int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table_type);
if (bt.is_explicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Turn off adaptive time stepping if R-K method is not embedded.
if (bt.is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) {
Hermes::Mixins::Loggable::Static::warn("R-K method not embedded, turning off adaptive time stepping.");
ADAPTIVE_TIME_STEP_ON = false;
}
// Load the mesh.
MeshSharedPtr mesh(new Mesh), basemesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("wall.mesh", basemesh);
mesh->copy(basemesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();
mesh->refine_towards_boundary(BDY_RIGHT, 2);
mesh->refine_towards_boundary(BDY_FIRE, INIT_REF_NUM_BDY);
// Initialize essential boundary conditions (none).
EssentialBCs<double> bcs;
// Initialize an H1 space with default shapeset.
SpaceSharedPtr<double> space(new H1Space<double>(mesh, &bcs, P_INIT));
int ndof = Space<double>::get_num_dofs(space);
Hermes::Mixins::Loggable::Static::info("ndof = %d.", ndof);
// Convert initial condition into a Solution.
MeshFunctionSharedPtr<double> sln_prev_time(new ConstantSolution<double> (mesh, TEMP_INIT));
// Initialize the weak formulation.
double current_time = 0;
CustomWeakFormHeatRK wf(BDY_FIRE, BDY_AIR, ALPHA_FIRE, ALPHA_AIR,
RHO, HEATCAP, TEMP_EXT_AIR, TEMP_INIT, ¤t_time);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, space);
// Create a refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST);
// Visualize initial condition.
char title[100];
ScalarView sln_view("Initial condition", new WinGeom(0, 0, 1500, 360));
OrderView ordview("Initial mesh", new WinGeom(0, 410, 1500, 360));
ScalarView time_error_view("Temporal error", new WinGeom(0, 800, 1500, 360));
time_error_view.fix_scale_width(40);
ScalarView space_error_view("Spatial error", new WinGeom(0, 1220, 1500, 360));
space_error_view.fix_scale_width(40);
sln_view.show(sln_prev_time);
ordview.show(space);
// Graph for time step history.
SimpleGraph time_step_graph;
if (ADAPTIVE_TIME_STEP_ON) Hermes::Mixins::Loggable::Static::info("Time step history will be saved to file time_step_history.dat.");
// Class for projections.
OGProjection<double> ogProjection;
// Time stepping loop:
int ts = 1;
do
{
Hermes::Mixins::Loggable::Static::info("Begin time step %d.", ts);
// Periodic global derefinement.
if (ts > 1 && ts % UNREF_FREQ == 0)
{
Hermes::Mixins::Loggable::Static::info("Global mesh derefinement.");
switch (UNREF_METHOD) {
case 1: mesh->copy(basemesh);
space->set_uniform_order(P_INIT);
break;
case 2: space->unrefine_all_mesh_elements();
space->set_uniform_order(P_INIT);
break;
case 3: space->unrefine_all_mesh_elements();
//space->adjust_element_order(-1, P_INIT);
space->adjust_element_order(-1, -1, P_INIT, P_INIT);
break;
default: throw Hermes::Exceptions::Exception("Wrong global derefinement method.");
}
space->assign_dofs();
ndof = Space<double>::get_num_dofs(space);
}
// Spatial adaptivity loop. Note: sln_prev_time must not be
// changed during spatial adaptivity.
MeshFunctionSharedPtr<double> ref_sln(new Solution<double>());
MeshFunctionSharedPtr<double> time_error_fn(new Solution<double>(mesh));
bool done = false; int as = 1;
double err_est;
do {
// Construct globally refined reference mesh and setup reference space.
Mesh::ReferenceMeshCreator refMeshCreator(mesh);
MeshSharedPtr ref_mesh = refMeshCreator.create_ref_mesh();
Space<double>::ReferenceSpaceCreator refSpaceCreator(space, ref_mesh);
SpaceSharedPtr<double> ref_space = refSpaceCreator.create_ref_space();
// Initialize Runge-Kutta time stepping on the reference mesh.
RungeKutta<double> runge_kutta(&wf, ref_space, &bt);
try
{
ogProjection.project_global(ref_space, sln_prev_time,
sln_prev_time);
}
catch(Exceptions::Exception& e)
{
std::cout << e.what() << std::endl;
Hermes::Mixins::Loggable::Static::error("Projection failed.");
return -1;
}
// Runge-Kutta step on the fine mesh->
Hermes::Mixins::Loggable::Static::info("Runge-Kutta time step on fine mesh (t = %g s, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool jacobian_changed = false;
try
{
runge_kutta.set_time(current_time);
runge_kutta.set_time_step(time_step);
runge_kutta.set_max_allowed_iterations(NEWTON_MAX_ITER);
runge_kutta.set_tolerance(NEWTON_TOL_FINE);
runge_kutta.rk_time_step_newton(sln_prev_time, ref_sln, bt.is_embedded() ? time_error_fn : NULL);
}
catch(Exceptions::Exception& e)
{
std::cout << e.what() << std::endl;
Hermes::Mixins::Loggable::Static::error("Runge-Kutta time step failed");
return -1;
}
/* If ADAPTIVE_TIME_STEP_ON == true, estimate temporal error.
If too large or too small, then adjust it and restart the time step. */
double rel_err_time = 0;
if (bt.is_embedded() == true)
{
Hermes::Mixins::Loggable::Static::info("Calculating temporal error estimate.");
// Show temporal error.
char title[100];
sprintf(title, "Temporal error est, spatial adaptivity step %d", as);
time_error_view.set_title(title);
//time_error_view.show_mesh(false);
time_error_view.show(time_error_fn);
rel_err_time = Global<double>::calc_norm(time_error_fn.get(), HERMES_H1_NORM)
/ Global<double>::calc_norm(ref_sln.get(), HERMES_H1_NORM) * 100;
if (ADAPTIVE_TIME_STEP_ON == false) Hermes::Mixins::Loggable::Static::info("rel_err_time: %g%%", rel_err_time);
}
if (ADAPTIVE_TIME_STEP_ON)
{
if (rel_err_time > TIME_ERR_TOL_UPPER)
{
Hermes::Mixins::Loggable::Static::info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
Hermes::Mixins::Loggable::Static::info("Decreasing tau from %g to %g s and restarting time step.",
time_step, time_step * TIME_STEP_DEC_RATIO);
time_step *= TIME_STEP_DEC_RATIO;
continue;
}
else if (rel_err_time < TIME_ERR_TOL_LOWER)
{
Hermes::Mixins::Loggable::Static::info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_LOWER);
Hermes::Mixins::Loggable::Static::info("Increasing tau from %g to %g s.", time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
}
else
{
Hermes::Mixins::Loggable::Static::info("rel_err_time = %g%% is in acceptable interval (%g%%, %g%%)",
rel_err_time, TIME_ERR_TOL_LOWER, TIME_ERR_TOL_UPPER);
}
// Add entry to time step history graph.
time_step_graph.add_values(current_time, time_step);
time_step_graph.save("time_step_history.dat");
}
/* Estimate spatial errors and perform mesh refinement */
Hermes::Mixins::Loggable::Static::info("Spatial adaptivity step %d.", as);
// Project the fine mesh solution onto the coarse mesh.
