int main(int argc, char **args)
{
// Test variable.
int success_test = 1;
if (argc < 3) error("Not enough parameters.");
// Load the mesh.
Mesh mesh;
H3DReader mloader;
if (!mloader.load(args[1], &mesh)) error("Loading mesh file '%s'.", args[1]);
// Initialize the space according to the
// command-line parameters passed.
int o;
sscanf(args[2], "%d", &o);
Ord3 order(o, o, o);
HcurlSpace space(&mesh, bc_types, NULL, order);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_UNSYM);
wf.add_matrix_form_surf(bilinear_form_surf<double, scalar>, bilinear_form_surf<Ord, Ord>);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>);
wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<Ord, Ord>);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Initialize the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
initialize_solution_environment(matrix_solver, argc, args);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Assemble the linear problem.
info("Assembling (ndof: %d).", Space::get_num_dofs(&space));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving.");
Solution sln(&mesh);
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
ExactSolution ex_sln(&mesh, exact_solution);
// Calculate exact error.
info("Calculating exact error.");
Adapt *adaptivity = new Adapt(&space, HERMES_HCURL_NORM);
bool solutions_for_adapt = false;
double err_exact = adaptivity->calc_err_exact(&sln, &ex_sln, solutions_for_adapt, HERMES_TOTAL_ERROR_ABS);
printf("err_exact = %lf", err_exact);
if (err_exact > EPS)
// Calculated solution is not precise enough.
success_test = 0;
// Clean up.
delete matrix;
delete rhs;
delete solver;
delete adaptivity;
// Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
finalize_solution_environment(matrix_solver);
if (success_test) {
info("Success!");
return ERR_SUCCESS;
}
else {
info("Failure!");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements.
for(int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(BDY_LEFT);
bc_types.add_bc_neumann(Hermes::vector<int>(BDY_OUTER, BDY_INNER));
bc_types.add_bc_newton(BDY_BOTTOM);
// Enter Dirichlet boudnary values.
BCValues bc_values;
bc_values.add_const(BDY_LEFT, T1);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d", ndof);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form_1), HERMES_SYM, MATERIAL_1);
wf.add_matrix_form(callback(bilinear_form_2), HERMES_SYM, MATERIAL_2);
wf.add_matrix_form_surf(callback(bilinear_form_surf_bottom), BDY_BOTTOM);
wf.add_vector_form_surf(callback(linear_form_surf_bottom), BDY_BOTTOM);
wf.add_vector_form_surf(callback(linear_form_surf_outer), BDY_OUTER);
// Initialize coarse and reference mesh solution.
Solution sln;
// Initialize views.
ScalarView sview("Solution", new WinGeom(0, 0, 410, 600));
sview.fix_scale_width(50);
sview.show_mesh(false);
OrderView oview("Polynomial orders", new WinGeom(420, 0, 400, 600));
// DOF and CPU convergence graphs initialization.
SimpleGraph graph_dof, graph_cpu;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Initialize matrix solver.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Assemble reference problem.
info("Solving on reference mesh.");
bool is_linear = true;
DiscreteProblem* dp = new DiscreteProblem(&wf, &space, is_linear);
dp->assemble(matrix, rhs);
// Time measurement.
cpu_time.tick();
// Solve the linear system of the reference problem.
// If successful, obtain the solution.
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// View the coarse mesh solution and polynomial orders.
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.");
KellyTypeAdapt* adaptivity = new KellyTypeAdapt(&space);
adaptivity->add_error_estimator_surf(callback(kelly_interface_estimator));
adaptivity->add_error_estimator_surf(callback(kelly_newton_boundary_estimator), BDY_BOTTOM);
adaptivity->add_error_estimator_surf(callback(kelly_neumann_boundary_estimator), BDY_OUTER);
adaptivity->add_error_estimator_surf(callback(kelly_zero_neumann_boundary_estimator), BDY_INNER);
double err_est_rel = adaptivity->calc_err_est(&sln, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Report results.
