v0.9.0
testing_jacobian_of_hook_scaled_with_density_element.cpp

Testing implementation of Hook element by verifying tangent stiffness matrix. Test like this is an example of how to verify the implementation of Jacobian.

/** \file testing_jacobian_of_hook_scaled_with_density_element.cpp
* \example testing_jacobian_of_hook_scaled_with_density_element.cpp
Testing implementation of Hook element by verifying tangent stiffness matrix.
Test like this is an example of how to verify the implementation of Jacobian.
*/
/* MoFEM is free software: you can redistribute it and/or modify it under
* the terms of the GNU Lesser General Public License as published by the
* Free Software Foundation, either version 3 of the License, or (at your
* option) any later version.
*
* MoFEM 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 Lesser General Public
* License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
#include <BasicFiniteElements.hpp>
using namespace boost::numeric;
using namespace MoFEM;
static char help[] = "\n";
template <bool ALE>
struct OpGetDensityField : public HookeElement::VolUserDataOperator {
boost::shared_ptr<MatrixDouble> matCoordsPtr;
boost::shared_ptr<VectorDouble> rhoAtGaussPtsPtr;
boost::shared_ptr<MatrixDouble> rhoGradAtGaussPtsPtr;
OpGetDensityField(const std::string row_field,
boost::shared_ptr<MatrixDouble> mat_coords_ptr,
boost::shared_ptr<VectorDouble> density_at_pts,
boost::shared_ptr<MatrixDouble> rho_grad_at_gauss_pts_ptr)
: HookeElement::VolUserDataOperator(row_field, OPROW),
matCoordsPtr(mat_coords_ptr), rhoAtGaussPtsPtr(density_at_pts),
rhoGradAtGaussPtsPtr(rho_grad_at_gauss_pts_ptr) {}
MoFEMErrorCode doWork(int row_side, EntityType row_type,
HookeElement::EntData &row_data) {
MoFEMFunctionBegin;
if (row_type != MBVERTEX)
MoFEMFunctionReturnHot(0);
// get number of integration points
const int nb_integration_pts = getGaussPts().size2();
rhoAtGaussPtsPtr->resize(nb_integration_pts, false);
rhoAtGaussPtsPtr->clear();
rhoGradAtGaussPtsPtr->resize(3, nb_integration_pts, false);
rhoGradAtGaussPtsPtr->clear();
auto t_rho = getFTensor0FromVec(*rhoAtGaussPtsPtr);
auto t_grad_rho = getFTensor1FromMat<3>(*rhoGradAtGaussPtsPtr);
MatrixDouble coords;
if (ALE)
coords = *matCoordsPtr;
else
coords = trans(getCoordsAtGaussPts()); // because the size is (nb_gg,3)
FTensor::Index<'i', 3> i;
auto t_coords = getFTensor1FromMat<3>(coords);
for (int gg = 0; gg != nb_integration_pts; ++gg) {
t_rho = 1 + t_coords(i) * t_coords(i); // density is equal to
// 1+x^2+y^2+z^2 (x,y,z coordines)
t_grad_rho(i) = 2 * t_coords(i);
++t_rho;
++t_coords;
++t_grad_rho;
}
MoFEMFunctionReturn(0);
}
};
int main(int argc, char *argv[]) {
// Initialize MoFEM
MoFEM::Core::Initialize(&argc, &argv, (char *)0, help);
// Create mesh database
moab::Core mb_instance; // create database
moab::Interface &moab = mb_instance; // create interface to database
try {
// Create MoFEM database and link it to MoAB
MoFEM::Core core(moab);
MoFEM::Interface &m_field = core;
PetscBool ale = PETSC_FALSE;
CHKERR PetscOptionsGetBool(PETSC_NULL, "", "-ale", &ale, PETSC_NULL);
PetscBool test_jacobian = PETSC_FALSE;
