int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable* bt = new ButcherTable(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());
// Turn off adaptive time stepping if R-K method is not embedded.
if (bt->is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) {
warn("R-K method not embedded, turning off adaptive time stepping.");
ADAPTIVE_TIME_STEP_ON = false;
}
// Load the mesh.
Mesh mesh, basemesh;
H2DReader mloader;
mloader.load("square.mesh", &basemesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) basemesh.refine_all_elements();
mesh.copy(&basemesh);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(BDY_DIRICHLET);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_function(BDY_DIRICHLET, essential_bc_values);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
// Convert initial condition into a Solution.
Solution* sln_prev_time = new Solution(&mesh, init_cond);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(stac_jacobian), HERMES_NONSYM, HERMES_ANY, sln_prev_time);
wf.add_vector_form(callback(stac_residual), HERMES_ANY, sln_prev_time);
// Initialize the discrete problem.
bool is_linear = false;
DiscreteProblem dp_coarse(&wf, &space, is_linear);
// Create a refinement selector.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Graph for time step history.
SimpleGraph time_step_graph;
if (ADAPTIVE_TIME_STEP_ON) info("Time step history will be saved to file time_step_history.dat.");
// Time stepping loop.
double current_time = time_step; int ts = 1;
do
{
info("Begin time step %d.", ts);
// Periodic global derefinement.
if (ts > 1 && ts % UNREF_FREQ == 0)
{
info("Global mesh derefinement.");
if (UNREF_LEVEL == 1) mesh.unrefine_all_elements();
else mesh.copy(&basemesh);
space.set_uniform_order(P_INIT);
ndof = Space::get_num_dofs(&space);
}
// Spatial adaptivity loop. Note: sln_prev_time must not be
// changed during spatial adaptivity.
Solution ref_sln;
Solution* time_error_fn;
if (bt->is_embedded() == true) time_error_fn = new Solution(&mesh);
else time_error_fn = NULL;
bool done = false; int as = 1;
double err_est;
do {
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space);
// Initialize discrete problem on reference mesh.
DiscreteProblem* ref_dp = new DiscreteProblem(&wf, ref_space);
// Runge-Kutta step on the fine mesh.
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 is_linear = false;
if (!rk_time_step(current_time, time_step, bt, sln_prev_time, &ref_sln, time_error_fn,
ref_dp, matrix_solver, verbose, is_linear, NEWTON_TOL_FINE, NEWTON_MAX_ITER)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
/* 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;
if (bt->is_embedded() == true) {
info("Calculating temporal error estimate.");
rel_err_time = calc_norm(time_error_fn, HERMES_H1_NORM) / calc_norm(&ref_sln, HERMES_H1_NORM) * 100;
if (ADAPTIVE_TIME_STEP_ON == false) info("rel_err_time: %g%%", rel_err_time);
}
if (ADAPTIVE_TIME_STEP_ON) {
if (rel_err_time > TIME_ERR_TOL_UPPER) {
info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
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;
delete ref_space;
delete ref_dp;
continue;
}
else if (rel_err_time < TIME_ERR_TOL_LOWER) {
info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
info("Increasing tau from %g to %g s and restarting time step.",
time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
delete ref_space;
delete ref_dp;
continue;
}
else {
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 */
info("Spatial adaptivity step %d.", as);
// Project the fine mesh solution onto the coarse mesh.
Solution sln;
info("Projecting fine mesh solution on coarse mesh for error estimation.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
// Calculate element errors and spatial error estimate.
info("Calculating spatial error estimate.");
Adapt* adaptivity = new Adapt(&space);
double err_rel_space = adaptivity->calc_err_est(&sln, &ref_sln) * 100;
// Report results.
info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%",
Space::get_num_dofs(&space), Space::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
{
info("Adapting the coarse mesh.");
done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
if (Space::get_num_dofs(&space) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
// Clean up.
delete adaptivity;
delete ref_space;
delete ref_dp;
}
while (done == false);
// Clean up.
if (time_error_fn != NULL) delete time_error_fn;
// 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);
// Clean up.
delete sln_prev_time;
delete bt;
ndof = Space::get_num_dofs(&space);
printf("ndof allowed = %d\n", 130);
printf("ndof actual = %d\n", ndof);
if (ndof < 130) { // ndofs was 121 at the time this test was created.
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 = new ButcherTable(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());
// Turn off adaptive time stepping if R-K method is not embedded.
if (bt->is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) {
warn("R-K method not embedded, turning off adaptive time stepping.");
ADAPTIVE_TIME_STEP_ON = false;
}
// Load the mesh.
Mesh mesh, basemesh;
H2DReader mloader;
mloader.load("wall.mesh", &basemesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) basemesh.refine_all_elements();
basemesh.refine_towards_boundary(BDY_BOTTOM, INIT_REF_NUM_BDY);
mesh.copy(&basemesh);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_neumann(Hermes::vector<int>(BDY_RIGHT, BDY_LEFT));
bc_types.add_bc_newton(Hermes::vector<int>(BDY_BOTTOM, BDY_TOP));
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, NULL, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Convert initial condition into a Solution.
