int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr u_mesh(new Mesh), v_mesh(new Mesh);
MeshReaderH2DXML mloader;
mloader.load("domain.xml", u_mesh);
u_mesh->refine_all_elements();
v_mesh->copy(u_mesh);
v_mesh->refine_towards_boundary("Bdy", INIT_REF_BDY);
// Define right-hand sides.
CustomRightHandSide1* g1 = new CustomRightHandSide1(K, D_u, SIGMA);
CustomRightHandSide2* g2 = new CustomRightHandSide2(K, D_v);
// Initialize the weak formulation.
CustomWeakForm wf(g1, g2);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_u("Bdy", 0.0);
EssentialBCs<double> bcs_u(&bc_u);
DefaultEssentialBCConst<double> bc_v("Bdy", 0.0);
EssentialBCs<double> bcs_v(&bc_v);
// Create H1 spaces with default shapeset for both displacement components.
SpaceSharedPtr<double> u_space(new H1Space<double>(u_mesh, &bcs_u, P_INIT_U));
SpaceSharedPtr<double> v_space(new H1Space<double>(v_mesh, &bcs_v, P_INIT_V));
Hermes::vector<SpaceSharedPtr<double> > spaces(u_space, v_space);
NewtonSolver<double> newton(&wf, spaces);
MeshFunctionSharedPtr<double> u_sln(new Solution<double>());
MeshFunctionSharedPtr<double> u_sln1(new Solution<double>());
MeshFunctionSharedPtr<double> v_sln(new Solution<double>());
MeshFunctionSharedPtr<double> v_sln1(new Solution<double>());
Hermes::vector<MeshFunctionSharedPtr<double> > slns(u_sln, v_sln);
Hermes::vector<MeshFunctionSharedPtr<double> > slns1(u_sln1, v_sln1);
newton.solve();
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, slns);
u_sln1->copy(u_sln);
v_sln1->copy(v_sln);
u_sln->free();
v_sln->free();
u_sln->copy(u_sln1);
v_sln->copy(v_sln1);
newton.solve(slns);
Solution<double>::vector_to_solutions(newton.get_sln_vector(), spaces, slns1);
Linearizer lin(FileExport);
lin.process_solution(u_sln);
lin.process_solution(u_sln1);
lin.process_solution(v_sln1);
lin.process_solution(u_sln1);
lin.process_solution(u_sln1);
lin.process_solution(v_sln1);
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
cpu_time.tick();
// Load the mesh.
MeshSharedPtr u_mesh(new Mesh), v_mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", u_mesh);
if (MULTI == false)
u_mesh->refine_towards_boundary("Bdy", INIT_REF_BDY);
// Create initial mesh (master mesh).
v_mesh->copy(u_mesh);
// Initial mesh refinements in the v_mesh towards the boundary.
if (MULTI == true)
v_mesh->refine_towards_boundary("Bdy", INIT_REF_BDY);
// Set exact solutions.
MeshFunctionSharedPtr<double> exact_u(new ExactSolutionFitzHughNagumo1(u_mesh));
MeshFunctionSharedPtr<double> exact_v(new ExactSolutionFitzHughNagumo2(MULTI ? v_mesh : u_mesh, K));
// Define right-hand sides.
CustomRightHandSide1 g1(K, D_u, SIGMA);
CustomRightHandSide2 g2(K, D_v);
// Initialize the weak formulation.
CustomWeakForm wf(&g1, &g2);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_u("Bdy", 0.0);
EssentialBCs<double> bcs_u(&bc_u);
DefaultEssentialBCConst<double> bc_v("Bdy", 0.0);
EssentialBCs<double> bcs_v(&bc_v);
// Create H1 spaces with default shapeset for both displacement components.
SpaceSharedPtr<double> u_space(new H1Space<double>(u_mesh, &bcs_u, P_INIT_U));
SpaceSharedPtr<double> v_space(new H1Space<double>(MULTI ? v_mesh : u_mesh, &bcs_v, P_INIT_V));
// Initialize coarse and reference mesh solutions.
MeshFunctionSharedPtr<double> u_sln(new Solution<double>()), v_sln(new Solution<double>()), u_ref_sln(new Solution<double>()), v_ref_sln(new Solution<double>());
Hermes::vector<MeshFunctionSharedPtr<double> > slns(u_sln, v_sln);
Hermes::vector<MeshFunctionSharedPtr<double> > ref_slns(u_ref_sln, v_ref_sln);
Hermes::vector<MeshFunctionSharedPtr<double> > exact_slns(exact_u, exact_v);
// Initialize refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST);
//HOnlySelector<double> selector;
// Initialize views.
