix::computeBMatrix<DisplacementDim,
-  ShapeFunction::NPOINTS,
-  typename BMatricesType::BMatrixType>(
- dNdx, N, x_coord, _is_axially_symmetric);
+
+ auto const B = LinearBMatrix::computeBMatrixPossiblyWithBbar<
+ DisplacementDim, ShapeFunction::NPOINTS, BBarMatrixType,
+ typename BMatricesType::BMatrixType>(dNdx, N, B_dil_bar, x_coord,
+  this->_is_axially_symmetric);
 
  auto const& eps_prev = _ip_data[ip]._eps_prev;
  auto const& sigma_prev = _ip_data[ip]._sigma_prev;

diff --git a/ProcessLib/LIE/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrix.h b/ProcessLib/LIE/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrix.h
@@ -10,6 +10,7 @@
 
 #pragma once
 
+#include <optional>
 #include <vector>
 
 #include "IntegrationPointDataMatrix.h"
@@ -41,6 +42,7 @@ class SmallDeformationLocalAssemblerMatrix
  using NodalVectorType = typename ShapeMatricesType::NodalVectorType;
  using ShapeMatrices = typename ShapeMatricesType::ShapeMatrices;
  using BMatricesType = BMatrixPolicyType<ShapeFunction, DisplacementDim>;
+ using BBarMatrixType = typename BMatricesType::BBarMatrixType;
 
  using StiffnessMatrixType = typename BMatricesType::StiffnessMatrixType;
  using NodalForceVectorType = typename BMatricesType::NodalForceVectorType;
@@ -148,6 +150,20 @@ class SmallDeformationLocalAssemblerMatrix
  MeshLib::Element const& _element;
  bool const _is_axially_symmetric;
  SecondaryData<typename ShapeMatrices::ShapeType> _secondary_data;
+
+ std::optional<BBarMatrixType> getDilatationalBBarMatrix() const
+ {
+ if (!(_process_data.use_b_bar))
+ {
+ return std::nullopt;
+ }
+
+ return LinearBMatrix::computeDilatationalBbar<
+ DisplacementDim, ShapeFunction::NPOINTS, ShapeFunction,
+ BBarMatrixType, ShapeMatricesType, IntegrationPointDataType>(
+ _ip_data, this->_element, this->_integration_method,
+ this->_is_axially_symmetric);
+ }
 };
 
 } // namespace SmallDeformation

diff --git a/...E/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrixNearFracture-impl.h b/...E/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrixNearFracture-impl.h
@@ -82,8 +82,8 @@ SmallDeformationLocalAssemblerMatrixNearFracture<ShapeFunction,
  _ip_data.emplace_back(solid_material);
  auto& ip_data = _ip_data[ip];
  auto const& sm = shape_matrices[ip];
- ip_data.N = sm.N;
- ip_data.dNdx = sm.dNdx;
+ ip_data.N_u = sm.N;
+ ip_data.dNdx_u = sm.dNdx;
  ip_data.integration_weight =
  _integration_method.getWeightedPoint(ip).getWeight() *
  sm.integralMeasure * sm.detJ;
@@ -201,15 +201,17 @@ void SmallDeformationLocalAssemblerMatrixNearFracture<
  ParameterLib::SpatialPosition x_position;
  x_position.setElementID(_element.getID());
 
+ auto const B_dil_bar = getDilatationalBBarMatrix();
+
  for (unsigned ip = 0; ip < n_integration_points; ip++)
  {
  x_position.setIntegrationPoint(ip);
 
  auto& ip_data = _ip_data[ip];
  auto const& w = _ip_data[ip].integration_weight;
 
- auto const& N = ip_data.N;
- auto const& dNdx = ip_data.dNdx;
+ auto const& N = ip_data.N_u;
+ auto const& dNdx = ip_data.dNdx_u;
 
