int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("motor.mesh", &mesh);
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Motor", EPS_MOTOR, "Air", EPS_AIR, &mesh);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential_out("Outer", 0.0);
DefaultEssentialBCConst<double> bc_essential_stator("Stator", VOLTAGE);
EssentialBCs<double> bcs(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_essential_out, &bc_essential_stator));
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
// Initialize coarse and reference mesh solution.
Solution<double> sln;
// Initialize views.
Views::ScalarView sview("Solution", new Views::WinGeom(0, 0, 410, 600));
sview.fix_scale_width(50);
sview.show_mesh(false);
Views::OrderView oview("Polynomial orders", new Views::WinGeom(420, 0, 400, 600));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
// Adaptivity loop:
int as = 1; bool done = false;
do
{
Hermes::Mixins::Loggable::Static::info("---- Adaptivity step %d:", as);
// Time measurement.
cpu_time.tick();
// Initialize reference problem.
Hermes::Mixins::Loggable::Static::info("Solving.");
DiscreteProblem<double> dp(&wf, &space);
NewtonSolver<double> newton(&dp);
newton.set_verbose_output(false);
// Initial ndof.
int ndof = space.get_num_dofs();
// Perform Newton's iteration.
try
{
newton.solve();
}
catch(std::exception& e)
{
std::cout << e.what();
}
// Translate the resulting coefficient vector into the instance of Solution.
Solution<double>::vector_to_solution(newton.get_sln_vector(), &space, &sln);
// Time measurement.
cpu_time.tick();
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Views::Linearizer lin;
char* title = new char[100];
sprintf(title, "sln-%d.vtk", as);
lin.save_solution_vtk(&sln, title, "Potential", false);
Hermes::Mixins::Loggable::Static::info("Solution in VTK format saved to file %s.", title);
// Output mesh and element orders in VTK format.
Views::Orderizer ord;
sprintf(title, "ord-%d.vtk", as);
ord.save_orders_vtk(&space, title);
Hermes::Mixins::Loggable::Static::info("Element orders in VTK format saved to file %s.", title);
}
// View the coarse mesh solution and polynomial orders.
if (HERMES_VISUALIZATION)
{
sview.show(&sln);
oview.show(&space);
}
// Skip visualization time.
cpu_time.tick();
// Calculate element errors and total error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating error estimate.");
bool ignore_visited_segments = true;
KellyTypeAdapt<double> adaptivity(&space, ignore_visited_segments,
USE_EPS_IN_INTERFACE_ESTIMATOR
?
new CustomInterfaceEstimatorScalingFunction("Motor", EPS_MOTOR, "Air", EPS_AIR)
:
new CustomInterfaceEstimatorScalingFunction);
adaptivity.add_error_estimator_surf(new Hermes::Hermes2D::BasicKellyAdapt<double>::ErrorEstimatorFormKelly());
if (USE_RESIDUAL_ESTIMATOR)
{
adaptivity.add_error_estimator_vol(new ResidualErrorFormMotor("Motor", EPS_MOTOR));
adaptivity.add_error_estimator_vol(new ResidualErrorFormAir("Air", EPS_AIR));
}
if (USE_EPS_IN_INTERFACE_ESTIMATOR)
// Use normalization by energy norm.
adaptivity.set_error_form(new EnergyErrorForm(&wf));
// Note that there is only one solution (the only one available) passed to BasicKellyAdapt::calc_err_est
// and there is also no "solutions_for_adapt" parameter. The last parameter, "error_flags", is left
// intact and has the meaning explained in P04-adaptivity/01-intro. You may however still call
// adaptivity.calc_err_est with a solution, an exact solution and solutions_for_adapt=false to calculate
// error wrt. an exact solution (if provided).
double err_est_rel = adaptivity.calc_err_est(&sln, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof: %d, err_est_rel: %g%%", space.get_num_dofs(), err_est_rel);
// Add entry to DOF and CPU convergence graphs.
cpu_time.tick();
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.save("conv_cpu_est.dat");
graph_dof.add_values(space.get_num_dofs(), err_est_rel);
graph_dof.save("conv_dof_est.dat");
// Skip the time spent to save the convergence graphs.
cpu_time.tick();
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP)
done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting coarse mesh.");
// h-refinement is automatically selected here, no need for parameter "selector".
done = adaptivity.adapt(THRESHOLD, STRATEGY, MESH_REGULARITY);
// Increase the counter of performed adaptivity steps.
if (done == false)
as++;
}
if (space.get_num_dofs() >= NDOF_STOP)
done = true;
}
while (done == false);
Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());
// The final result has already been shown in the final step of the adaptivity loop, so we only
// adjust the title and hide the mesh here.
sview.set_title("Fine mesh solution");
sview.show_mesh(false);
// Wait for all views to be closed.
Views::View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH1DXML mloader;
mloader.load("domain.xml", &mesh);
// Perform initial mesh refinements (optional).
// Split elements vertically.
int refinement_type = 2;
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(refinement_type);
// 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.