info("ndof: %d, err_est_rel: %g%%", Space::get_num_dofs(&space), err_est_rel);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof.save("conv_dof_est.dat");
graph_cpu.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu.save("conv_cpu_est.dat");
// If err_est too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else
{
info("Adapting coarse mesh.");
done = adaptivity->adapt(THRESHOLD, STRATEGY, MESH_REGULARITY);
}
if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true;
// Increase the counter of performed adaptivity steps.
if (done == false) as++;
// Clean up.
delete adaptivity;
delete dp;
}
while (done == false);
// Clean up.
delete solver;
delete matrix;
delete rhs;
verbose("Total running time: %g s", cpu_time.accumulated());
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_AIR, INIT_REF_NUM_BDY);
mesh.refine_towards_boundary(BDY_GROUND, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<std::string>(BDY_GROUND));
bc_types.add_bc_newton(BDY_AIR);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(BDY_GROUND, TEMP_INIT);
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous time level solution (initialized by the external temperature).
Solution tsln(&mesh, TEMP_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form));
wf.add_matrix_form_surf(callback(bilinear_form_surf), BDY_AIR);
wf.add_vector_form(callback(linear_form), HERMES_ANY, &tsln);
wf.add_vector_form_surf(callback(linear_form_surf), BDY_AIR);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
solver->set_factorization_scheme(HERMES_REUSE_FACTORIZATION_COMPLETELY);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
Tview.set_min_max_range(0,20);
Tview.fix_scale_width(30);
// Time stepping:
int ts = 1; bool rhs_only = false;
do
{
info("---- Time step %d, time %3.5f s, ext_temp %g C", ts, current_time, temp_ext(current_time));
// First time assemble both the stiffness matrix and right-hand side vector,
// then just the right-hand side vector.
if (rhs_only == false) info("Assembling the stiffness matrix and right-hand side vector.");
else info("Assembling the right-hand side vector (only).");
dp.assemble(matrix, rhs, rhs_only);
rhs_only = true;
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &tsln);
else error ("Matrix solver failed.\n");
// Visualize the solution.
char title[100];
sprintf(title, "Time %3.2f s, exterior temperature %3.5f C", current_time, temp_ext(current_time));
Tview.set_title(title);
Tview.show(&tsln);
// Increase current time and time step counter.
current_time += time_step;
ts++;
}
while (current_time < T_FINAL);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("square.mesh", &mesh);
//mloader.load("square-tri.mesh", &mesh);
// Perform initial mesh refinements.
for (int i=0; i<INIT_REF; i++) mesh.refine_all_elements();
// Create an L2 space with default shapeset.
L2Space space(&mesh, bc_types, NULL, Ord2(P_H, P_V));
int ndof = Space::get_num_dofs(&space);
info("ndof = %d", ndof);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form));
wf.add_vector_form(callback(linear_form));
wf.add_matrix_form_surf(callback(bilinear_form_boundary), H2D_DG_BOUNDARY_EDGE);
wf.add_vector_form_surf(callback(linear_form_boundary), H2D_DG_BOUNDARY_EDGE);
wf.add_matrix_form_surf(callback(bilinear_form_interface), H2D_DG_INNER_EDGE);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Initialize the solution.
Solution sln;
// Assemble the stiffness matrix and right-hand side vector.
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else
error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// Clean up.
delete solver;
delete matrix;
delete rhs;
// Visualize the solution.
ScalarView view1("Solution", new WinGeom(860, 0, 400, 350));
view1.show(&sln);
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh file.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements.
for(int i=0; i<UNIFORM_REF_LEVEL; i++) mesh.refine_all_elements();
mesh.refine_towards_vertex(3, CORNER_REF_LEVEL);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(BDY_LEFT);
bc_types.add_bc_neumann(Hermes::Tuple<int>(BDY_OUTER, BDY_INNER));
bc_types.add_bc_newton(BDY_BOTTOM);
// Enter Dirichlet boudnary values.
