int main(int argc, char* argv[])
{
// Load the mesh.
Hermes::Hermes2D::Mesh mesh;
Hermes::Hermes2D::MeshReaderH2DXML mloader;
mloader.load("domain.xml", &mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++)
mesh.refine_all_elements();
// This is here basically to show off that we can save a mesh with refinements and load it back again.
mloader.save("domain2.xml", &mesh);
mloader.load("domain2.xml", &mesh);
// Initialize the weak formulation.
CustomWeakFormPoisson wf(new Hermes::Hermes1DFunction<double>(LAMBDA_AL), "Aluminum",
new Hermes::Hermes1DFunction<double>(LAMBDA_CU), "Copper", new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC));
// Initialize essential boundary conditions.
Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"),
FIXED_BDY_TEMP);
Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
Hermes::Hermes2D::DiscreteProblem<double> dp(&wf, &space);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Hermes::Hermes2D::Solution<double> sln;
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
try
{
newton.solve_keep_jacobian(coeff_vec, 1e-3, 10);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Hermes::Hermes2D::Views::Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Hermes::Hermes2D::Views::Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION)
{
Hermes::Hermes2D::Views::ScalarView view("Solution", new Hermes::Hermes2D::Views::WinGeom(0, 0, 440, 350));
// Hermes uses adaptive FEM to approximate higher-order FE solutions with linear
// triangles for OpenGL. The second parameter of View::show() sets the error
// tolerance for that. Options are HERMES_EPS_LOW, HERMES_EPS_NORMAL (default),
// HERMES_EPS_HIGH and HERMES_EPS_VERYHIGH. The size of the graphics file grows
// considerably with more accurate representation, so use it wisely.
view.show(&sln, Hermes::Hermes2D::Views::HERMES_EPS_HIGH);
Hermes::Hermes2D::Views::View::wait();
}
// Clean up.
delete [] coeff_vec;
}
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Hermes::Hermes2D::Views::Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Hermes::Hermes2D::Views::Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION)
{
Hermes::Hermes2D::Views::ScalarView view("Solution", new Hermes::Hermes2D::Views::WinGeom(0, 0, 440, 350));
// Hermes uses adaptive FEM to approximate higher-order FE solutions with linear
// triangles for OpenGL. The second parameter of View::show() sets the error
// tolerance for that. Options are HERMES_EPS_LOW, HERMES_EPS_NORMAL (default),
// HERMES_EPS_HIGH and HERMES_EPS_VERYHIGH. The size of the graphics file grows
// considerably with more accurate representation, so use it wisely.
view.show(&sln, Hermes::Hermes2D::Views::HERMES_EPS_HIGH);
Hermes::Hermes2D::Views::View::wait();
}
// Clean up.
delete [] coeff_vec;
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Hermes::Hermes2D::Mesh mesh;
Hermes::Hermes2D::MeshReaderH2DXML mloader;
mloader.load("../domain.xml", &mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++)
mesh.refine_all_elements();
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Aluminum", new Hermes::Hermes1DFunction<double>(LAMBDA_AL), "Copper",
new Hermes::Hermes1DFunction<double>(LAMBDA_CU), new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC));
// Initialize essential boundary conditions.
Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Outer", "Left"),
FIXED_BDY_TEMP);
Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
Hermes::Hermes2D::DiscreteProblem<double> dp(&wf, &space);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Hermes::Hermes2D::Solution<double> sln;
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
try{
newton.solve(coeff_vec);
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
error("Newton's iteration failed.");
}
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// Actual test. The values of 'sum' depend on the
// current shapeset. If you change the shapeset,
// you need to correct these numbers.
double sum = 0;
for (int i = 0; i < ndof; i++)
sum += newton.get_sln_vector()[i];
printf("coefficient sum = %g\n", sum);
// Clean up.
delete [] coeff_vec;
bool success = true;
if (std::abs(sum + 0.357318) > 1e-4) success = false;
if (success == true)
{
printf("Success!\n");
return TEST_SUCCESS;
}
else
{
printf("Failure!\n");
return TEST_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
Hermes::Hermes2D::Mesh mesh;
Hermes::Hermes2D::MeshReaderH2D mloader;
mloader.load("../domain.mesh", &mesh);
// Perform initial mesh refinements (optional).
for (int i=0; i < INIT_REF_NUM; i++)
mesh.refine_all_elements();
// Initialize the weak formulation.
CustomWeakFormPoissonNewton wf("Aluminum", new Hermes::Hermes1DFunction<double>(LAMBDA_AL),
"Copper", new Hermes::Hermes1DFunction<double>(LAMBDA_CU),
new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC),
"Outer", ALPHA, T_EXTERIOR);
// Initialize boundary conditions.
CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Left"),
BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
// Testing n_dof and correctness of solution vector
// for p_init = 1, 2, ..., 10
bool success = true;
for (int p_init = 1; p_init <= 10; p_init++)
{
info("********* p_init = %d *********\n", p_init);
space.set_uniform_order(p_init);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
Hermes::Hermes2D::DiscreteProblem<double> dp(&wf, &space);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Hermes::Hermes2D::Solution<double> sln;
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
if (!newton.solve(coeff_vec))
error("Newton's iteration failed.");
else
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
double sum = 0;
for (int i=0; i < ndof; i++) sum += coeff_vec[i];
printf("coefficient sum = %g\n", sum);
// Actual test. The values of 'sum' depend on the
// current shapeset. If you change the shapeset,
// you need to correct these numbers.
if (p_init == 1 && fabs(sum - 61.8227) > 1e-1) success = false;
if (p_init == 2 && fabs(sum - 60.8105) > 1e-1) success = false;
if (p_init == 3 && fabs(sum - 61.5511) > 1e-1) success = false;
if (p_init == 4 && fabs(sum - 60.8191) > 1e-1) success = false;
if (p_init == 5 && fabs(sum - 61.5304) > 1e-1) success = false;
if (p_init == 6 && fabs(sum - 60.8064) > 1e-1) success = false;
if (p_init == 7 && fabs(sum - 61.5323) > 1e-1) success = false;
if (p_init == 8 && fabs(sum - 60.7863) > 1e-1) success = false;
if (p_init == 9 && fabs(sum - 61.5408) > 1e-1) success = false;
if (p_init == 10 && fabs(sum - 60.7637) > 1e-1) success = false;
// Clean up.
delete [] coeff_vec;
}
if (success == 1) {
printf("Success!\n");
return TEST_SUCCESS;
}
else {
printf("Failure!\n");
return TEST_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
Hermes::Hermes2D::Mesh mesh;
Hermes::Hermes2D::H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements (optional).
int refinement_type = 2; // Split elements vertically.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(refinement_type);
// Show the mesh.
Hermes::Hermes2D::Views::MeshView mview("Mesh", new Hermes::Hermes2D::Views::WinGeom(0, 0, 900, 250));
if (HERMES_VISUALIZATION) {
mview.show(&mesh);
//mview.wait();
}
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Al", new Hermes::Hermes1DFunction<double>(LAMBDA_AL), "Cu",
new Hermes::Hermes1DFunction<double>(LAMBDA_CU), new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC));
// Initialize essential boundary conditions.
Hermes::Hermes2D::DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Left", "Right"),
FIXED_BDY_TEMP);
Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
Hermes::Hermes2D::DiscreteProblem<double> dp(&wf, &space);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Hermes::Hermes2D::Solution<double> sln;
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
if (!newton.solve(coeff_vec))
error("Newton's iteration failed.");
else
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// Get info about time spent during assembling in its respective parts.
dp.get_all_profiling_output(std::cout);
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Hermes::Hermes2D::Views::Linearizer<double> lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Hermes::Hermes2D::Views::Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION)
{
Hermes::Hermes2D::Views::ScalarView<double> view("Solution", new Hermes::Hermes2D::Views::WinGeom(0, 300, 900, 350));
// Hermes uses adaptive FEM to approximate higher-order FE solutions with linear
// triangles for OpenGL. The second parameter of View::show() sets the error
// tolerance for that. Options are HERMES_EPS_LOW, HERMES_EPS_NORMAL (default),
// HERMES_EPS_HIGH and HERMES_EPS_VERYHIGH. The size of the graphics file grows
// considerably with more accurate representation, so use it wisely.
view.show(&sln, Hermes::Hermes2D::Views::HERMES_EPS_HIGH);
Hermes::Hermes2D::Views::View::wait();
}
// Clean up.
delete [] coeff_vec;
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Hermes::Hermes2D::Mesh mesh;
Hermes::Hermes2D::MeshReaderH2D mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements (optional).
for (int i=0; i < INIT_REF_NUM; i++)
mesh.refine_all_elements();
// Initialize the weak formulation.
CustomWeakFormPoissonNewton wf("Aluminum", new Hermes::Hermes1DFunction<double>(LAMBDA_AL),
"Copper", new Hermes::Hermes1DFunction<double>(LAMBDA_CU),
new Hermes::Hermes2DFunction<double>(-VOLUME_HEAT_SRC),
"Outer", ALPHA, T_EXTERIOR);
// Initialize boundary conditions.
CustomDirichletCondition bc_essential(Hermes::vector<std::string>("Bottom", "Inner", "Left"),
BDY_A_PARAM, BDY_B_PARAM, BDY_C_PARAM);
Hermes::Hermes2D::EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
Hermes::Hermes2D::H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
info("ndof = %d", ndof);
// Initialize the FE problem.
Hermes::Hermes2D::DiscreteProblem<double> dp(&wf, &space);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof];
memset(coeff_vec, 0, ndof*sizeof(double));
// Initialize the Newton solver.
Hermes::Hermes2D::NewtonSolver<double> newton(&dp, matrix_solver_type);
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Hermes::Hermes2D::Solution<double> sln;
if (!newton.solve(coeff_vec))
error("Newton's iteration failed.");
else
Hermes::Hermes2D::Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// VTK output.
if (VTK_VISUALIZATION) {
// Output solution in VTK format.
Hermes::Hermes2D::Views::Linearizer lin(&sln);
bool mode_3D = true;
lin.save_solution_vtk("sln.vtk", "Temperature", mode_3D);
info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Hermes::Hermes2D::Views::Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION) {
Hermes::Hermes2D::Views::ScalarView view("Solution", new Hermes::Hermes2D::Views::WinGeom(0, 0, 440, 350));
view.show(&sln, Hermes::Hermes2D::Views::HERMES_EPS_VERYHIGH);
Hermes::Hermes2D::Views::View::wait();
}
// Clean up.
delete [] coeff_vec;
return 0;
}