int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", mesh);
// Perform initial mesh refinements.
for (int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();
// Initialize boundary conditions.
Hermes::Hermes2D::DefaultEssentialBCConst<complex> bc_essential("Dirichlet", complex(0.0, 0.0));
EssentialBCs<complex> bcs(&bc_essential);
// Create an H1 space with default shapeset.
SpaceSharedPtr<complex> space(new H1Space<complex>(mesh, &bcs, P_INIT));
int ndof = space->get_num_dofs();
// Initialize the weak formulation.
CustomWeakForm wf("Air", MU_0, "Iron", MU_IRON, GAMMA_IRON,
"Wire", MU_0, complex(J_EXT, 0.0), OMEGA);
// Initialize coarse and reference mesh solution.
MeshFunctionSharedPtr<complex> sln(new Hermes::Hermes2D::Solution<complex>());
MeshFunctionSharedPtr<complex> ref_sln(new Hermes::Hermes2D::Solution<complex>());
// Initialize refinement selector.
H1ProjBasedSelector<complex> selector(CAND_LIST);
// Initialize views.
#ifdef SHOW_OUTPUT
Views::ScalarView sview("Solution", new Views::WinGeom(0, 0, 600, 350));
Views::ScalarView sview2("Ref. Solution", new Views::WinGeom(0, 0, 600, 350));
Views::OrderView oview("Polynomial orders", new Views::WinGeom(610, 0, 520, 350));
#endif
DiscreteProblem<complex> dp(&wf, space);
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Hermes::Hermes2D::NewtonSolver<complex> newton(&dp);
// Adaptivity loop:
int as = 1; bool done = false;
adaptivity.set_space(space);
do
{
// Construct globally refined reference mesh and setup reference space->
Mesh::ReferenceMeshCreator ref_mesh_creator(mesh);
MeshSharedPtr ref_mesh = ref_mesh_creator.create_ref_mesh();
Space<complex>::ReferenceSpaceCreator ref_space_creator(space, ref_mesh);
SpaceSharedPtr<complex> ref_space = ref_space_creator.create_ref_space();
newton.set_space(ref_space);
ref_space->save("space-complex.xml");
ref_space->free();
ref_space->load("space-complex.xml");
#ifdef WITH_BSON
ref_space->save_bson("space-complex.bson");
ref_space->free();
ref_space->load_bson("space-complex.bson");
#endif
int ndof_ref = ref_space->get_num_dofs();
// Initialize reference problem.
// Initial coefficient vector for the Newton's method.
complex* coeff_vec = new complex[ndof_ref];
memset(coeff_vec, 0, ndof_ref * sizeof(complex));
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
SpaceSharedPtr<complex> space_test = Space<complex>::load("space-complex.xml", ref_mesh, false, &bcs);
newton.set_space(space_test);
newton.solve(coeff_vec);
Hermes::Hermes2D::Solution<complex>::vector_to_solution(newton.get_sln_vector(), ref_space, ref_sln);
// Project the fine mesh solution onto the coarse mesh.
OGProjection<complex> ogProjection;
#ifdef WITH_BSON
space->save_bson("space-complex-coarse.bson");
SpaceSharedPtr<complex> space_test2 = Space<complex>::load_bson("space-complex-coarse.bson", mesh, &bcs);
ogProjection.project_global(space_test2, ref_sln, sln);
#else
space->save("space-complex-coarse.xml2");
SpaceSharedPtr<complex> space_test2 = Space<complex>::load("space-complex-coarse.xml2", mesh, false, &bcs);
ogProjection.project_global(space_test2, ref_sln, sln);
#endif
// View the coarse mesh solution and polynomial orders.
#ifdef SHOW_OUTPUT
MeshFunctionSharedPtr<double> real_filter(new RealFilter(sln));
MeshFunctionSharedPtr<double> rreal_filter(new RealFilter(ref_sln));
sview2.show(rreal_filter);
oview.show(space);
#endif
// Calculate element errors and total error estimate.
errorCalculator.calculate_errors(sln, ref_sln);
#ifdef SHOW_OUTPUT
std::cout << "Relative error: " << errorCalculator.get_total_error_squared() * 100. << '%' << std::endl;
#endif
// Add entry to DOF and CPU convergence graphs.
#ifdef SHOW_OUTPUT
sview.show(errorCalculator.get_errorMeshFunction());
#endif
// If err_est too large, adapt the mesh->
if(errorCalculator.get_total_error_squared() * 100. < ERR_STOP)
done = true;
else
{
std::cout << "Adapting..." << std::endl << std::endl;
adaptivity.adapt(&selector);
}
// Clean up.
delete [] coeff_vec;
// Increase counter.
as++;
}
while (done == false);
#ifdef SHOW_OUTPUT
// Show the reference solution - the final result.
sview.set_title("Fine mesh solution");
MeshFunctionSharedPtr<double> real_filter(new RealFilter(ref_sln));
sview.show(real_filter);
// Wait for all views to be closed.
Views::View::wait();
#endif
return as;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("square_quad.mesh", &mesh);
// mloader.load("square_tri.mesh", &mesh);
for (int i=0; i<INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(2, INIT_REF_NUM_BDY);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form));
if (STABILIZATION_ON == true) {
wf.add_biform(0, 0, bilinear_form_stabilization,
bilinear_form_stabilization_order);
}
if (SHOCK_CAPTURING_ON == true) {
wf.add_biform(0, 0, bilinear_form_shock_capturing, bilinear_form_shock_capturing_order);
}
// visualize solution and mesh
OrderView oview("Coarse mesh", 0, 0, 500, 400);
ScalarView sview("Coarse mesh solution", 510, 0, 500, 400);
ScalarView sview2("Fine mesh solution", 1020, 0, 500, 400);
// matrix solver
UmfpackSolver solver;
// DOF convergence graph
SimpleGraph graph_dof_est, graph_cpu_est;
// prepare selector
RefinementSelectors::H1NonUniformHP selector(ISO_ONLY, ADAPT_TYPE, CONV_EXP, H2DRS_DEFAULT_ORDER, &shapeset);
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// solve the fine mesh problem
int p_increase;
if (ADAPT_TYPE == RefinementSelectors::H2DRS_CAND_HP) p_increase = 1;
else p_increase = 0;
RefSystem rs(&ls, p_increase, 1); // the '1' is for one level of global refinement in space
rs.assemble();
rs.solve(1, &sln_fine);
// time measurement
cpu += end_time();
// show fine mesh solution
// view the solution and mesh
oview.show(&space);
sview.show(&sln_coarse);
sview2.show(&sln_fine);
//sview.wait_for_keypress();
// time measurement
begin_time();
// calculate error estimate wrt. fine mesh solution
H1AdaptHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// add entries to DOF and CPU convergence graphs
graph_dof_est.add_values(space.get_num_dofs(), err_est);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu, err_est);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, &selector, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
sview.set_title("Final solution");
sview.show(&sln_fine);
// wait for keyboard or mouse input
View::wait();
return 0;
}