MeshFunctionSharedPtr<double> sln(new Solution<double>());
Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solution on coarse mesh for error estimation.");
ogProjection.project_global(space, ref_sln, sln);
// Show spatial error.
sprintf(title, "Spatial error est, spatial adaptivity step %d", as);
MeshFunctionSharedPtr<double> space_error_fn(new DiffFilter<double>(Hermes::vector<MeshFunctionSharedPtr<double> >(ref_sln, sln)));
space_error_view.set_title(title);
//space_error_view.show_mesh(false);
MeshFunctionSharedPtr<double> abs_sef(new AbsFilter(space_error_fn));
space_error_view.show(abs_sef);
// Calculate element errors and spatial error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating spatial error estimate.");
adaptivity.set_space(space);
double err_rel_space = errorCalculator.get_total_error_squared() * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%",
Space<double>::get_num_dofs(space), Space<double>::get_num_dofs(ref_space), err_rel_space);
// If err_est too large, adapt the mesh.
if (err_rel_space < SPACE_ERR_TOL) done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting the coarse mesh.");
done = adaptivity.adapt(&selector);
if (Space<double>::get_num_dofs(space) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
// Clean up.
if(!done)
}
while (done == false);
// Visualize the solution and mesh->
char title[100];
sprintf(title, "Solution, time %g s", current_time);
sln_view.set_title(title);
//sln_view.show_mesh(false);
sln_view.show(ref_sln);
sprintf(title, "Mesh, time %g s", current_time);
ordview.set_title(title);
ordview.show(space);
// Copy last reference solution into sln_prev_time
sln_prev_time->copy(ref_sln);
// Increase current time and counter of time steps.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for all views to be closed.
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()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Load the mesh.
MeshSharedPtr mesh(new Mesh), basemesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("square.mesh", basemesh);
mesh->copy(basemesh);
// Initial mesh refinements.
for(int i = 0; i < INIT_GLOB_REF_NUM; i++) mesh->refine_all_elements();
mesh->refine_towards_boundary("Top", INIT_REF_NUM_BDY);
// Initialize boundary conditions.
CustomEssentialBCNonConst bc_essential(Hermes::vector<std::string>("Bottom", "Right", "Top", "Left"));
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
SpaceSharedPtr<double> space(new H1Space<double>(mesh, &bcs, P_INIT));
int ndof_coarse = Space<double>::get_num_dofs(space);
adaptivity.set_space(space);
Hermes::Mixins::Loggable::Static::info("ndof_coarse = %d.", ndof_coarse);
// Zero initial solution. This is why we use H_OFFSET.
MeshFunctionSharedPtr<double> h_time_prev(new ZeroSolution<double>(mesh)), h_time_new(new ZeroSolution<double>(mesh));
// Initialize the constitutive relations.
ConstitutiveRelations* constitutive_relations;
if(constitutive_relations_type == CONSTITUTIVE_GENUCHTEN)
constitutive_relations = new ConstitutiveRelationsGenuchten(ALPHA, M, N, THETA_S, THETA_R, K_S, STORATIVITY);
else
constitutive_relations = new ConstitutiveRelationsGardner(ALPHA, THETA_S, THETA_R, K_S);
// Initialize the weak formulation.
CustomWeakFormRichardsRK wf(constitutive_relations);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, space);
// Create a refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST);
// Visualize initial condition.
char title[100];
ScalarView view("Initial condition", new WinGeom(0, 0, 440, 350));
OrderView ordview("Initial mesh", new WinGeom(445, 0, 440, 350));
view.show(h_time_prev);
ordview.show(space);
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
Hermes::Mixins::TimeMeasurable cpu_time;
cpu_time.tick();
// Time stepping loop.
double current_time = 0; int ts = 1;
do
{
// Periodic global derefinement.
if (ts > 1 && ts % UNREF_FREQ == 0)
{
Hermes::Mixins::Loggable::Static::info("Global mesh derefinement.");
switch (UNREF_METHOD) {
case 1: mesh->copy(basemesh);
space->set_uniform_order(P_INIT);
break;
case 2: mesh->unrefine_all_elements();
space->set_uniform_order(P_INIT);
break;
case 3: space->unrefine_all_mesh_elements();
space->adjust_element_order(-1, -1, P_INIT, P_INIT);
break;
default: throw Hermes::Exceptions::Exception("Wrong global derefinement method.");
}
space->assign_dofs();
ndof_coarse = Space<double>::get_num_dofs(space);
}
// Spatial adaptivity loop. Note: h_time_prev must not be changed
// during spatial adaptivity.
bool done = false; int as = 1;
double err_est;
do {
Hermes::Mixins::Loggable::Static::info("Time step %d, adaptivity step %d:", ts, as);
// Construct globally refined reference mesh and setup reference space.
Mesh::ReferenceMeshCreator refMeshCreator(mesh);
MeshSharedPtr ref_mesh = refMeshCreator.create_ref_mesh();
Space<double>::ReferenceSpaceCreator refSpaceCreator(space, ref_mesh);
SpaceSharedPtr<double> ref_space = refSpaceCreator.create_ref_space();
int ndof_ref = Space<double>::get_num_dofs(ref_space);
// Time measurement.
cpu_time.tick();
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&wf, ref_space, &bt);
// Perform one Runge-Kutta time step according to the selected Butcher's table.
Hermes::Mixins::Loggable::Static::info("Runge-Kutta time step (t = %g s, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
try
{
runge_kutta.set_time(current_time);
runge_kutta.set_time_step(time_step);
runge_kutta.set_max_allowed_iterations(NEWTON_MAX_ITER);
runge_kutta.set_tolerance(NEWTON_TOL);
runge_kutta.rk_time_step_newton(h_time_prev, h_time_new);
}
catch(Exceptions::Exception& e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Runge-Kutta time step failed");
}
// Project the fine mesh solution onto the coarse mesh.
MeshFunctionSharedPtr<double> sln_coarse(new Solution<double>);
Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solution on coarse mesh for error estimation.");
OGProjection<double> ogProjection; ogProjection.project_global(space, h_time_new, sln_coarse);
// Calculate element errors and total error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating error estimate.");
errorCalculator.calculate_errors(sln_coarse, h_time_new, true);
double err_est_rel_total = errorCalculator.get_total_error_squared() * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof_coarse: %d, ndof_ref: %d, err_est_rel: %g%%",
Space<double>::get_num_dofs(space), Space<double>::get_num_dofs(ref_space), err_est_rel_total);
// Time measurement.
cpu_time.tick();
// If err_est too large, adapt the mesh.
if (err_est_rel_total < ERR_STOP) done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting the coarse mesh.");
done = adaptivity.adapt(&selector);
// Increase the counter of performed adaptivity steps.
as++;
}
}
while (done == false);
// Add entry to DOF and CPU convergence graphs.
graph_dof.add_values(current_time, Space<double>::get_num_dofs(space));
graph_dof.save("conv_dof_est.dat");
graph_cpu.add_values(current_time, cpu_time.accumulated());
graph_cpu.save("conv_cpu_est.dat");
// Visualize the solution and mesh->
char title[100];
sprintf(title, "Solution, time %g", current_time);
view.set_title(title);
view.show_mesh(false);
view.show(h_time_new);
sprintf(title, "Mesh, time %g", current_time);
ordview.set_title(title);
ordview.show(space);
// Copy last reference solution into h_time_prev.
h_time_prev->copy(h_time_new);
// Increase current time and counter of time steps.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for all views to be closed.
