Vega FEM Library (v1.1) User's Manual - University of Southern ...

internal forces and stiffness matrices for arbitrary deformed object configurations. Let us use the corotational
linear FEM model. Because that model only supports tet meshes, we need to first check if the mesh is indeed
a TetMesh.
#include "corotationalLinearFEM.h"
...
TetMesh * tetMesh;
if (volumetricMesh->getElementType() == VolumetricMesh::TET)
tetMesh = (TetMesh*) volumetricMesh; // such down-casting is safe in Vega
else
{
printf("Error: not a tet mesh.\n");
exit(1);
}
CorotationalLinearFEM * deformableModel = new CorotationalLinearFEM(tetMesh);
Note that the down-casting can be avoided if the mesh is known to be a tet mesh: simply initialize
TetMesh directly using the constructor in the TetMesh class. We now have a valid deformable model, and
it is possible to query internal forces and tangent stiffness matrices in any mesh configuration. Typically,
we want to timestep the model in time, however, so let’s proceed with building an integrator for the model.
We need to first create a ForceModel object, to connect our deformable model to an integrator. We also
need the mass matrix, and specify which model vertices (if any) are to be fixed. Then, we can initialize the
integrator. Let us use the implicit backward Euler integrator. Note that the sparse linear system solver to
use for implicit integration is selected by editing the file ”integratorSolverSelection.h” inside the Integrator
library. The default selection is to use Vega’s conjugate gradient solver.
#include "corotationalLinearFEMForceModel.h"
#include "generateMassMatrix.h"
#include "implicitBackwardEulerSparse.h"
...
// create the class to connect the deformable model to the integrator
ForceModel * forceModel = new CorotationalLinearFEMForceModel(deformableModel);
int r = 3 * tetMesh->getNumVertices(); // total number of DOFs
double timestep = 0.0333; // the timestep
SparseMatrix * massMatrix;
// create consistent (non-lumped) mass matrix
GenerateMassMatrix::computeMassMatrix(tetMesh, &massMatrix, true);
// This option only affects PARDISO and SPOOLES solvers, where it is best
// to keep it at 0, which implies a symmetric, non-PD solve.
// With CG, this option is ignored.
int positiveDefiniteSolver = 0;
// constraining vertices 4, 10, 14 (constrained DOFs are specified 0-indexed):
int numConstrainedDOFs = 9;
int constrainedDOFs[9] = { 12, 13, 14, 30, 31, 32, 42, 43, 44 };
// (tangential) Rayleigh damping
double dampingMassCoef = 0.0; // "underwater"-like damping (here turned off)
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