Views::ScalarView s_view_0("Solution[0]", new Views::WinGeom(0, 0, 440, 350));
s_view_0.show_mesh(false);
Views::OrderView o_view_0("Mesh[0]", new Views::WinGeom(450, 0, 420, 350));
Views::ScalarView s_view_1("Solution[1]", new Views::WinGeom(880, 0, 440, 350));
s_view_1.show_mesh(false);
Views::OrderView o_view_1("Mesh[1]", new Views::WinGeom(1330, 0, 420, 350));
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est;
SimpleGraph graph_dof_exact, graph_cpu_exact;
NewtonSolver<double> newton;
newton.set_weak_formulation(&wf);
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
Hermes::Mixins::Loggable::Static::info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space->
Mesh::ReferenceMeshCreator u_ref_mesh_creator(u_mesh);
MeshSharedPtr u_ref_mesh = u_ref_mesh_creator.create_ref_mesh();
Mesh::ReferenceMeshCreator v_ref_mesh_creator(v_mesh);
MeshSharedPtr v_ref_mesh = v_ref_mesh_creator.create_ref_mesh();
Space<double>::ReferenceSpaceCreator u_ref_space_creator(u_space, u_ref_mesh);
SpaceSharedPtr<double> u_ref_space = u_ref_space_creator.create_ref_space();
Space<double>::ReferenceSpaceCreator v_ref_space_creator(v_space, MULTI ? v_ref_mesh : u_ref_mesh);
SpaceSharedPtr<double> v_ref_space = v_ref_space_creator.create_ref_space();
Hermes::vector<SpaceSharedPtr<double> > ref_spaces_const(u_ref_space, v_ref_space);
newton.set_spaces(ref_spaces_const);
int ndof_ref = Space<double>::get_num_dofs(ref_spaces_const);
// Initialize reference problem.
Hermes::Mixins::Loggable::Static::info("Solving on reference mesh.");
// Time measurement.
cpu_time.tick();
// Perform Newton's iteration.
try
{
newton.solve();
}
catch (Hermes::Exceptions::Exception& e)
{
std::cout << e.info();
}
catch (std::exception& e)
{
std::cout << e.what();
}
// Translate the resulting coefficient vector into the instance of Solution.
Solution<double>::vector_to_solutions(newton.get_sln_vector(), ref_spaces_const, Hermes::vector<MeshFunctionSharedPtr<double> >(u_ref_sln, v_ref_sln));
// Project the fine mesh solution onto the coarse mesh.
Hermes::Mixins::Loggable::Static::info("Projecting reference solution on coarse mesh.");
OGProjection<double> ogProjection; ogProjection.project_global(Hermes::vector<SpaceSharedPtr<double> >(u_space, v_space), ref_slns, slns);
cpu_time.tick();
// View the coarse mesh solution and polynomial orders.
s_view_0.show(u_sln);
o_view_0.show(u_space);
s_view_1.show(v_sln);
o_view_1.show(v_space);
// Calculate element errors.
Hermes::Mixins::Loggable::Static::info("Calculating error estimate and exact error.");
errorCalculator.calculate_errors(slns, exact_slns, false);
double err_exact_rel_total = errorCalculator.get_total_error_squared() * 100;
Hermes::vector<double> err_exact_rel;
err_exact_rel.push_back(errorCalculator.get_error_squared(0) * 100);
err_exact_rel.push_back(errorCalculator.get_error_squared(1) * 100);
errorCalculator.calculate_errors(slns, ref_slns, true);
double err_est_rel_total = errorCalculator.get_total_error_squared() * 100;
Hermes::vector<double> err_est_rel;
err_est_rel.push_back(errorCalculator.get_error_squared(0) * 100);
err_est_rel.push_back(errorCalculator.get_error_squared(1) * 100);
adaptivity.set_spaces(Hermes::vector<SpaceSharedPtr<double> >(u_space, v_space));
// Time measurement.