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;
}
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;
MeshReaderH2D mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize solutions.
CustomInitialConditionWave E_sln(&mesh);
ZeroSolution B_sln(&mesh);
Hermes::vector<Solution<double>*> slns(&E_sln, &B_sln);
// Initialize the weak formulation.
CustomWeakFormWave wf(C_SQUARED);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential("Perfect conductor", 0.0);
EssentialBCs<double> bcs_E(&bc_essential);
EssentialBCs<double> bcs_B;
// Create x- and y- displacement space using the default H1 shapeset.
HcurlSpace<double> E_space(&mesh, &bcs_E, P_INIT);
H1Space<double> B_space(&mesh, &bcs_B, P_INIT);
//L2Space<double> B_space(&mesh, P_INIT);
Hermes::vector<Space<double> *> spaces = Hermes::vector<Space<double> *>(&E_space, &B_space);
info("ndof = %d.", Space<double>::get_num_dofs(spaces));
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, spaces);
// Initialize views.
ScalarView E1_view("Solution E1", new WinGeom(0, 0, 400, 350));
E1_view.fix_scale_width(50);
ScalarView E2_view("Solution E2", new WinGeom(410, 0, 400, 350));
E2_view.fix_scale_width(50);
ScalarView B_view("Solution B", new WinGeom(0, 405, 400, 350));
B_view.fix_scale_width(50);
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&dp, &bt, matrix_solver_type);
// Time stepping loop.
double current_time = time_step; 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;
try
{
runge_kutta.rk_time_step_newton(current_time, time_step, slns, slns, jacobian_changed, verbose);
}
catch(Exceptions::Exception& e)
{
e.printMsg();
error("Runge-Kutta time step failed");
}
// Visualize the solutions.
char title[100];
sprintf(title, "E1, t = %g", current_time);
E1_view.set_title(title);
E1_view.show(&E_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_0);
sprintf(title, "E2, t = %g", current_time);
E2_view.set_title(title);
E2_view.show(&E_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_1);
sprintf(title, "B, t = %g", current_time);
B_view.set_title(title);
B_view.show(&B_sln, HERMES_EPS_NORMAL, H2D_FN_VAL_0);
// Update time.
current_time += time_step;
} while (current_time < T_FINAL);
// Wait for the view to be closed.
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);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize solutions.
CustomInitialConditionWave E_sln(&mesh);
Solution F_sln(&mesh, 0.0, 0.0);
Hermes::vector<Solution*> slns(&E_sln, &F_sln);
// Initialize the weak formulation.
CustomWeakFormWave wf(C_SQUARED);
// Initialize boundary conditions
DefaultEssentialBCConst bc_essential(BDY, 0.0);
EssentialBCs bcs(&bc_essential);
// Create x- and y- displacement space using the default H1 shapeset.
HcurlSpace E_space(&mesh, &bcs, P_INIT);
HcurlSpace F_space(&mesh, &bcs, P_INIT);
Hermes::vector<Space *> spaces = Hermes::vector<Space *>(&E_space, &F_space);
info("ndof = %d.", Space::get_num_dofs(spaces));
// Initialize the FE problem.
DiscreteProblem dp(&wf, spaces);
// 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 verbose = true;
bool jacobian_changed = 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] = {0.3, 0.6, 0.9, 1.4};
double coord_y[4] = {0, 0.3, 0.5, 0.7};
info("Coordinate (0.3, 0.0) value = %lf", F_sln.get_pt_value(coord_x[0], coord_y[0]));
info("Coordinate (0.6, 0.3) value = %lf", F_sln.get_pt_value(coord_x[1], coord_y[1]));
info("Coordinate (0.9, 0.5) value = %lf", F_sln.get_pt_value(coord_x[2], coord_y[2]));
info("Coordinate (1.4, 0.7) value = %lf", F_sln.get_pt_value(coord_x[3], coord_y[3]));
double t_value[4] = {-0.144673, -0.264077, -0.336536, -0.368983};
bool success = true;
for (int i = 0; i < 4; i++)
{
if (fabs(t_value[i] - F_sln.get_pt_value(coord_x[i], coord_y[i])) > 1E-6) success = false;
}
if (success) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
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, basemesh;
MeshReaderH2D mloader;
mloader.load("square.mesh", &basemesh);
mesh.copy(&basemesh);
// Initial mesh refinements.
for(int i = 0; i < INIT_GLOB_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary("Top", INIT_REF_NUM_BDY);
// Initialize boundary conditions.
CustomEssentialBCNonConst bc_essential(Hermes::vector<std::string>("Bottom", "Right", "Top", "Left"));
EssentialBCs<double> bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof_coarse = Space<double>::get_num_dofs(&space);
info("ndof_coarse = %d.", ndof_coarse);
// Zero initial solution. This is why we use H_OFFSET.
ZeroSolution h_time_prev(&mesh), h_time_new(&mesh);
// Initialize the constitutive relations.
ConstitutiveRelations* constitutive_relations;
if(constitutive_relations_type == CONSTITUTIVE_GENUCHTEN)
constitutive_relations = new ConstitutiveRelationsGenuchten(ALPHA, M, N, THETA_S, THETA_R, K_S, STORATIVITY);
else
constitutive_relations = new ConstitutiveRelationsGardner(ALPHA, THETA_S, THETA_R, K_S);
// Initialize the weak formulation.
CustomWeakFormRichardsRK wf(constitutive_relations);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Create a refinement selector.
H1ProjBasedSelector<double> selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Visualize initial condition.
char title[100];
ScalarView view("Initial condition", new WinGeom(0, 0, 440, 350));
OrderView ordview("Initial mesh", new WinGeom(445, 0, 440, 350));
view.show(&h_time_prev);
ordview.show(&space);
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Time stepping loop.
double current_time = 0; int ts = 1;
do
{
// Periodic global derefinement.
if (ts > 1 && ts % UNREF_FREQ == 0)
{
info("Global mesh derefinement.");
switch (UNREF_METHOD) {
case 1: mesh.copy(&basemesh);
space.set_uniform_order(P_INIT);
break;
case 2: mesh.unrefine_all_elements();
space.set_uniform_order(P_INIT);
break;
case 3: space.unrefine_all_mesh_elements();
space.adjust_element_order(-1, -1, P_INIT, P_INIT);
break;
default: error("Wrong global derefinement method.");
}
ndof_coarse = Space<double>::get_num_dofs(&space);
}
// Spatial adaptivity loop. Note: h_time_prev must not be changed
// during spatial adaptivity.
bool done = false; int as = 1;
double err_est;
do {
info("Time step %d, adaptivity step %d:", ts, as);
// Construct globally refined reference mesh and setup reference space.