BCValues bc_values;
bc_values.add_const(BDY_LEFT, T1);
// Create an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d", ndof);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form));
wf.add_matrix_form_surf(callback(bilinear_form_surf), BDY_BOTTOM);
wf.add_vector_form_surf(callback(linear_form_surf), BDY_BOTTOM);
// Testing n_dof and correctness of solution vector
// for p_init = 1, 2, ..., 10
int success = 1;
Solution sln;
for (int p_init = 1; p_init <= 10; p_init++) {
printf("********* p_init = %d *********\n", p_init);
space.set_uniform_order(p_init);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the solution.
Solution sln;
// Assemble the stiffness matrix and right-hand side vector.
info("Assembling the stiffness matrix and right-hand side vector.");
bool rhsonly = false;
dp.assemble(matrix, rhs, rhsonly);
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else
error ("Matrix solver failed.\n");
int ndof = Space::get_num_dofs(&space);
printf("ndof = %d\n", ndof);
double sum = 0;
for (int i=0; i < ndof; i++) sum += solver->get_solution()[i];
printf("coefficient sum = %g\n", sum);
// Actual test. The values of 'sum' depend on the
// current shapeset. If you change the shapeset,
// you need to correct these numbers.
if (p_init == 1 && fabs(sum - 1146.15) > 1e-1) success = 0;
if (p_init == 2 && fabs(sum - 1145.97) > 1e-1) success = 0;
if (p_init == 3 && fabs(sum - 1145.97) > 1e-1) success = 0;
if (p_init == 4 && fabs(sum - 1145.96) > 1e-1) success = 0;
if (p_init == 5 && fabs(sum - 1145.96) > 1e-1) success = 0;
if (p_init == 6 && fabs(sum - 1145.96) > 1e-1) success = 0;
if (p_init == 7 && fabs(sum - 1145.96) > 1e-1) success = 0;
if (p_init == 8 && fabs(sum - 1145.96) > 1e-1) success = 0;
if (p_init == 9 && fabs(sum - 1145.96) > 1e-1) success = 0;
if (p_init == 10 && fabs(sum - 1145.96) > 1e-1) success = 0;
}
if (success == 1) {
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);
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_AIR, INIT_REF_NUM_BDY);
mesh.refine_towards_boundary(BDY_GROUND, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<std::string>(BDY_GROUND));
bc_types.add_bc_newton(BDY_AIR);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(BDY_GROUND, TEMP_INIT);
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous time level solution (initialized by the external temperature).
Solution u_prev_time(&mesh, TEMP_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(stac_jacobian));
wf.add_vector_form(callback(stac_residual));
wf.add_matrix_form_surf(callback(bilinear_form_surf), BDY_AIR);
wf.add_vector_form_surf(callback(linear_form_surf), BDY_AIR);
// Project the initial condition on the FE space to obtain initial solution coefficient vector.
info("Projecting initial condition to translate initial condition into a vector.");
scalar* coeff_vec = new scalar[ndof];
OGProjection::project_global(&space, &u_prev_time, coeff_vec, matrix_solver);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, &space, is_linear);
// Initialize views.
ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600));
//Tview.set_min_max_range(0,20);
Tview.fix_scale_width(30);
// Time stepping loop:
double current_time = 0.0; int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g, tau = %g, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool is_linear = true;
if (!rk_time_step(current_time, time_step, &bt, coeff_vec, &dp, matrix_solver,
verbose, is_linear)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
// Convert coeff_vec into a new time level solution.
Solution::vector_to_solution(coeff_vec, &space, &u_prev_time);
// Update time.
current_time += time_step;
// Show the new time level solution.
char title[100];
sprintf(title, "Time %3.2f, exterior temperature %3.5f", current_time, temp_ext(current_time));
Tview.set_title(title);
Tview.show(&u_prev_time);
// Increase counter of time steps.
ts++;
}
while (current_time < T_FINAL);
// Cleanup.
delete [] coeff_vec;
// 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("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_BOTTOM, INIT_REF_NUM_BDY);
// 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);
// Previous and next time level solutions.