CHKERR PetscOptionsGetBool(PETSC_NULL, "", "-test_jacobian", &test_jacobian,
PETSC_NULL);
CHKERR DMRegister_MoFEM("DMMOFEM");
Simple *si = m_field.getInterface<MoFEM::Simple>();
CHKERR si->getOptions();
CHKERR si->loadFile();
CHKERR si->addDomainField("x", H1, AINSWORTH_LEGENDRE_BASE, 3);
const int order = 2;
CHKERR si->setFieldOrder("x", order);
if (ale == PETSC_TRUE) {
CHKERR si->addDomainField("X", H1, AINSWORTH_LEGENDRE_BASE, 3);
CHKERR si->setFieldOrder("X", 2);
}
CHKERR si->setUp();
// create DM
DM dm;
CHKERR si->getDM(&dm);
// Projection on "x" field
{
Projection10NodeCoordsOnField ent_method(m_field, "x");
CHKERR m_field.loop_dofs("x", ent_method);
// CHKERR m_field.getInterface<FieldBlas>()->fieldScale(1.5, "x");
}
// Project coordinates on "X" field
if (ale == PETSC_TRUE) {
Projection10NodeCoordsOnField ent_method(m_field, "X");
CHKERR m_field.loop_dofs("X", ent_method);
// CHKERR m_field.getInterface<FieldBlas>()->fieldScale(1.5, "X");
}
boost::shared_ptr<ForcesAndSourcesCore> fe_lhs_ptr(
new VolumeElementForcesAndSourcesCore(m_field));
boost::shared_ptr<ForcesAndSourcesCore> fe_rhs_ptr(
new VolumeElementForcesAndSourcesCore(m_field));
struct VolRule {
int operator()(int, int, int) const { return 2 * (order - 1); }
};
fe_lhs_ptr->getRuleHook = VolRule();
fe_rhs_ptr->getRuleHook = VolRule();
CHKERR DMMoFEMSNESSetJacobian(dm, si->getDomainFEName(), fe_lhs_ptr,
nullptr, nullptr);
CHKERR DMMoFEMSNESSetFunction(dm, si->getDomainFEName(), fe_rhs_ptr,
nullptr, nullptr);
using BlockData = NonlinearElasticElement::BlockData;
boost::shared_ptr<map<int, BlockData>> block_sets_ptr =
boost::make_shared<map<int, BlockData>>();
(*block_sets_ptr)[0].iD = 0;
(*block_sets_ptr)[0].E = 1;
(*block_sets_ptr)[0].PoissonRatio = 0.25;
CHKERR m_field.get_finite_element_entities_by_dimension(
si->getDomainFEName(), 3, (*block_sets_ptr)[0].tEts);
// Parameters for density
const double rho_n = 2.0;
const double rho_0 = 0.5;
auto my_operators = [&](boost::shared_ptr<ForcesAndSourcesCore> &fe_lhs_ptr,
boost::shared_ptr<ForcesAndSourcesCore> &fe_rhs_ptr,
boost::shared_ptr<map<int, BlockData>>
&block_sets_ptr,
const std::string x_field,
const std::string X_field, const bool ale,
const bool field_disp) {
MoFEMFunctionBeginHot;
boost::shared_ptr<HookeElement::DataAtIntegrationPts> data_at_pts(
new HookeElement::DataAtIntegrationPts());
boost::shared_ptr<MatrixDouble> mat_coords_ptr =
boost::make_shared<MatrixDouble>();
boost::shared_ptr<VectorDouble> rho_at_gauss_pts_ptr =
boost::make_shared<VectorDouble>();
boost::shared_ptr<MatrixDouble> rho_grad_at_gauss_pts_ptr =
boost::make_shared<MatrixDouble>();
if (fe_lhs_ptr) {
if (ale == PETSC_FALSE) {
fe_lhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldValues<3>(x_field, mat_coords_ptr));
fe_lhs_ptr->getOpPtrVector().push_back(new OpGetDensityField<false>(
x_field, mat_coords_ptr, rho_at_gauss_pts_ptr,
rho_grad_at_gauss_pts_ptr));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStiffnessScaledByDensityField(
x_field, x_field, block_sets_ptr, data_at_pts,
rho_at_gauss_pts_ptr, rho_n, rho_0));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpLhs_dx_dx<1>(x_field, x_field, data_at_pts));
} else {