Space<double>* ref_space = Space<double>::construct_refined_space(&space);
int ndof_ref = Space<double>::get_num_dofs(ref_space);
// Time measurement.
cpu_time.tick();
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&wf, ref_space, &bt, matrix_solver);
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g s, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool freeze_jacobian = false;
bool block_diagonal_jacobian = false;
bool verbose = true;
double damping_coeff = 1.0;
double max_allowed_residual_norm = 1e10;
try
{
runge_kutta.rk_time_step_newton(current_time, time_step, &h_time_prev,
&h_time_new, freeze_jacobian, block_diagonal_jacobian, verbose,
NEWTON_TOL, NEWTON_MAX_ITER, damping_coeff, max_allowed_residual_norm);
}
catch(Exceptions::Exception& e)
{
e.printMsg();
error("Runge-Kutta time step failed");
}
// Project the fine mesh solution onto the coarse mesh.
Solution<double> sln_coarse;
info("Projecting fine mesh solution on coarse mesh for error estimation.");
OGProjection<double>::project_global(&space, &h_time_new, &sln_coarse, matrix_solver);
// Calculate element errors and total error estimate.
info("Calculating error estimate.");
Adapt<double>* adaptivity = new Adapt<double>(&space);
double err_est_rel_total = adaptivity->calc_err_est(&sln_coarse, &h_time_new) * 100;
// Report results.
info("ndof_coarse: %d, ndof_ref: %d, err_est_rel: %g%%",
Space<double>::get_num_dofs(&space), Space<double>::get_num_dofs(ref_space), err_est_rel_total);
// Time measurement.
cpu_time.tick();
// If err_est too large, adapt the mesh.
if (err_est_rel_total < ERR_STOP) done = true;
else
{
info("Adapting the coarse mesh.");
done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
if (Space<double>::get_num_dofs(&space) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
// Clean up.
delete adaptivity;
if(!done)
{
delete h_time_new.get_space();
delete h_time_new.get_mesh();
}
}
while (done == false);
// Add entry to DOF and CPU convergence graphs.
graph_dof.add_values(current_time, Space<double>::get_num_dofs(&space));
graph_dof.save("conv_dof_est.dat");
graph_cpu.add_values(current_time, cpu_time.accumulated());
graph_cpu.save("conv_cpu_est.dat");
// Visualize the solution and mesh.
char title[100];
sprintf(title, "Solution, time %g", current_time);
view.set_title(title);
view.show_mesh(false);
view.show(&h_time_new);
sprintf(title, "Mesh, time %g", current_time);
ordview.set_title(title);
ordview.show(&space);
// Copy last reference solution into h_time_prev.
h_time_prev.copy(&h_time_new);
delete h_time_new.get_mesh();
// Increase current time and counter of time steps.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
try
{
// Sanity check for omega.
double K_squared = Hermes::sqr(OMEGA / M_PI) * (OMEGA - 2) / (1 - OMEGA);
if (K_squared <= 0) throw Hermes::Exceptions::Exception("Wrong choice of omega, K_squared < 0!");
double K_norm_coeff = std::sqrt(K_squared) / std::sqrt(Hermes::sqr(K_x) + Hermes::sqr(K_y));
Hermes::Mixins::Loggable::Static::info("Wave number K = %g", std::sqrt(K_squared));
K_x *= K_norm_coeff;
K_y *= K_norm_coeff;
// Wave number.
double K = std::sqrt(Hermes::sqr(K_x) + Hermes::sqr(K_y));
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table);
if (bt.is_explicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Load the mesh.
MeshSharedPtr E_mesh(new Mesh), H_mesh(new Mesh), P_mesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("domain.mesh", E_mesh);
mloader.load("domain.mesh", H_mesh);
mloader.load("domain.mesh", P_mesh);
// Perform initial mesh refinemets.
for (int i = 0; i < INIT_REF_NUM; i++)
{
E_mesh->refine_all_elements();
H_mesh->refine_all_elements();
P_mesh->refine_all_elements();
}
// Initialize solutions.
double current_time = 0;
MeshFunctionSharedPtr<double> E_time_prev(new CustomInitialConditionE(E_mesh, current_time, OMEGA, K_x, K_y));
MeshFunctionSharedPtr<double> H_time_prev(new CustomInitialConditionH(H_mesh, current_time, OMEGA, K_x, K_y));
MeshFunctionSharedPtr<double> P_time_prev(new CustomInitialConditionP(P_mesh, current_time, OMEGA, K_x, K_y));
Hermes::vector<MeshFunctionSharedPtr<double> > slns_time_prev(E_time_prev, H_time_prev, P_time_prev);
MeshFunctionSharedPtr<double> E_time_new(new Solution<double>(E_mesh)), H_time_new(new Solution<double>(H_mesh)), P_time_new(new Solution<double>(P_mesh));
MeshFunctionSharedPtr<double> E_time_new_coarse(new Solution<double>(E_mesh)), H_time_new_coarse(new Solution<double>(H_mesh)), P_time_new_coarse(new Solution<double>(P_mesh));
Hermes::vector<MeshFunctionSharedPtr<double> > slns_time_new(E_time_new, H_time_new, P_time_new);
// Initialize the weak formulation.
CustomWeakFormMD wf(OMEGA, K_x, K_y, MU_0, EPS_0, EPS_INF, EPS_Q, TAU);
// Initialize boundary conditions
DefaultEssentialBCConst<double> bc_essential("Bdy", 0.0);
EssentialBCs<double> bcs(&bc_essential);
SpaceSharedPtr<double> E_space(new HcurlSpace<double>(E_mesh, &bcs, P_INIT));
SpaceSharedPtr<double> H_space(new H1Space<double>(H_mesh, NULL, P_INIT));
//L2Space<double> H_space(mesh, P_INIT));
SpaceSharedPtr<double> P_space(new HcurlSpace<double>(P_mesh, &bcs, P_INIT));
Hermes::vector<SpaceSharedPtr<double> > spaces = Hermes::vector<SpaceSharedPtr<double> >(E_space, H_space, P_space);
// Initialize views.
ScalarView E1_view("Solution E1", new WinGeom(0, 0, 400, 350));
E1_view.fix_scale_width(50);
ScalarView E2_view("Solution E2", new WinGeom(410, 0, 400, 350));
E2_view.fix_scale_width(50);
ScalarView H_view("Solution H", new WinGeom(0, 410, 400, 350));
H_view.fix_scale_width(50);
ScalarView P1_view("Solution P1", new WinGeom(410, 410, 400, 350));
P1_view.fix_scale_width(50);
ScalarView P2_view("Solution P2", new WinGeom(820, 410, 400, 350));
P2_view.fix_scale_width(50);
// Visualize initial conditions.
char title[100];
sprintf(title, "E1 - Initial Condition");
E1_view.set_title(title);
E1_view.show(E_time_prev, H2D_FN_VAL_0);
sprintf(title, "E2 - Initial Condition");
E2_view.set_title(title);
E2_view.show(E_time_prev, H2D_FN_VAL_1);
sprintf(title, "H - Initial Condition");
H_view.set_title(title);
H_view.show(H_time_prev);
sprintf(title, "P1 - Initial Condition");
P1_view.set_title(title);
P1_view.show(P_time_prev, H2D_FN_VAL_0);
sprintf(title, "P2 - Initial Condition");
P2_view.set_title(title);
P2_view.show(P_time_prev, H2D_FN_VAL_1);
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&wf, spaces, &bt);
runge_kutta.set_max_allowed_iterations(NEWTON_MAX_ITER);
runge_kutta.set_tolerance(NEWTON_TOL);
runge_kutta.set_verbose_output(true);
// Initialize refinement selector.