Solution* sln_time_prev = new Solution(&mesh, TEMP_INIT);
Solution* sln_time_new = new Solution(&mesh);
Solution* time_error_fn = new Solution(&mesh, 0.0);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(stac_jacobian_vol, stac_jacobian_vol_ord, HERMES_NONSYM, HERMES_ANY, sln_time_prev);
wf.add_vector_form(stac_residual_vol, stac_residual_vol_ord, HERMES_ANY, sln_time_prev);
wf.add_matrix_form_surf(stac_jacobian_bottom, stac_jacobian_bottom_ord, BDY_BOTTOM, sln_time_prev);
wf.add_vector_form_surf(stac_residual_bottom, stac_residual_bottom_ord, BDY_BOTTOM, sln_time_prev);
wf.add_matrix_form_surf(stac_jacobian_top, stac_jacobian_top_ord, BDY_TOP, sln_time_prev);
wf.add_vector_form_surf(stac_residual_top, stac_residual_top_ord, BDY_TOP, sln_time_prev);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// 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.");
// 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, tau = %g s, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
bool is_linear = true;
if (!rk_time_step(current_time, time_step, &bt, sln_time_prev, sln_time_new, time_error_fn, &dp, matrix_solver,
verbose, is_linear)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
// 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 = calc_norm(time_error_fn, HERMES_H1_NORM) / 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);
// Cleanup.
delete sln_time_prev;
delete sln_time_new;
delete time_error_fn;
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh, basemesh;
H2DReader mloader;
mloader.load("domain.mesh", &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(3, INIT_REF_NUM_BDY);
// Create an H1 space with default shapeset.
H1Space space(&mesh, bc_types, essential_bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Create a selector which will select optimal candidate.
H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Solutions for the time stepping and the Newton's method.
Solution sln, ref_sln, sln_prev_time;
// Adapt mesh to represent initial condition with given accuracy.
info("Mesh adaptivity to an exact function:");
int as = 1; bool done = false;
do
{
// Setup space for the reference solution.
Space *rspace = construct_refined_space(&space);
// Assign the function f() to the fine mesh.
ref_sln.set_exact(rspace->get_mesh(), init_cond);
// Project the function f() on the coarse mesh.
OGProjection::project_global(&space, &ref_sln, &sln_prev_time, matrix_solver);
// Calculate element errors and total error estimate.
Adapt adaptivity(&space, HERMES_H1_NORM);
bool solutions_for_adapt = true;
double err_est_rel = adaptivity.calc_err_est(&sln_prev_time, &ref_sln, solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
info("Step %d, ndof %d, proj_error %g%%", as, Space::get_num_dofs(&space), err_est_rel);
// If err_est_rel too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else {
double to_be_processed = 0;
done = adaptivity.adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY, to_be_processed);
if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true;
}
as++;
}
while (done == false);
// Project the initial condition on the FE space
// to obtain initial coefficient vector for the Newton's method.
info("Projecting initial condition to obtain coefficient vector for Newton on coarse mesh.");
scalar* coeff_vec_coarse = new scalar[Space::get_num_dofs(&space)];
OGProjection::project_global(&space, init_cond, coeff_vec_coarse, matrix_solver);
OGProjection::project_global(&space, &sln_prev_time, &sln, matrix_solver);
// Initialize the weak formulation.
WeakForm wf;
if (TIME_INTEGRATION == 1) {
wf.add_matrix_form(jac_form_vol_euler, jac_form_vol_ord, HERMES_UNSYM, HERMES_ANY,
&sln_prev_time);
wf.add_matrix_form_surf(jac_form_surf_1_euler, jac_form_surf_1_ord, BDY_1);
wf.add_matrix_form_surf(jac_form_surf_4_euler, jac_form_surf_4_ord, BDY_4);
wf.add_matrix_form_surf(jac_form_surf_6_euler, jac_form_surf_6_ord, BDY_6);
wf.add_vector_form(res_form_vol_euler, res_form_vol_ord, HERMES_ANY,
&sln_prev_time);
wf.add_vector_form_surf(res_form_surf_1_euler, res_form_surf_1_ord, BDY_1);
wf.add_vector_form_surf(res_form_surf_4_euler, res_form_surf_4_ord, BDY_4);
wf.add_vector_form_surf(res_form_surf_6_euler, res_form_surf_6_ord, BDY_6);
}
else {
wf.add_matrix_form(jac_form_vol_cranic, jac_form_vol_ord, HERMES_UNSYM, HERMES_ANY,
&sln_prev_time);
wf.add_matrix_form_surf(jac_form_surf_1_cranic, jac_form_surf_1_ord, BDY_1);
wf.add_matrix_form_surf(jac_form_surf_4_cranic, jac_form_surf_4_ord, BDY_4);
wf.add_matrix_form_surf(jac_form_surf_6_cranic, jac_form_surf_6_ord, BDY_6);
wf.add_vector_form(res_form_vol_cranic, res_form_vol_ord, HERMES_ANY,
&sln_prev_time);
wf.add_vector_form_surf(res_form_surf_1_cranic, res_form_surf_1_ord, BDY_1,
&sln_prev_time);
wf.add_vector_form_surf(res_form_surf_4_cranic, res_form_surf_4_ord, BDY_4,
&sln_prev_time);
wf.add_vector_form_surf(res_form_surf_6_cranic, res_form_surf_6_ord, BDY_6,
&sln_prev_time);
}
// Error estimate and discrete problem size as a function of physical time.