  // levelset functions
  Eigen::Vector3d const ip_physical_coords(
@@ -229,11 +231,10 @@ void SmallDeformationLocalAssemblerMatrixNearFracture<
  auto const x_coord =
  NumLib::interpolateXCoordinate<ShapeFunction, ShapeMatricesType>(
  _element, N);
- auto const B =
- LinearBMatrix::computeBMatrix<DisplacementDim,
- ShapeFunction::NPOINTS,
- typename BMatricesType::BMatrixType>(
- dNdx, N, x_coord, _is_axially_symmetric);
+ auto const B = LinearBMatrix::computeBMatrixPossiblyWithBbar<
+ DisplacementDim, ShapeFunction::NPOINTS, BBarMatrixType,
+ typename BMatricesType::BMatrixType>(dNdx, N, B_dil_bar, x_coord,
+ this->_is_axially_symmetric);
 
  // strain, stress
  auto const& eps_prev = ip_data._eps_prev;

diff --git a/...ib/LIE/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrixNearFracture.h b/...ib/LIE/SmallDeformation/LocalAssembler/SmallDeformationLocalAssemblerMatrixNearFracture.h
@@ -44,6 +44,7 @@ class SmallDeformationLocalAssemblerMatrixNearFracture
  using NodalVectorType = typename ShapeMatricesType::NodalVectorType;
  using ShapeMatrices = typename ShapeMatricesType::ShapeMatrices;
  using BMatricesType = BMatrixPolicyType<ShapeFunction, DisplacementDim>;
+ using BBarMatrixType = typename BMatricesType::BBarMatrixType;
 
  using BMatrixType = typename BMatricesType::BMatrixType;
  using StiffnessMatrixType = typename BMatricesType::StiffnessMatrixType;
@@ -158,6 +159,20 @@ class SmallDeformationLocalAssemblerMatrixNearFracture
  MeshLib::Element const& _element;
  bool const _is_axially_symmetric;
  SecondaryData<typename ShapeMatrices::ShapeType> _secondary_data;
+
+ std::optional<BBarMatrixType> getDilatationalBBarMatrix() const
+ {
+ if (!(_process_data.use_b_bar))
+ {
+ return std::nullopt;
+ }
+
+ return LinearBMatrix::computeDilatationalBbar<
+ DisplacementDim, ShapeFunction::NPOINTS, ShapeFunction,
+ BBarMatrixType, ShapeMatricesType, IntegrationPointDataType>(
+ _ip_data, this->_element, this->_integration_method,
+ this->_is_axially_symmetric);
+ }
 };
 
 } // namespace SmallDeformation

diff --git a/ProcessLib/LIE/SmallDeformation/SmallDeformationProcessData.h b/ProcessLib/LIE/SmallDeformation/SmallDeformationProcessData.h
@@ -46,6 +46,10 @@ struct SmallDeformationProcessData
 
  double const reference_temperature;
 
+ /// An indicator to use the B bar method \cite hughes1980generalization to
+ /// tackle the volumetric locking.
+ const bool use_b_bar;
+
  std::vector<JunctionProperty> junction_properties = {};
 
  MeshLib::PropertyVector<int> const* mesh_prop_materialIDs = nullptr;