H1ProjBasedSelector<double> H1selector(CAND_LIST);
HcurlProjBasedSelector<double> HcurlSelector(CAND_LIST);
// Time stepping loop.
int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
Hermes::Mixins::Loggable::Static::info("\nRunge-Kutta time step (t = %g s, time_step = %g s, stages: %d).",
current_time, time_step, bt.get_size());
// Periodic global derefinements.
if (ts > 1 && ts % UNREF_FREQ == 0 && REFINEMENT_COUNT > 0)
{
Hermes::Mixins::Loggable::Static::info("Global mesh derefinement.");
REFINEMENT_COUNT = 0;
E_space->unrefine_all_mesh_elements(true);
H_space->unrefine_all_mesh_elements(true);
P_space->unrefine_all_mesh_elements(true);
E_space->adjust_element_order(-1, P_INIT);
H_space->adjust_element_order(-1, P_INIT);
P_space->adjust_element_order(-1, P_INIT);
E_space->assign_dofs();
H_space->assign_dofs();
P_space->assign_dofs();
}
// 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.
int order_increase = 1;
Mesh::ReferenceMeshCreator refMeshCreatorE(E_mesh);
Mesh::ReferenceMeshCreator refMeshCreatorH(H_mesh);
Mesh::ReferenceMeshCreator refMeshCreatorP(P_mesh);
MeshSharedPtr ref_mesh_E = refMeshCreatorE.create_ref_mesh();
MeshSharedPtr ref_mesh_H = refMeshCreatorH.create_ref_mesh();
MeshSharedPtr ref_mesh_P = refMeshCreatorP.create_ref_mesh();
Space<double>::ReferenceSpaceCreator refSpaceCreatorE(E_space, ref_mesh_E, order_increase);
SpaceSharedPtr<double> ref_space_E = refSpaceCreatorE.create_ref_space();
Space<double>::ReferenceSpaceCreator refSpaceCreatorH(H_space, ref_mesh_H, order_increase);
SpaceSharedPtr<double> ref_space_H = refSpaceCreatorH.create_ref_space();
Space<double>::ReferenceSpaceCreator refSpaceCreatorP(P_space, ref_mesh_P, order_increase);
SpaceSharedPtr<double> ref_space_P = refSpaceCreatorP.create_ref_space();
Hermes::vector<SpaceSharedPtr<double> > ref_spaces(ref_space_E, ref_space_H, ref_space_P);
int ndof = Space<double>::get_num_dofs(ref_spaces);
Hermes::Mixins::Loggable::Static::info("ndof = %d.", ndof);
try
{
runge_kutta.set_spaces(ref_spaces);
runge_kutta.set_time(current_time);
runge_kutta.set_time_step(time_step);
runge_kutta.rk_time_step_newton(slns_time_prev, slns_time_new);
}
catch (Exceptions::Exception& e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Runge-Kutta time step failed");
}
// Visualize the solutions.
char title[100];
sprintf(title, "E1, t = %g", current_time + time_step);
E1_view.set_title(title);
E1_view.show(E_time_new, H2D_FN_VAL_0);
sprintf(title, "E2, t = %g", current_time + time_step);
E2_view.set_title(title);
E2_view.show(E_time_new, H2D_FN_VAL_1);
sprintf(title, "H, t = %g", current_time + time_step);
H_view.set_title(title);
H_view.show(H_time_new);
sprintf(title, "P1, t = %g", current_time + time_step);
P1_view.set_title(title);
P1_view.show(P_time_new, H2D_FN_VAL_0);
sprintf(title, "P2, t = %g", current_time + time_step);
P2_view.set_title(title);
P2_view.show(P_time_new, H2D_FN_VAL_1);
// 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> >(E_space, H_space,
P_space), Hermes::vector<MeshFunctionSharedPtr<double> >(E_time_new, H_time_new, P_time_new), Hermes::vector<MeshFunctionSharedPtr<double> >(E_time_new_coarse, H_time_new_coarse, P_time_new_coarse));
// Calculate element errors and total error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating error estimate.");
adaptivity.set_spaces(Hermes::vector<SpaceSharedPtr<double> >(E_space, H_space, P_space));
errorCalculator.calculate_errors(Hermes::vector<MeshFunctionSharedPtr<double> >(E_time_new_coarse, H_time_new_coarse, P_time_new_coarse),
Hermes::vector<MeshFunctionSharedPtr<double> >(E_time_new, H_time_new, P_time_new));
double err_est_rel_total = errorCalculator.get_total_error_squared() * 100.;
// Report results.
Hermes::Mixins::Loggable::Static::info("Error estimate: %g%%", err_est_rel_total);
// If err_est too large, adapt the mesh.
if (err_est_rel_total < ERR_STOP)
{
Hermes::Mixins::Loggable::Static::info("Error estimate under the specified threshold -> moving to next time step.");
done = true;
}
else
{
Hermes::Mixins::Loggable::Static::info("Adapting coarse mesh.");
REFINEMENT_COUNT++;
done = adaptivity.adapt(Hermes::vector<RefinementSelectors::Selector<double> *>(&HcurlSelector, &H1selector, &HcurlSelector));
if (!done)
as++;
}
} while (!done);
//View::wait();
E_time_prev->copy(E_time_new);
H_time_prev->copy(H_time_new);
P_time_prev->copy(P_time_new);
// Update time.
current_time += time_step;
ts++;
} while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
}
catch (std::exception& e)
{
std::cout << e.what();
}
return 0;
}
// Main function.
int main(int argc, char* argv[])
{
ConstitutiveRelationsGenuchtenWithLayer constitutive_relations(CONSTITUTIVE_TABLE_METHOD, NUM_OF_INSIDE_PTS, LOW_LIMIT, TABLE_PRECISION, TABLE_LIMIT, K_S_vals, ALPHA_vals, N_vals, M_vals, THETA_R_vals, THETA_S_vals, STORATIVITY_vals);
// Either use exact constitutive relations (slow) (method 0) or precalculate
// their linear approximations (faster) (method 1) or
// precalculate their quintic polynomial approximations (method 2) -- managed by
// the following loop "Initializing polynomial approximation".
if (CONSTITUTIVE_TABLE_METHOD == 1)
constitutive_relations.constitutive_tables_ready = get_constitutive_tables(1, &constitutive_relations, MATERIAL_COUNT); // 1 stands for the Newton's method.
// The van Genuchten + Mualem K(h) function is approximated by polynomials close
// to zero in case of CONSTITUTIVE_TABLE_METHOD==1.
