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EigenLinearSolvers

SOFA plugin wrapping the Eigen linear solvers into SOFA components

Components

EigenConjugateGradient

This linear solver component is based on Eigen::ConjugateGradient (https://eigen.tuxfamily.org/dox/classEigen_1_1ConjugateGradient.html). Its equivalent in SOFA is CGLinearSolver (without preconditioner), or ShewchukPCGLinearSolver (with preconditioner).

The available templates are:

  • EigenSparseMatrixd
  • CompressedRowSparseMatrixMat3x3d
  • CompressedRowSparseMatrixd

In XML, the declaration of this component looks like:

<EigenConjugateGradient template="EigenSparseMatrixd" iterations="1000" tolerance="1e-9" preconditioner="diagonal"/>

A scene example is available.

EigenSimplicialLDLT

This linear solver component is based on Eigen::SimplicialLDLT (https://eigen.tuxfamily.org/dox/classEigen_1_1SimplicialLDLT.html). Its equivalent in SOFA is SparseLDLSolver.

The available templates are:

  • EigenSparseMatrixd
  • CompressedRowSparseMatrixMat3x3d
  • CompressedRowSparseMatrixd

In XML, the declaration of this component looks like:

<EigenSimplicialLDLT template="CompressedRowSparseMatrixMat3x3d"/>

Scene examples are available:

Choice of the template

EigenConjugateGradient and EigenSimplicialLDLT can have the choice of a template based on an Eigen sparse matrix, or a SOFA type CompressedRowSparseMatrix. Both templates have different approaches and can have an impact on the performances. If possible, the use of CompressedRowSparseMatrixMat3x3d is preferable as it brings significant speed up of the matrix assembly.

Performances

The following measures are given on a indicative basis.

FEMBAR_EigenSimplicialLDLT.scn

Both solvers have been templated with CompressedRowSparseMatrixMat3x3d. The measurements were made without GUI, running 1000 time steps.

Measure SparseLDLSolver EigenSimplicialLDLT
total (s) 3.79887 2.45837
total (FPS) 263.236 406.774
MBKBuild (average ms) 0.53 0.52
MBKSolve (average ms) 3.07 1.74

The scene is available in FEMBAR_EigenSimplicialLDLT.scn.

Cylinder_EigenSimplicialLDLT.scn

Both solvers have been templated with CompressedRowSparseMatrixMat3x3d. The measurements were made without GUI, running 1000 time steps.

Measure SparseLDLSolver EigenSimplicialLDLT
total (s) 13.3605 10.5815
total (FPS) 74.8476 94.5048
MBKBuild (average ms) 5.79 5.84
MBKSolve (average ms) 7.02 4.16

The scene is available in Cylinder_EigenSimplicialLDLT.scn

DiamondRobot.py3scn

Both solvers have been templated with CompressedRowSparseMatrixMat3x3d. The measurements were made without GUI, running 200 time steps.

Measure SparseLDLSolver EigenSimplicialLDLT
total (s) 3.9661 3.30239
total (FPS) 50.4274 60.5622
MBKBuild (average ms) 9.57 9.07
MBKSolve (average ms) 7.75 4.96

The scene is available in DiamondRobot.py3scn.scn

Build Instructions

As any SOFA plugin, follow the build procedure on sofa-framework.org/community/doc/plugins/build-a-plugin-from-sources/