diff --git a/ProcessLib/LIE/SmallDeformation/Tests.cmake b/ProcessLib/LIE/SmallDeformation/Tests.cmake
@@ -142,3 +142,20 @@ AddTest(
  sfrac_ts_1_t_1.000000.vtu sfrac_ts_1_t_1.000000.vtu displacement_jump4 displacement_jump4 1e-16 1e-16
  sfrac_ts_1_t_1.000000.vtu sfrac_ts_1_t_1.000000.vtu fracture_stress_avg fracture_stress_avg 1e-6 5e-6
 )
+
+AddTest(
+ NAME LIE_M_great_cell_2D_point_injection_embedded_fracture_F_PMMA
+ PATH LIE/Mechanics/GreatCellWithBBar
+ EXECUTABLE ogs
+ EXECUTABLE_ARGS mechanics_embedded_fracture_F.prj
+ WRAPPER time
+ TESTER vtkdiff
+ REQUIREMENTS NOT OGS_USE_MPI
+ DIFF_DATA
+ mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu displacement displacement 1e-15 1e-15
+ mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu displacement_jump1 displacement_jump1 1e-15 1e-15
+ mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu sigma sigma 1e-8 1e-11
+ mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu epsilon epsilon 1e-15 1e-15
+ mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu fracture_stress fracture_stress 5e-8 1e-11
+ mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu mechanics_embedded_fracture_F_PMMA_ts_1_t_1.000000.vtu fracture_aperture fracture_aperture 1e-15 1e-15
+)
diff --git a/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG1.vtu b/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG1.vtu
@@ -0,0 +1,24 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <Piece NumberOfPoints="9" NumberOfCells="8" >
+ <PointData>
+ <DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="0" RangeMax="239" offset="0" />
+ </PointData>
+ <CellData>
+ <DataArray type="UInt64" Name="bulk_element_ids" format="appended" RangeMin="2063" RangeMax="2129" offset="108" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0.09894003955" RangeMax="0.1" offset="204" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="504" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="688" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="784" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
+ _SAAAAAAAAAAAAAAAAAAAAAEAAAAAAAAAAgAAAAAAAADqAAAAAAAAAOsAAAAAAAAA7AAAAAAAAADtAAAAAAAAAO4AAAAAAAAA7wAAAAAAAAA=QAAAAAAAAAAPCAAAAAAAAFEIAAAAAAAAUAgAAAAAAAA/CAAAAAAAAD4IAAAAAAAARggAAAAAAABHCAAAAAAAABgIAAAAAAAA2AAAAAAAAADJkCFqIlS5P2UE5tVZvY2/AAAAAAAAAADJkCFqIlS5PwAAAAAAAAAAAAAAAAAAAADJkCFqIlS5P2UE5tVZvY0/AAAAAAAAAADJkCFqIlS5P8GSbGADToa/AAAAAAAAAADJkCFqIlS5P9tW5tVZvX2/AAAAAAAAAADJkCFqIlS5PxtW5tVZvW2/AAAAAAAAAADJkCFqIlS5Pya45dVZvW0/AAAAAAAAAADJkCFqIlS5P6yv5dVZvX0/AAAAAAAAAADJkCFqIlS5P0xubGADToY/AAAAAAAAAAA=gAAAAAAAAAAAAAAAAAAAAAMAAAAAAAAAAwAAAAAAAAAEAAAAAAAAAAQAAAAAAAAABQAAAAAAAAAFAAAAAAAAAAEAAAAAAAAAAQAAAAAAAAAGAAAAAAAAAAYAAAAAAAAABwAAAAAAAAAHAAAAAAAAAAgAAAAAAAAACAAAAAAAAAACAAAAAAAAAA==QAAAAAAAAAACAAAAAAAAAAQAAAAAAAAABgAAAAAAAAAIAAAAAAAAAAoAAAAAAAAADAAAAAAAAAAOAAAAAAAAABAAAAAAAAAACAAAAAAAAAADAwMDAwMDAw==