DefaultEssentialBCConst<double> bc_essential(Hermes::vector<std::string>("Left", "Right"),
FIXED_BDY_TEMP);
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Show the mesh and poly degrees.
Views::OrderView oview("Mesh", new Views::WinGeom(0, 0, 900, 250));
if (HERMES_VISUALIZATION) oview.show(&space);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Perform Newton's iteration and translate the resulting coefficient vector into a Solution.
Solution<double> sln;
NewtonSolver<double> newton(&dp);
try
{
newton.solve();
}
catch(Hermes::Exceptions::Exception e)
{
e.printMsg();
throw Hermes::Exceptions::Exception("Newton's iteration failed.");
};
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.
Views::Linearizer lin;
bool mode_3D = true;
lin.save_solution_vtk(&sln, "sln.vtk", "Temperature", mode_3D);
Hermes::Mixins::Loggable::Static::info("Solution in VTK format saved to file %s.", "sln.vtk");
// Output mesh and element orders in VTK format.
Views::Orderizer ord;
ord.save_orders_vtk(&space, "ord.vtk");
Hermes::Mixins::Loggable::Static::info("Element orders in VTK format saved to file %s.", "ord.vtk");
}
// Visualize the solution.
if (HERMES_VISUALIZATION)
{
Views::ScalarView view("Solution", new 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, Views::HERMES_EPS_HIGH);
Views::View::wait();
}
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("motor.mesh", &mesh);
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Motor", EPS_MOTOR, "Air", EPS_AIR);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential_out("Outer", 0.0);
DefaultEssentialBCConst<double> bc_essential_stator("Stator", VOLTAGE);
EssentialBCs<double> bcs(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_essential_out, &bc_essential_stator));
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
// Initialize coarse and reference mesh solution.
Solution<double> sln, ref_sln;
// Initialize refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
Views::ScalarView sview("Solution", new Views::WinGeom(0, 0, 410, 600));
sview.fix_scale_width(50);
sview.show_mesh(false);
Views::OrderView<double> oview("Polynomial orders", new Views::WinGeom(420, 0, 400, 600));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
TimePeriod cpu_time;
// Adaptivity loop:
int as = 1; bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Time measurement.
cpu_time.tick();
// Construct globally refined reference mesh and setup reference space.
Space<double>* ref_space = Space<double>::construct_refined_space(&space);
int ndof_ref = ref_space->get_num_dofs();
// Initialize reference problem.
info("Solving on reference mesh.");
DiscreteProblem<double> dp(&wf, ref_space);
NewtonSolver<double> newton(&dp, matrix_solver_type);
newton.set_verbose_output(false);
// Initial coefficient vector for the Newton's method.
double* coeff_vec = new double[ndof_ref];
memset(coeff_vec, 0, ndof_ref * sizeof(double));
// Perform Newton's iteration.
if (!newton.solve(coeff_vec))
error("Newton's iteration failed.");
else
// Translate the resulting coefficient vector into the instance of Solution.
Solution<double>::vector_to_solution(newton.get_sln_vector(), ref_space, &ref_sln);
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection<double>::project_global(&space, &ref_sln, &sln, matrix_solver_type);
// Time measurement.
cpu_time.tick();
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Views::Linearizer lin(&sln);
char* title = new char[100];
sprintf(title, "sln-%d.vtk", as);
lin.save_solution_vtk(title, "Potential", false);
info("Solution in VTK format saved to file %s.", title);
// Output mesh and element orders in VTK format.
Views::Orderizer ord;
sprintf(title, "ord-%d.vtk", as);
ord.save_orders_vtk(&space, title);
info("Element orders in VTK format saved to file %s.", title);
}
// View the coarse mesh solution and polynomial orders.
if (HERMES_VISUALIZATION)
{
sview.show(&sln);
oview.show(&space);
}
// Skip visualization time.
cpu_time.tick(HERMES_SKIP);
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt<double> adaptivity(&space);
bool solutions_for_adapt = true;
// In the following function, the Boolean parameter "solutions_for_adapt" determines whether
// the calculated errors are intended for use with adaptivity (this may not be the case, for example,
// when error wrt. an exact solution is calculated). The default value is solutions_for_adapt = true,
// The last parameter "error_flags" determine whether the total and element errors are treated as
// absolute or relative. Its default value is error_flags = HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL.
// In subsequent examples and benchmarks, these two parameters will be often used with
// their default values, and thus they will not be present in the code explicitly.
double err_est_rel = adaptivity.calc_err_est(&sln, &ref_sln, solutions_for_adapt,
HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%",
space.get_num_dofs(), ref_space->get_num_dofs(), err_est_rel);
// Add entry to DOF and CPU convergence graphs.
cpu_time.tick();
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.save("conv_cpu_est.dat");
graph_dof.add_values(space.get_num_dofs(), err_est_rel);
graph_dof.save("conv_dof_est.dat");
// Skip the time spent to save the convergence graphs.
cpu_time.tick(HERMES_SKIP);
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP)
done = true;
else
{
info("Adapting coarse mesh.");
done = adaptivity.adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
// Increase the counter of performed adaptivity steps.
if (done == false)
as++;
}
if (space.get_num_dofs() >= NDOF_STOP)
done = true;
// Clean up.
delete [] coeff_vec;
// Keep the mesh from final step to allow further working with the final reference solution.
if(done == false)
delete ref_space->get_mesh();
delete ref_space;
}
while (done == false);
verbose("Total running time: %g s", cpu_time.accumulated());
// Show the reference solution - the final result.
sview.set_title("Fine mesh solution");
sview.show_mesh(false);
sview.show(&ref_sln);
// Wait for all views to be closed.
