int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("screen-quad.mesh", &mesh);
// mloader.load("screen-tri.mesh", &mesh);
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace 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), SYM);
// visualize solution and mesh
ScalarView Xview_r("Electric field X - real", 0, 0, 450, 420);
ScalarView Yview_r("Electric field Y - real", 460, 0, 450, 420);
ScalarView Xview_i("Electric field X - imag", 920, 0, 450, 420);
ScalarView Yview_i("Electric field Y - imag", 1380, 0, 450, 420);
OrderView ord("Polynomial Orders", 0, 460, 450, 420);
/*
// view the basis functions
VectorBaseView bview;
vbview.show(&space);
vbview.wait_for_keypress();
*/
// matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// 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 sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculating error wrt. exact solution
Solution ex;
ex.set_exact(&mesh, exact);
double err_exact = 100 * hcurl_error(&sln_coarse, &ex);
info("Exact solution error: %g%%", err_exact);
// visualization
RealFilter real(&sln_coarse);
ImagFilter imag(&sln_coarse);
Xview_r.set_min_max_range(-3.0, 1.0);
//Xview_r.show_scale(false);
Xview_r.show(&real, EPS_NORMAL, FN_VAL_0);
Yview_r.set_min_max_range(-4.0, 4.0);
//Yview_r.show_scale(false);
Yview_r.show(&real, EPS_NORMAL, FN_VAL_1);
Xview_i.set_min_max_range(-1.0, 4.0);
//Xview_i.show_scale(false);
Xview_i.show(&imag, EPS_NORMAL, FN_VAL_0);
Yview_i.set_min_max_range(-4.0, 4.0);
//Yview_i.show_scale(false);
Yview_i.show(&imag, EPS_NORMAL, FN_VAL_1);
ord.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem ref(&sys);
ref.assemble();
ref.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
double err_est_adapt = hp.calc_error(&sln_coarse, &sln_fine) * 100;
double err_est_hcurl = hcurl_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate (adapt): %g%%", err_est_adapt);
info("Error estimate (hcurl): %g%%", err_est_hcurl);
// add entries to DOF convergence graphs
graph_dof_exact.add_values(space.get_num_dofs(), err_exact);
graph_dof_exact.save("conv_dof_exact.dat");
graph_dof_est.add_values(space.get_num_dofs(), err_est_hcurl);
graph_dof_est.save("conv_dof_est.dat");
// add entries to CPU convergence graphs
graph_cpu_exact.add_values(cpu, err_exact);
graph_cpu_exact.save("conv_cpu_exact.dat");
graph_cpu_est.add_values(cpu, err_est_hcurl);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est_adapt too large, adapt the mesh
if (err_est_adapt < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait("Waiting for all views to be closed.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
mesh.load("screen-quad.mesh");
// mesh.load("screen-tri.mesh");
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace 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), SYM);
// visualize solution and mesh
ScalarView Xview_r("Electric field X - real", 0, 0, 320, 320);
ScalarView Yview_r("Electric field Y - real", 325, 0, 320, 320);
ScalarView Xview_i("Electric field X - imag", 650, 0, 320, 320);
ScalarView Yview_i("Electric field Y - imag", 975, 0, 320, 320);
OrderView ord("Polynomial Orders", 325, 400, 600, 600);
// matrix solver
UmfpackSolver solver;
// convergence graph wrt. the number of degrees of freedom
GnuplotGraph graph;
graph.set_captions("Error Convergence for the Screen Problem in H(curl)", "Degrees of Freedom", "Error [%]");
graph.add_row("exact error", "k", "-", "o");
graph.add_row("error estimate", "k", "--");
graph.set_log_y();
// convergence graph wrt. CPU time
GnuplotGraph graph_cpu;
graph_cpu.set_captions("Error Convergence for the Screen Problem in H(curl)", "CPU Time", "Error [%]");
graph_cpu.add_row("exact error", "k", "-", "o");
graph_cpu.add_row("error estimate", "k", "--");
graph_cpu.set_log_y();
// 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 sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculating error wrt. exact solution
Solution ex;
ex.set_exact(&mesh, exact);
double error = 100 * hcurl_error(&sln_coarse, &ex);
info("Exact solution error: %g%%", error);
// visualization
RealFilter real(&sln_coarse);
ImagFilter imag(&sln_coarse);
Xview_r.set_min_max_range(-3.0, 1.0);
Xview_r.show_scale(false);
Xview_r.show(&real, EPS_NORMAL, FN_VAL_0);
Yview_r.set_min_max_range(-4.0, 4.0);
Yview_r.show_scale(false);
Yview_r.show(&real, EPS_NORMAL, FN_VAL_1);
Xview_i.set_min_max_range(-1.0, 4.0);
Xview_i.show_scale(false);
Xview_i.show(&imag, EPS_NORMAL, FN_VAL_0);
Yview_i.set_min_max_range(-4.0, 4.0);
Yview_i.show_scale(false);
Yview_i.show(&imag, EPS_NORMAL, FN_VAL_1);
ord.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem ref(&sys);
ref.assemble();
ref.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%%", err_est);
// add entry to DOF convergence graph
graph.add_values(0, space.get_num_dofs(), error);
graph.add_values(1, space.get_num_dofs(), err_est);
graph.save("conv_dof.gp");
// add entry to CPU convergence graph
graph_cpu.add_values(0, cpu, error);
graph_cpu.add_values(1, cpu, err_est);
graph_cpu.save("conv_cpu.gp");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait("Waiting for keyboard or mouse input.");
return 0;
}