+ </AppendedData>
+</VTKFile>
diff --git a/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG10.vtu b/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG10.vtu
@@ -0,0 +1,24 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <Piece NumberOfPoints="9" NumberOfCells="8" >
+ <PointData>
+ <DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="28" RangeMax="295" offset="0" />
+ </PointData>
+ <CellData>
+ <DataArray type="UInt64" Name="bulk_element_ids" format="appended" RangeMin="2176" RangeMax="2211" offset="108" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0.09894003955" RangeMax="0.1" offset="204" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="504" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="688" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="784" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
+ _SAAAAAAAAAAcAAAAAAAAAB0AAAAAAAAAHgAAAAAAAAAiAQAAAAAAACMBAAAAAAAAJAEAAAAAAAAlAQAAAAAAACYBAAAAAAAAJwEAAAAAAAA=QAAAAAAAAACACAAAAAAAAJQIAAAAAAAAnwgAAAAAAACXCAAAAAAAAJ0IAAAAAAAAowgAAAAAAACVCAAAAAAAAIEIAAAAAAAA2AAAAAAAAABzpaYFX/q1v/tNHUgyQao/AAAAAAAAAAAKV18gj2a3v1R/Kdy9YqM/AAAAAAAAAAChCBg7v9K4v1tha+CSCJk/AAAAAAAAAAA30VQMa1W2v11dIC2Viag/AAAAAAAAAADI/AITd7C2v7VtIxL40aY/AAAAAAAAAADgKbEZgwu3v692JvdaGqU/AAAAAAAAAACNgg0nm8G3v/KPLMEgq6E/AAAAAAAAAAD5rbstpxy4v/1BX0wH558/AAAAAAAAAAAr22k0s3e4v/ZSZRbNd5w/AAAAAAAAAAA=gAAAAAAAAAAAAAAAAAAAAAMAAAAAAAAAAwAAAAAAAAAEAAAAAAAAAAQAAAAAAAAABQAAAAAAAAAFAAAAAAAAAAEAAAAAAAAAAQAAAAAAAAAGAAAAAAAAAAYAAAAAAAAABwAAAAAAAAAHAAAAAAAAAAgAAAAAAAAACAAAAAAAAAACAAAAAAAAAA==QAAAAAAAAAACAAAAAAAAAAQAAAAAAAAABgAAAAAAAAAIAAAAAAAAAAoAAAAAAAAADAAAAAAAAAAOAAAAAAAAABAAAAAAAAAACAAAAAAAAAADAwMDAwMDAw==
+ </AppendedData>
+</VTKFile>
diff --git a/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG11.vtu b/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG11.vtu
@@ -0,0 +1,24 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <Piece NumberOfPoints="9" NumberOfCells="8" >
+ <PointData>
+ <DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="24" RangeMax="287" offset="0" />
+ </PointData>
+ <CellData>
+ <DataArray type="UInt64" Name="bulk_element_ids" format="appended" RangeMin="2071" RangeMax="2145" offset="108" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0.09894003955" RangeMax="0.1" offset="204" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="504" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="688" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="784" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