fe_lhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldGradient<3, 3>(X_field,
data_at_pts->HMat));
fe_lhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldValues<3>(X_field, mat_coords_ptr));
fe_lhs_ptr->getOpPtrVector().push_back(new OpGetDensityField<true>(
X_field, mat_coords_ptr, rho_at_gauss_pts_ptr,
rho_grad_at_gauss_pts_ptr));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStiffnessScaledByDensityField(
x_field, x_field, block_sets_ptr, data_at_pts,
rho_at_gauss_pts_ptr, rho_n, rho_0));
fe_lhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldGradient<3, 3>(x_field,
data_at_pts->hMat));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStrainAle(x_field, x_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStress<1>(x_field, x_field,
data_at_pts)); // FIXME:
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhs_dx_dx<1>(x_field, x_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhs_dx_dX<1>(x_field, X_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateEnergy(X_field, X_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateEshelbyStress(X_field, X_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhs_dX_dX<1>(X_field, X_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhsPre_dX_dx<1>(X_field, x_field,
data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhs_dX_dx(X_field, x_field, data_at_pts));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhsWithDensity_dx_dX(
x_field, X_field, data_at_pts, rho_at_gauss_pts_ptr,
rho_grad_at_gauss_pts_ptr, rho_n, rho_0));
fe_lhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleLhsWithDensity_dX_dX(
X_field, X_field, data_at_pts, rho_at_gauss_pts_ptr,
rho_grad_at_gauss_pts_ptr, rho_n, rho_0));
}
}
if (fe_rhs_ptr) {
if (ale == PETSC_FALSE) {
fe_rhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldGradient<3, 3>(x_field,
data_at_pts->hMat));
fe_rhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldValues<3>(x_field, mat_coords_ptr));
fe_rhs_ptr->getOpPtrVector().push_back(new OpGetDensityField<false>(
x_field, mat_coords_ptr, rho_at_gauss_pts_ptr,
rho_grad_at_gauss_pts_ptr));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStiffnessScaledByDensityField(
x_field, x_field, block_sets_ptr, data_at_pts,
rho_at_gauss_pts_ptr, rho_n, rho_0));
if (field_disp) {
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStrain<1>(x_field, x_field,
data_at_pts));
} else {
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStrain<0>(x_field, x_field,
data_at_pts));
}
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStress<1>(x_field, x_field,
data_at_pts));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpRhs_dx(x_field, x_field, data_at_pts));
} else {
fe_rhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldGradient<3, 3>(X_field,
data_at_pts->HMat));
fe_rhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldValues<3>(X_field, mat_coords_ptr));
fe_rhs_ptr->getOpPtrVector().push_back(new OpGetDensityField<true>(
X_field, mat_coords_ptr, rho_at_gauss_pts_ptr,
rho_grad_at_gauss_pts_ptr));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStiffnessScaledByDensityField(
x_field, x_field, block_sets_ptr, data_at_pts,