Views::View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
MeshSharedPtr mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", mesh);
// Initialize the weak formulation.
CustomWeakFormPoisson wf("Motor", EPS_MOTOR, "Air", EPS_AIR);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential_out("Outer", 0.0);
DefaultEssentialBCConst<double> bc_essential_stator("Stator", VOLTAGE);
EssentialBCs<double> bcs(Hermes::vector<EssentialBoundaryCondition<double> *>(&bc_essential_out, &bc_essential_stator));
// Create an H1 space with default shapeset.
SpaceSharedPtr<double> space(new H1Space<double>(mesh, &bcs, P_INIT));
// Set the space to adaptivity.
adaptivity.set_space(space);
// Initialize coarse and fine mesh solution.
MeshFunctionSharedPtr<double> sln(new Solution<double>), ref_sln(new Solution<double>);
// Initialize refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST, H2DRS_DEFAULT_ORDER);
// Initialize views.
Views::ScalarView sview("Solution", new Views::WinGeom(0, 0, 410, 600));
sview.fix_scale_width(50);
sview.show_mesh(false);
Views::OrderView oview("Polynomial orders", new Views::WinGeom(420, 0, 400, 600));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
DiscreteProblem<double> dp(&wf, space);
NewtonSolver<double> newton(&dp);
newton.set_verbose_output(true);
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
Hermes::Mixins::Loggable::Static::info("---- Adaptivity step %d:", as);
// Time measurement.
cpu_time.tick();
// Construct globally refined mesh and setup fine mesh space.
Mesh::ReferenceMeshCreator ref_mesh_creator(mesh);
MeshSharedPtr ref_mesh = ref_mesh_creator.create_ref_mesh();
Space<double>::ReferenceSpaceCreator ref_space_creator(space, ref_mesh);
SpaceSharedPtr<double> ref_space = ref_space_creator.create_ref_space();
int ndof_ref = ref_space->get_num_dofs();
// Initialize fine mesh problem.
Hermes::Mixins::Loggable::Static::info("Solving on fine mesh.");
newton.set_space(ref_space);
// Perform Newton's iteration.
try
{
newton.solve();
}
catch(std::exception& e)
{
std::cout << e.what();
}
// Translate the resulting coefficient vector into the instance of Solution.
Solution<double>::vector_to_solution(newton.get_sln_vector(), ref_space, ref_sln);
// Project the fine mesh solution onto the coarse mesh.
Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solution on coarse mesh.");
OGProjection<double>::project_global(space, ref_sln, sln);
// Time measurement.
cpu_time.tick();
// VTK output.
if (VTK_VISUALIZATION)
{
// Output solution in VTK format.
Views::Linearizer lin;
char* title = new char[100];
sprintf(title, "sln-%d.vtk", as);
lin.save_solution_vtk(ref_sln, title, "Potential", false);
Hermes::Mixins::Loggable::Static::info("Solution in VTK format saved to file %s.", title);
// Output mesh and element orders in VTK format.
Views::Orderizer ord;
sprintf(title, "ord-%d.vtk", as);
ord.save_orders_vtk(space, title);
Hermes::Mixins::Loggable::Static::info("Element orders in VTK format saved to file %s.", title);
}
// View the coarse mesh solution and polynomial orders.
if (HERMES_VISUALIZATION)
{
sview.show(sln);
oview.show(space);
}
// Skip visualization time.
cpu_time.tick();
// Calculate element errors and total error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating error estimate.");
errorCalculator.calculate_errors(sln, ref_sln);
double err_est_rel = errorCalculator.get_total_error_squared() * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%",
space->get_num_dofs(), ref_space->get_num_dofs(), err_est_rel);
// Add entry to DOF and CPU convergence graphs.
cpu_time.tick();
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.save("conv_cpu_est.dat");
graph_dof.add_values(space->get_num_dofs(), err_est_rel);
graph_dof.save("conv_dof_est.dat");
// Skip the time spent to save the convergence graphs.
cpu_time.tick();
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP)
done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting coarse mesh.");
done = adaptivity.adapt(&selector);
// Increase the counter of performed adaptivity steps.
if (done == false)
as++;
}
}
while (done == false);
Hermes::Mixins::Loggable::Static::info("Total running time: %g s", cpu_time.accumulated());
// Show the fine mesh solution - final result.
sview.set_title("Fine mesh solution");
sview.show_mesh(false);
sview.show(ref_sln);
// Wait for all views to be closed.
Views::View::wait();
return 0;
}