+ _SAAAAAAAAAAYAAAAAAAAABkAAAAAAAAAGgAAAAAAAAAaAQAAAAAAABsBAAAAAAAAHAEAAAAAAAAdAQAAAAAAAB4BAAAAAAAAHwEAAAAAAAA=QAAAAAAAAAAXCAAAAAAAAFwIAAAAAAAAXggAAAAAAABdCAAAAAAAAF8IAAAAAAAAYAgAAAAAAABhCAAAAAAAABwIAAAAAAAA2AAAAAAAAAD91I58FpCuvyWq4SzoibQ/AAAAAAAAAABSipS1+eixv1KKlLX56LE/AAAAAAAAAAAlquEs6Im0v/3UjnwWkK4/AAAAAAAAAAC1YDW4jeCvv0lkDo+s4bM/AAAAAAAAAAB09e15gpiwvzAfO/FwObM/AAAAAAAAAAAUQMEXvkCxv5DUZ1M1kbI/AAAAAAAAAADx0GdTNZGyv7NDwRe+QLE/AAAAAAAAAAAvFzvxcDmzv3X97XmCmLA/AAAAAAAAAACFXw6PrOGzvz1qNbiN4K8/AAAAAAAAAAA=gAAAAAAAAAAAAAAAAAAAAAMAAAAAAAAAAwAAAAAAAAAEAAAAAAAAAAQAAAAAAAAABQAAAAAAAAAFAAAAAAAAAAEAAAAAAAAAAQAAAAAAAAAGAAAAAAAAAAYAAAAAAAAABwAAAAAAAAAHAAAAAAAAAAgAAAAAAAAACAAAAAAAAAACAAAAAAAAAA==QAAAAAAAAAACAAAAAAAAAAQAAAAAAAAABgAAAAAAAAAIAAAAAAAAAAoAAAAAAAAADAAAAAAAAAAOAAAAAAAAABAAAAAAAAAACAAAAAAAAAADAwMDAwMDAw==
+ </AppendedData>
+</VTKFile>
diff --git a/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG12.vtu b/Tests/Data/LIE/Mechanics/GreatCellWithBBar/2D_BAG12.vtu
@@ -0,0 +1,24 @@
+<?xml version="1.0"?>
+<VTKFile type="UnstructuredGrid" version="1.0" byte_order="LittleEndian" header_type="UInt64">
+ <UnstructuredGrid>
+ <Piece NumberOfPoints="9" NumberOfCells="8" >
+ <PointData>
+ <DataArray type="UInt64" Name="bulk_node_ids" format="appended" RangeMin="20" RangeMax="279" offset="0" />
+ </PointData>
+ <CellData>
+ <DataArray type="UInt64" Name="bulk_element_ids" format="appended" RangeMin="2174" RangeMax="2213" offset="108" />
+ </CellData>
+ <Points>
+ <DataArray type="Float64" Name="Points" NumberOfComponents="3" format="appended" RangeMin="0.09894003955" RangeMax="0.1" offset="204" />
+ </Points>
+ <Cells>
+ <DataArray type="Int64" Name="connectivity" format="appended" RangeMin="" RangeMax="" offset="504" />
+ <DataArray type="Int64" Name="offsets" format="appended" RangeMin="" RangeMax="" offset="688" />
+ <DataArray type="UInt8" Name="types" format="appended" RangeMin="" RangeMax="" offset="784" />
+ </Cells>
+ </Piece>
+ </UnstructuredGrid>
+ <AppendedData encoding="base64">
+ _SAAAAAAAAAAUAAAAAAAAABUAAAAAAAAAFgAAAAAAAAASAQAAAAAAABMBAAAAAAAAFAEAAAAAAAAVAQAAAAAAABYBAAAAAAAAFwEAAAAAAAA=QAAAAAAAAAB+CAAAAAAAAJIIAAAAAAAAoQgAAAAAAACZCAAAAAAAAJsIAAAAAAAApQgAAAAAAACTCAAAAAAAAH8IAAAAAAAA2AAAAAAAAABbYWvgkgiZv6EIGDu/0rg/AAAAAAAAAABUfyncvWKjvwpXXyCPZrc/AAAAAAAAAAD7TR1IMkGqv3OlpgVf+rU/AAAAAAAAAABEQmUWzXecv+XcaTSzd7g/AAAAAAAAAACwHF9MB+efv9axuy2nHLg/AAAAAAAAAADOhyzBIKuhvzyEDSebwbc/AAAAAAAAAABobSb3Whqlv8wrsRmDC7c/AAAAAAAAAABgWyMS+NGmv5UAAxN3sLY/AAAAAAAAAAAxVCAtlYmovx3TVAxrVbY/AAAAAAAAAAA=gAAAAAAAAAAAAAAAAAAAAAMAAAAAAAAAAwAAAAAAAAAEAAAAAAAAAAQAAAAAAAAABQAAAAAAAAAFAAAAAAAAAAEAAAAAAAAAAQAAAAAAAAAGAAAAAAAAAAYAAAAAAAAABwAAAAAAAAAHAAAAAAAAAAgAAAAAAAAACAAAAAAAAAACAAAAAAAAAA==QAAAAAAAAAACAAAAAAAAAAQAAAAAAAAABgAAAAAAAAAIAAAAAAAAAAoAAAAAAAAADAAAAAAAAAAOAAAAAAAAABAAAAAAAAAACAAAAAAAAAADAwMDAwMDAw==
+ </AppendedData>
+</VTKFile>