// In case of CONSTITUTIVE_TABLE_METHOD==2, all constitutive functions are approximated by polynomials.
info("Initializing polynomial approximations.");
for (int i=0; i < MATERIAL_COUNT; i++)
{
// Points to be used for polynomial approximation of K(h).
double* points = new double[NUM_OF_INSIDE_PTS];
init_polynomials(6 + NUM_OF_INSIDE_PTS, LOW_LIMIT, points, NUM_OF_INSIDE_PTS, i, &constitutive_relations, MATERIAL_COUNT, NUM_OF_INTERVALS, INTERVALS_4_APPROX);
}
constitutive_relations.polynomials_ready = true;
if (CONSTITUTIVE_TABLE_METHOD == 2)
{
constitutive_relations.constitutive_tables_ready = true;
//Assign table limit to global definition.
constitutive_relations.table_limit = INTERVALS_4_APPROX[NUM_OF_INTERVALS-1];
}
// 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, basemesh;
MeshReaderH2D mloader;
mloader.load(mesh_file, &basemesh);
// Perform initial mesh refinements.
mesh.copy(&basemesh);
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary("Top", INIT_REF_NUM_BDY_TOP);
// Initialize boundary conditions.
RichardsEssentialBC bc_essential("Top", H_ELEVATION, PULSE_END_TIME, H_INIT, STARTUP_TIME);
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();
info("ndof = %d.", ndof);
// Convert initial condition into a Solution.
ZeroSolution h_time_prev(&mesh), h_time_new(&mesh), time_error_fn(&mesh);
// Initialize views.
ScalarView view("Initial condition", new WinGeom(0, 0, 600, 500));
view.fix_scale_width(80);
// Visualize the initial condition.
view.show(&h_time_prev);
// Initialize the weak formulation.
CustomWeakFormRichardsRK wf(&constitutive_relations);
// Visualize the projection and mesh.
ScalarView sview("Initial condition", new WinGeom(0, 0, 400, 350));
sview.fix_scale_width(50);
sview.show(&h_time_prev, HERMES_EPS_VERYHIGH);
ScalarView eview("Temporal error", new WinGeom(405, 0, 400, 350));
eview.fix_scale_width(50);
eview.show(&time_error_fn, HERMES_EPS_VERYHIGH);
OrderView oview("Initial mesh", new WinGeom(810, 0, 350, 350));
oview.show(&space);
// Graph for time step history.
SimpleGraph time_step_graph;
info("Time step history will be saved to file time_step_history.dat.");
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&wf, &space, &bt, matrix_solver);
// Time stepping:
double current_time = 0;
int ts = 1;
do
{
info("---- Time step %d, time %3.5f s", ts, current_time);
Space<double>::update_essential_bc_values(&space, current_time);
// 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 freeze_jacobian = false;
bool block_diagonal_jacobian = false;
bool verbose = true;
double damping_coeff = 1.0;
double max_allowed_residual_norm = 1e10;
try
{
runge_kutta.rk_time_step_newton(current_time, time_step, &h_time_prev,
&h_time_new, &time_error_fn, freeze_jacobian, block_diagonal_jacobian, verbose,
NEWTON_TOL, NEWTON_MAX_ITER, damping_coeff, max_allowed_residual_norm);
}
catch(Exceptions::Exception& e)
{
info("Runge-Kutta time step failed, decreasing time step size from %g to %g days.",
time_step, time_step * time_step_dec);
time_step *= time_step_dec;
if (time_step < time_step_min)
error("Time step became too small.");
continue;
}
// Copy solution for the new time step.
h_time_prev.copy(&h_time_new);
// Show error function.
char title[100];
sprintf(title, "Temporal error, t = %g", current_time);
eview.set_title(title);
eview.show(&time_error_fn, HERMES_EPS_VERYHIGH);
// Calculate relative time stepping error and decide whether the
// time step can be accepted. If not, then the time step size is
// reduced and the entire time step repeated. If yes, then another
// check is run, and if the relative error is very low, time step
// is increased.
double rel_err_time = Global<double>::calc_norm(&time_error_fn, HERMES_H1_NORM) / Global<double>::calc_norm(&h_time_new, HERMES_H1_NORM) * 100;
info("rel_err_time = %g%%", rel_err_time);
if (rel_err_time > time_tol_upper) {
info("rel_err_time above upper limit %g%% -> decreasing time step from %g to %g days and repeating time step.",
time_tol_upper, time_step, time_step * time_step_dec);
time_step *= time_step_dec;
continue;
}
if (rel_err_time < time_tol_lower) {
info("rel_err_time = below lower limit %g%% -> increasing time step from %g to %g days",
time_tol_lower, time_step, time_step * time_step_inc);
time_step *= time_step_inc;
}
// Add entry to the timestep graph.
time_step_graph.add_values(current_time, time_step);
time_step_graph.save("time_step_history.dat");
// Update time.
current_time += time_step;
// Show the new time level solution.
sprintf(title, "Solution, t = %g", current_time);
sview.set_title(title);
sview.show(&h_time_new, HERMES_EPS_VERYHIGH);
oview.show(&space);
// Save complete Solution.
char filename[100];
sprintf(filename, "outputs/tsln_%f.dat", current_time);
h_time_new.save(filename);
info("Solution at time %g saved to file %s.", current_time, filename);
// Save solution for the next time step.
h_time_prev.copy(&h_time_new);
// Increase time step counter.
ts++;
}
while (current_time < T_FINAL);
// Wait for the view to be closed.
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()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Turn off adaptive time stepping if R-K method is not embedded.
if (bt.is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) {
Hermes::Mixins::Loggable::Static::warn("R-K method not embedded, turning off adaptive time stepping.");
ADAPTIVE_TIME_STEP_ON = false;
}
// Load the mesh.
MeshSharedPtr mesh(new Mesh), basemesh(new Mesh);
MeshReaderH2D mloader;
mloader.load("square.mesh", basemesh);
mesh->copy(basemesh);
// Initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh->refine_all_elements();
// Convert initial condition into a Solution<complex>.
MeshFunctionSharedPtr<complex> psi_time_prev(new CustomInitialCondition(mesh));
// Initialize the weak formulation.
double current_time = 0;
// Initialize weak formulation.
CustomWeakFormGPRK wf(h, m, g, omega);
// Initialize boundary conditions.
DefaultEssentialBCConst<complex> bc_essential("Bdy", 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();
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the FE problem.
DiscreteProblem<complex> dp(&wf, space);
// Create a refinement selector.
H1ProjBasedSelector<complex> selector(CAND_LIST);
// Visualize initial condition.
char title[100];
ScalarView sview_real("Initial condition - real part", new WinGeom(0, 0, 600, 500));
ScalarView sview_imag("Initial condition - imaginary part", new WinGeom(610, 0, 600, 500));
sview_real.show_mesh(false);
sview_imag.show_mesh(false);
sview_real.fix_scale_width(50);
sview_imag.fix_scale_width(50);
OrderView ord_view("Initial mesh", new WinGeom(445, 0, 440, 350));
ord_view.fix_scale_width(50);
ScalarView time_error_view("Temporal error", new WinGeom(0, 400, 440, 350));
time_error_view.fix_scale_width(50);
time_error_view.fix_scale_width(60);
ScalarView space_error_view("Spatial error", new WinGeom(445, 400, 440, 350));
space_error_view.fix_scale_width(50);
MeshFunctionSharedPtr<double> real(new RealFilter(psi_time_prev));
MeshFunctionSharedPtr<double> imag(new ImagFilter(psi_time_prev));
sview_real.show(real);
sview_imag.show(imag);
ord_view.show(space);
// Graph for time step history.