rho_at_gauss_pts_ptr, rho_n, rho_0));
fe_rhs_ptr->getOpPtrVector().push_back(
new OpCalculateVectorFieldGradient<3, 3>(x_field,
data_at_pts->hMat));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStrainAle(x_field, x_field,
data_at_pts));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateStress<1>(x_field, x_field,
data_at_pts));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleRhs_dx(x_field, x_field, data_at_pts));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateEnergy(X_field, X_field,
data_at_pts));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpCalculateEshelbyStress(X_field, X_field,
data_at_pts));
fe_rhs_ptr->getOpPtrVector().push_back(
new HookeElement::OpAleRhs_dX(X_field, X_field, data_at_pts));
}
}
MoFEMFunctionReturnHot(0);
};
CHKERR my_operators(fe_lhs_ptr, fe_rhs_ptr, block_sets_ptr, "x", "X", ale,
false);
Vec x, f;
CHKERR DMCreateGlobalVector(dm, &x);
CHKERR VecDuplicate(x, &f);
CHKERR DMoFEMMeshToLocalVector(dm, x, INSERT_VALUES, SCATTER_FORWARD);
// CHKERR VecDuplicate(x, &dx);
// PetscRandom rctx;
// PetscRandomCreate(PETSC_COMM_WORLD, &rctx);
// VecSetRandom(dx, rctx);
// PetscRandomDestroy(&rctx);
// CHKERR DMoFEMMeshToGlobalVector(dm, x, INSERT_VALUES, SCATTER_REVERSE);
Mat A, fdA;
CHKERR DMCreateMatrix(dm, &A);
CHKERR MatDuplicate(A, MAT_DO_NOT_COPY_VALUES, &fdA);
if (test_jacobian == PETSC_TRUE) {
char testing_options[] =
"-snes_test_jacobian -snes_test_jacobian_display "
"-snes_no_convergence_test -snes_atol 0 -snes_rtol 0 -snes_max_it 1 "
"-pc_type none";
CHKERR PetscOptionsInsertString(NULL, testing_options);
} else {
char testing_options[] = "-snes_no_convergence_test -snes_atol 0 "
"-snes_rtol 0 -snes_max_it 1 -pc_type none";
CHKERR PetscOptionsInsertString(NULL, testing_options);
}
SNES snes;
CHKERR SNESCreate(PETSC_COMM_WORLD, &snes);
MoFEM::SnesCtx *snes_ctx;
CHKERR DMMoFEMGetSnesCtx(dm, &snes_ctx);
CHKERR SNESSetFunction(snes, f, SnesRhs, snes_ctx);
CHKERR SNESSetJacobian(snes, A, A, SnesMat, snes_ctx);
CHKERR SNESSetFromOptions(snes);
CHKERR SNESSolve(snes, NULL, x);
if (test_jacobian == PETSC_FALSE) {
double nrm_A0;
CHKERR MatNorm(A, NORM_INFINITY, &nrm_A0);
char testing_options_fd[] = "-snes_fd";
CHKERR PetscOptionsInsertString(NULL, testing_options_fd);
CHKERR SNESSetFunction(snes, f, SnesRhs, snes_ctx);
CHKERR SNESSetJacobian(snes, fdA, fdA, SnesMat, snes_ctx);
CHKERR SNESSetFromOptions(snes);
CHKERR SNESSolve(snes, NULL, x);
CHKERR MatAXPY(A, -1, fdA, SUBSET_NONZERO_PATTERN);
double nrm_A;
CHKERR MatNorm(A, NORM_INFINITY, &nrm_A);
PetscPrintf(PETSC_COMM_WORLD, "Matrix norms %3.4e %3.4e\n", nrm_A,
nrm_A / nrm_A0);
nrm_A /= nrm_A0;
const double tol = 1e-5;
if (nrm_A > tol) {
SETERRQ(PETSC_COMM_WORLD, MOFEM_ATOM_TEST_INVALID,
"Difference between hand-calculated tangent matrix and finite "
"difference matrix is too big");
}
}
CHKERR VecDestroy(&x);
CHKERR VecDestroy(&f);
CHKERR MatDestroy(&A);
CHKERR MatDestroy(&fdA);
CHKERR SNESDestroy(&snes);
// destroy DM
CHKERR DMDestroy(&dm);
}
CATCH_ERRORS;
// finish work cleaning memory, getting statistics, etc
MoFEM::Core::Finalize();
return 0;
}
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