Solution* sln_prev_time = new Solution(&mesh, TEMP_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(stac_jacobian_vol, stac_jacobian_vol_ord, HERMES_NONSYM, HERMES_ANY, sln_prev_time);
wf.add_vector_form(stac_residual_vol, stac_residual_vol_ord, HERMES_ANY, sln_prev_time);
wf.add_matrix_form_surf(stac_jacobian_bottom, stac_jacobian_bottom_ord, BDY_BOTTOM, sln_prev_time);
wf.add_vector_form_surf(stac_residual_bottom, stac_residual_bottom_ord, BDY_BOTTOM, sln_prev_time);
wf.add_matrix_form_surf(stac_jacobian_top, stac_jacobian_top_ord, BDY_TOP, sln_prev_time);
wf.add_vector_form_surf(stac_residual_top, stac_residual_top_ord, BDY_TOP, sln_prev_time);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Create a refinement selector.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// 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, HERMES_EPS_VERYHIGH);
ordview.show(&space);
// Graph for time step history.
SimpleGraph time_step_graph;
if (ADAPTIVE_TIME_STEP_ON) info("Time step history will be saved to file time_step_history.dat.");
// Time stepping loop:
double current_time = 0; int ts = 1;
do
{
info("Begin time step %d.", ts);
// Periodic global derefinement.
if (ts > 1 && ts % UNREF_FREQ == 0)
{
info("Global mesh derefinement.");
if (UNREF_LEVEL == 1) mesh.unrefine_all_elements();
else mesh.copy(&basemesh);
space.set_uniform_order(P_INIT);
ndof = Space::get_num_dofs(&space);
}
// Spatial adaptivity loop. Note: sln_prev_time must not be
// changed during spatial adaptivity.
Solution ref_sln;
Solution* time_error_fn;
if (bt->is_embedded() == true) time_error_fn = new Solution(&mesh);
else time_error_fn = NULL;
bool done = false; int as = 1;
double err_est;
do {
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space);
// Initialize discrete problem on reference mesh.
DiscreteProblem* ref_dp = new DiscreteProblem(&wf, ref_space);
// Runge-Kutta step on the fine mesh.
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 is_linear = false;
if (!rk_time_step(current_time, time_step, bt, sln_prev_time, &ref_sln, time_error_fn,
ref_dp, matrix_solver, verbose, is_linear, NEWTON_TOL_FINE, NEWTON_MAX_ITER)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
/* 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;
if (bt->is_embedded() == true) {
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, HERMES_EPS_VERYHIGH);
rel_err_time = calc_norm(time_error_fn, HERMES_H1_NORM) / calc_norm(&ref_sln, HERMES_H1_NORM) * 100;
if (ADAPTIVE_TIME_STEP_ON == false) info("rel_err_time: %g%%", rel_err_time);
}
if (ADAPTIVE_TIME_STEP_ON) {
if (rel_err_time > TIME_ERR_TOL_UPPER) {
info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
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;
delete ref_space;
delete ref_dp;
continue;
}
else if (rel_err_time < TIME_ERR_TOL_LOWER) {
info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER);
info("Increasing tau from %g to %g s.", time_step, time_step * TIME_STEP_INC_RATIO);
time_step *= TIME_STEP_INC_RATIO;
}
else {
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 */
info("Spatial adaptivity step %d.", as);
// Project the fine mesh solution onto the coarse mesh.
Solution sln;
info("Projecting fine mesh solution on coarse mesh for error estimation.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
// Show spatial error.
sprintf(title, "Spatial error est, spatial adaptivity step %d", as);
DiffFilter* space_error_fn = new DiffFilter(Hermes::vector<MeshFunction*>(&ref_sln, &sln));
space_error_view.set_title(title);
space_error_view.show_mesh(false);
AbsFilter abs_sef(space_error_fn);
space_error_view.show(&abs_sef, HERMES_EPS_VERYHIGH);
// Calculate element errors and spatial error estimate.
info("Calculating spatial error estimate.");
Adapt* adaptivity = new Adapt(&space);
double err_rel_space = adaptivity->calc_err_est(&sln, &ref_sln) * 100;
// Report results.
info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%",
Space::get_num_dofs(&space), Space::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
{
info("Adapting the coarse mesh.");
done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
if (Space::get_num_dofs(&space) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
// Clean up.
delete adaptivity;
delete ref_space;
delete ref_dp;
delete space_error_fn;
}
while (done == false);
// Clean up.
if (time_error_fn != NULL) delete time_error_fn;
// 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, HERMES_EPS_VERYHIGH);
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);
// Clean up.
delete sln_prev_time;
delete bt;
// Wait for all views to be closed.
View::wait();
return 0;
}