SimpleGraph time_step_graph;
if (ADAPTIVE_TIME_STEP_ON) Hermes::Mixins::Loggable::Static::info("Time step history will be saved to file time_step_history.dat.");
// Time stepping:
int num_time_steps = (int)(T_FINAL/time_step + 0.5);
for(int ts = 1; ts <= num_time_steps; ts++)
// Time stepping loop.
double current_time = 0.0; int ts = 1;
do
{
Hermes::Mixins::Loggable::Static::info("Begin time step %d.", ts);
// Periodic global derefinement.
if (ts > 1 && ts % UNREF_FREQ == 0)
{
Hermes::Mixins::Loggable::Static::info("Global mesh derefinement.");
switch (UNREF_METHOD) {
case 1: mesh->copy(basemesh);
space->set_uniform_order(P_INIT);
break;
case 2: space->unrefine_all_mesh_elements();
space->set_uniform_order(P_INIT);
break;
case 3: space->unrefine_all_mesh_elements();
space->adjust_element_order(-1, -1, P_INIT, P_INIT);
break;
default: throw Hermes::Exceptions::Exception("Wrong global derefinement method.");
}
ndof = Space<complex>::get_num_dofs(space);
}
Hermes::Mixins::Loggable::Static::info("ndof: %d", ndof);
// Spatial adaptivity loop. Note: psi_time_prev must not be
// changed during spatial adaptivity.
MeshFunctionSharedPtr<complex> ref_sln(new Solution<complex>());
MeshFunctionSharedPtr<complex> time_error_fn(new Solution<complex>);
bool done = false;
int as = 1;
double err_est;
do {
// Construct globally refined reference mesh and setup reference space.
Mesh::ReferenceMeshCreator refMeshCreator(mesh);
MeshSharedPtr ref_mesh = refMeshCreator.create_ref_mesh();
Space<complex>::ReferenceSpaceCreator refSpaceCreator(space, ref_mesh);
SpaceSharedPtr<complex> ref_space = refSpaceCreator.create_ref_space();
// Initialize discrete problem on reference mesh.
DiscreteProblem<complex>* ref_dp = new DiscreteProblem<complex>(&wf, ref_space);
RungeKutta<complex> runge_kutta(&wf, ref_space, &bt);
// Runge-Kutta step on the fine mesh->
Hermes::Mixins::Loggable::Static::info("Runge-Kutta time step on fine mesh (t = %g s, time step = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
try
{
runge_kutta.set_time(current_time);
runge_kutta.set_time_step(time_step);
runge_kutta.set_max_allowed_iterations(NEWTON_MAX_ITER);
runge_kutta.set_tolerance(NEWTON_TOL_FINE);
runge_kutta.rk_time_step_newton(psi_time_prev, ref_sln, time_error_fn);
}
catch(Exceptions::Exception& e)
{
e.print_msg();
throw Hermes::Exceptions::Exception("Runge-Kutta time step failed");
}
/* If ADAPTIVE_TIME_STEP_ON == true, estimate temporal error.
If too large or too small, then adjust it and restart the time step. */
double rel_err_time = 0;
if (bt.is_embedded() == true) {
Hermes::Mixins::Loggable::Static::info("Calculating temporal error estimate.");
// Show temporal error.
char title[100];
sprintf(title, "Temporal error est, spatial adaptivity step %d", as);
time_error_view.set_title(title);
time_error_view.show_mesh(false);
MeshFunctionSharedPtr<double> abs_time(new RealFilter(time_error_fn));
MeshFunctionSharedPtr<double> abs_tef(new AbsFilter(abs_time));
time_error_view.show(abs_tef);
rel_err_time = Global<complex>::calc_norm(time_error_fn.get(), HERMES_H1_NORM) /
Global<complex>::calc_norm(ref_sln.get(), HERMES_H1_NORM) * 100;
if (ADAPTIVE_TIME_STEP_ON == false) Hermes::Mixins::Loggable::Static::info("rel_err_time: %g%%", rel_err_time);
}
if (ADAPTIVE_TIME_STEP_ON) {
if (rel_err_time > TIME_ERR_TOL_UPPER) {
Hermes::Mixins::Loggable::Static::info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
Hermes::Mixins::Loggable::Static::info("Decreasing time step from %g to %g s and restarting time step.",
time_step, time_step * TIME_STEP_DEC_RATIO);
time_step *= TIME_STEP_DEC_RATIO;
delete ref_dp;
continue;
}
else if (rel_err_time < TIME_ERR_TOL_LOWER) {
Hermes::Mixins::Loggable::Static::info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_LOWER);
Hermes::Mixins::Loggable::Static::info("Increasing time step from %g to %g s.", time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
delete ref_dp;
continue;
}
else {
Hermes::Mixins::Loggable::Static::info("rel_err_time = %g%% is in acceptable interval (%g%%, %g%%)",
rel_err_time, TIME_ERR_TOL_LOWER, TIME_ERR_TOL_UPPER);
}
// Add entry to time step history graph.
time_step_graph.add_values(current_time, time_step);
time_step_graph.save("time_step_history.dat");
}
/* Estimate spatial errors and perform mesh refinement */
Hermes::Mixins::Loggable::Static::info("Spatial adaptivity step %d.", as);
// Project the fine mesh solution onto the coarse mesh.
MeshFunctionSharedPtr<complex> sln(new Solution<complex>);
Hermes::Mixins::Loggable::Static::info("Projecting fine mesh solution on coarse mesh for error estimation.");
OGProjection<complex> ogProjection; ogProjection.project_global(space, ref_sln, sln);
// Show spatial error.
sprintf(title, "Spatial error est, spatial adaptivity step %d", as);
MeshFunctionSharedPtr<complex> space_error_fn(new DiffFilter<complex>(Hermes::vector<MeshFunctionSharedPtr<complex> >(ref_sln, sln)));
space_error_view.set_title(title);
space_error_view.show_mesh(false);
MeshFunctionSharedPtr<double> abs_space(new RealFilter(space_error_fn));
MeshFunctionSharedPtr<double> abs_sef(new AbsFilter(abs_space));
space_error_view.show(abs_sef);
// Calculate element errors and spatial error estimate.
Hermes::Mixins::Loggable::Static::info("Calculating spatial error estimate.");
Adapt<complex> adaptivity(space);
double err_rel_space = errorCalculator.get_total_error_squared() * 100;
// Report results.