cpu_time.tick();
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof_coarse[0]: %d, ndof_fine[0]: %d",
u_space->get_num_dofs(), u_ref_space->get_num_dofs());
Hermes::Mixins::Loggable::Static::info("err_est_rel[0]: %g%%, err_exact_rel[0]: %g%%", err_est_rel[0], err_exact_rel[0]);
Hermes::Mixins::Loggable::Static::info("ndof_coarse[1]: %d, ndof_fine[1]: %d",
v_space->get_num_dofs(), v_ref_space->get_num_dofs());
Hermes::Mixins::Loggable::Static::info("err_est_rel[1]: %g%%, err_exact_rel[1]: %g%%", err_est_rel[1], err_exact_rel[1]);
Hermes::Mixins::Loggable::Static::info("ndof_coarse_total: %d, ndof_fine_total: %d",
Space<double>::get_num_dofs(Hermes::vector<SpaceSharedPtr<double> >(u_space, v_space)),
Space<double>::get_num_dofs(ref_spaces_const));
Hermes::Mixins::Loggable::Static::info("err_est_rel_total: %g%%, err_est_exact_total: %g%%", err_est_rel_total, err_exact_rel_total);
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space<double>::get_num_dofs(Hermes::vector<SpaceSharedPtr<double> >(u_space, v_space)),
err_est_rel_total);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total);
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.add_values(Space<double>::get_num_dofs(Hermes::vector<SpaceSharedPtr<double> >(u_space, v_space)),
err_exact_rel_total);
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel_total);
graph_cpu_exact.save("conv_cpu_exact.dat");
// If err_est too large, adapt the mesh->
if (err_est_rel_total < ERR_STOP)
done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting coarse mesh.");
Hermes::vector<RefinementSelectors::Selector<double> *> selectors(&selector, &selector);
done = adaptivity.adapt(selectors);
}
// Increase counter.
as++;
} while (done == false);
Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());
// Wait for all views to be closed.
Views::View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table_type);
if (bt.is_explicit()) info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("../domain.mesh", &mesh);
// Convert to quadrilaterals.
mesh.convert_triangles_to_quads();
// Refine towards boundary.
mesh.refine_towards_boundary("Bdy", 1, true);
// Refine once towards vertex #4.
mesh.refine_towards_vertex(4, 1);
// Initialize solutions.
CustomInitialConditionWave u_sln(&mesh);
Solution v_sln(&mesh, 0.0);
Hermes::vector<Solution*> slns(&u_sln, &v_sln);
// Initialize the weak formulation.
CustomWeakFormWave wf(time_step, C_SQUARED, &u_sln, &v_sln);
// Initialize boundary conditions
DefaultEssentialBCConst bc_essential("Bdy", 0.0);
EssentialBCs bcs(&bc_essential);
// Create x- and y- displacement space using the default H1 shapeset.
H1Space u_space(&mesh, &bcs, P_INIT);
H1Space v_space(&mesh, &bcs, P_INIT);
info("ndof = %d.", Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)));
// Initialize the FE problem.
DiscreteProblem dp(&wf, Hermes::vector<Space *>(&u_space, &v_space));
// Initialize Runge-Kutta time stepping.
RungeKutta runge_kutta(&dp, &bt, matrix_solver);
// Time stepping loop.
double current_time = 0; int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g s, time_step = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool jacobian_changed = false;
bool verbose = true;
if (!runge_kutta.rk_time_step(current_time, time_step, slns,
slns, jacobian_changed, verbose))
error("Runge-Kutta time step failed, try to decrease time step size.");
// Update time.
current_time += time_step;
} while (current_time < T_FINAL);
double coord_x[4] = {1, 3, 5, 7};
double coord_y[4] = {1, 3, 5, 7};
info("Coordinate (1.0, 0.0) value = %lf", u_sln.get_pt_value(coord_x[0], coord_y[0]));
info("Coordinate (3.0, 3.0) value = %lf", u_sln.get_pt_value(coord_x[1], coord_y[1]));
info("Coordinate (5.0, 5.0) value = %lf", u_sln.get_pt_value(coord_x[2], coord_y[2]));
info("Coordinate (7.0, 7.0) value = %lf", u_sln.get_pt_value(coord_x[3], coord_y[3]));
info("Coordinate (1.0, 0.0) value = %lf", v_sln.get_pt_value(coord_x[0], coord_y[0]));
info("Coordinate (3.0, 3.0) value = %lf", v_sln.get_pt_value(coord_x[1], coord_y[1]));
info("Coordinate (5.0, 5.0) value = %lf", v_sln.get_pt_value(coord_x[2], coord_y[2]));
info("Coordinate (7.0, 7.0) value = %lf", v_sln.get_pt_value(coord_x[3], coord_y[3]));
double t_value[8] = {0.212655, 0.000163, 0.000000, 0.000000, -0.793316, 0.007255, 0.000001, 0.000000};
bool success = true;
for (int i = 0; i < 4; i++)
{
if (fabs(t_value[i] - u_sln.get_pt_value(coord_x[i], coord_y[i])) > 1E-6) success = false;
}
for (int i = 4; i < 8; i++)
{
if (fabs(t_value[i] - v_sln.get_pt_value(coord_x[i-4], coord_y[i-4])) > 1E-6) success = false;
}
if (success) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
// Wait for the view to be closed.
View::wait();
return 0;
}