Hermes::Mixins::Loggable::Static::info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%",
Space<complex>::get_num_dofs(space), Space<complex>::get_num_dofs(ref_space), err_rel_space);
// If err_est too large, adapt the mesh.
if (err_rel_space < SPACE_ERR_TOL) done = true;
else
{
Hermes::Mixins::Loggable::Static::info("Adapting the coarse mesh.");
done = adaptivity.adapt(&selector);
// Increase the counter of performed adaptivity steps.
as++;
}
// Clean up.
delete ref_dp;
}
while (done == false);
// Visualize the solution and mesh->
char title[100];
sprintf(title, "Solution - real part, Time %3.2f s", current_time);
sview_real.set_title(title);
sprintf(title, "Solution - imaginary part, Time %3.2f s", current_time);
sview_imag.set_title(title);
MeshFunctionSharedPtr<double> real(new RealFilter(ref_sln));
MeshFunctionSharedPtr<double> imag(new ImagFilter(ref_sln));
sview_real.show(real);
sview_imag.show(imag);
sprintf(title, "Mesh, time %g s", current_time);
ord_view.set_title(title);
ord_view.show(space);
// Copy last reference solution into psi_time_prev.
psi_time_prev->copy(ref_sln);
// Increase current time and counter of time steps.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for all views to be closed.
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()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage explicit R-K method.", bt.get_size());
if (bt.is_diagonally_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage diagonally implicit R-K method.", bt.get_size());
if (bt.is_fully_implicit()) Hermes::Mixins::Loggable::Static::info("Using a %d-stage fully implicit R-K method.", bt.get_size());
// Load the mesh.
Mesh mesh;
MeshReaderH2D mloader;
mloader.load("square.mesh", &mesh);
// Initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Convert initial condition into a Solution<std::complex<double> >.
CustomInitialCondition psi_time_prev(&mesh);
Solution<std::complex<double> > psi_time_new(&mesh);
// Initialize the weak formulation.
double current_time = 0;
CustomWeakFormGPRK wf(h, m, g, omega);
// Initialize boundary conditions.
DefaultEssentialBCConst<std::complex<double> > bc_essential("Bdy", 0.0);
EssentialBCs<std::complex<double> > bcs(&bc_essential);
// Create an H1 space with default shapeset.
H1Space<std::complex<double> > space(&mesh, &bcs, P_INIT);
int ndof = space.get_num_dofs();
Hermes::Mixins::Loggable::Static::info("ndof = %d", ndof);
// Initialize the FE problem.
DiscreteProblem<std::complex<double> > dp(&wf, &space);
// Initialize views.
ScalarView sview_real("Solution - real part", new WinGeom(0, 0, 600, 500));
ScalarView sview_imag("Solution - imaginary part", new WinGeom(610, 0, 600, 500));
sview_real.fix_scale_width(80);
sview_imag.fix_scale_width(80);
// Initialize Runge-Kutta time stepping.
RungeKutta<std::complex<double> > runge_kutta(&wf, &space, &bt);
// Time stepping:
int ts = 1;
int nstep = (int)(T_FINAL/time_step + 0.5);
for(int ts = 1; ts <= nstep; ts++)
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
Hermes::Mixins::Loggable::Static::info("Runge-Kutta time step (t = %g s, time step = %g s, stages: %d).",
current_time, time_step, bt.get_size());
try
{
runge_kutta.setTime(current_time);
runge_kutta.setTimeStep(time_step);
runge_kutta.rk_time_step_newton(&psi_time_prev, &psi_time_new);
}
catch(Exceptions::Exception& e)
{
e.printMsg();
throw Hermes::Exceptions::Exception("Runge-Kutta time step failed");
}
// Show the new time level solution.
char title[100];
sprintf(title, "Solution - real part, Time %3.2f s", current_time);
sview_real.set_title(title);
sprintf(title, "Solution - imaginary part, Time %3.2f s", current_time);
sview_imag.set_title(title);
RealFilter real(&psi_time_new);
ImagFilter imag(&psi_time_new);
sview_real.show(&real);
sview_imag.show(&imag);
// Copy solution for the new time step.
psi_time_prev.copy(&psi_time_new);
// Increase current time and time step counter.
current_time += time_step;
ts++;
}
// Wait for the view to be closed.
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;
MeshReaderH2D mloader;
mloader.load("wall.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_RIGHT, 2);
mesh.refine_towards_boundary(BDY_FIRE, INIT_REF_NUM_BDY);
// Initialize essential boundary conditions (none).
EssentialBCs<double> bcs;
// Initialize an H1 space with default shapeset.
H1Space<double> space(&mesh, &bcs, P_INIT);
int ndof = Space<double>::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous and next time level solutions.
ConstantSolution<double> sln_time_prev(&mesh, TEMP_INIT);
ZeroSolution sln_time_new(&mesh);
ConstantSolution<double> time_error_fn(&mesh, 0.0);
// Initialize the weak formulation.
double current_time = 0;
CustomWeakFormHeatRK wf(BDY_FIRE, BDY_AIR, ALPHA_FIRE, ALPHA_AIR,
RHO, HEATCAP, TEMP_EXT_AIR, TEMP_INIT, ¤t_time);
// Initialize the FE problem.
DiscreteProblem<double> dp(&wf, &space);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 1500, 400));
Tview.fix_scale_width(40);
ScalarView eview("Temporal error", new WinGeom(0, 450, 1500, 400));
eview.fix_scale_width(40);
// Graph for time step history.
SimpleGraph time_step_graph;
info("Time step history will be saved to file time_step_history.dat.");
// Initialize Runge-Kutta time stepping.
RungeKutta<double> runge_kutta(&dp, &bt, matrix_solver_type);
// Time stepping loop:
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, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool jacobian_changed = false;
bool verbose = true;
try
{
runge_kutta.rk_time_step_newton(current_time, time_step, &sln_time_prev, &sln_time_new,
&time_error_fn, !jacobian_changed, false, verbose);
}
catch(Exceptions::Exception& e)
{
e.printMsg();
error("Runge-Kutta time step failed");
}
// Plot error function.
char title[100];
sprintf(title, "Temporal error, t = %g", current_time);
eview.set_title(title);
AbsFilter abs_tef(&time_error_fn);
eview.show(&abs_tef, HERMES_EPS_VERYHIGH);
// Calculate relative time stepping error and decide whether the
// time step can be accepted. If not, then the time step size is
// reduced and the entire time step repeated. If yes, then another
// check is run, and if the relative error is very low, time step
// is increased.
double rel_err_time = Global<double>::calc_norm(&time_error_fn, HERMES_H1_NORM)
/ Global<double>::calc_norm(&sln_time_new, HERMES_H1_NORM) * 100;
info("rel_err_time = %g%%", rel_err_time);
if (rel_err_time > TIME_TOL_UPPER) {
info("rel_err_time above upper limit %g%% -> decreasing time step from %g to %g and restarting time step.",
TIME_TOL_UPPER, time_step, time_step * TIME_STEP_DEC_RATIO);
time_step *= TIME_STEP_DEC_RATIO;
continue;
}
if (rel_err_time < TIME_TOL_LOWER) {
info("rel_err_time = below lower limit %g%% -> increasing time step from %g to %g",
TIME_TOL_UPPER, time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
}
// Add entry to the timestep graph.
time_step_graph.add_values(current_time, time_step);
time_step_graph.save("time_step_history.dat");
// Update time.
current_time += time_step;
// Show the new time level solution.
sprintf(title, "Time %3.2f s", current_time);
Tview.set_title(title);
Tview.show(&sln_time_new);
// Copy solution for the new time step.
sln_time_prev.copy(&sln_time_new);
// Increase counter of time steps.
ts++;
}
while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