SimpleGraph graph_time_err_est, graph_time_err_exact, graph_time_dof, graph_time_cpu;
// Time stepping loop.
int num_time_steps = (int)(T_FINAL/TAU + 0.5);
for(int ts = 1; ts <= num_time_steps; ts++)
{
// Time measurement.
cpu_time.tick();
// Updating current time.
TIME = ts*TAU;
info("---- Time step %d:", ts);
// Periodic global derefinements.
if (ts > 1 && ts % UNREF_FREQ == 0) {
info("Global mesh derefinement.");
mesh.copy(&basemesh);
space.set_uniform_order(P_INIT);
// Project fine mesh solution on the globally derefined mesh.
info("Projecting fine mesh solution on globally derefined mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
}
// Adaptivity loop (in space):
bool done = false;
int as = 1;
do
{
info("---- Time step %d, adaptivity step %d:", ts, as);
// Construct globally refined reference mesh
// and setup reference space.
Space* ref_space = construct_refined_space(&space);
scalar* coeff_vec = new scalar[Space::get_num_dofs(ref_space)];
// Calculate initial coefficient vector for Newton on the fine mesh.
if (as == 1 && ts == 1) {
info("Projecting coarse mesh solution to obtain initial vector on new fine mesh.");
OGProjection::project_global(ref_space, &sln, coeff_vec, matrix_solver);
}
else {
info("Projecting previous fine mesh solution to obtain initial vector on new fine mesh.");
OGProjection::project_global(ref_space, &ref_sln, coeff_vec, matrix_solver);
}
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, ref_space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Perform Newton's iteration.
int it = 1;
while (1)
{
// Obtain the number of degrees of freedom.
int ndof = Space::get_num_dofs(ref_space);
// Assemble the Jacobian matrix and residual vector.
dp.assemble(coeff_vec, matrix, rhs, false);
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
for (int i = 0; i < ndof; i++) rhs->set(i, -rhs->get(i));
// Calculate the l2-norm of residual vector.
double res_l2_norm = get_l2_norm(rhs);
// Info for user.
info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(ref_space), res_l2_norm);
// If l2 norm of the residual vector is within tolerance, or the maximum number
// of iteration has been reached, then quit.
if (res_l2_norm < NEWTON_TOL_FINE || it > NEWTON_MAX_ITER) break;
// Solve the linear system.
if(!solver->solve())
error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof; i++) coeff_vec[i] += solver->get_solution()[i];
if (it >= NEWTON_MAX_ITER)
error ("Newton method did not converge.");
it++;
}
// Translate the resulting coefficient vector into the actual solutions.
Solution::vector_to_solutions(coeff_vec, ref_space, &ref_sln);
// Project the fine mesh solution on the coarse mesh.
info("Projecting fine mesh solution on coarse mesh for error calculation.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
// Calculate element errors.
info("Calculating error estimate.");
Adapt* adaptivity = new Adapt(&space, HERMES_H1_NORM);
bool solutions_for_adapt = true;
// Calculate error estimate wrt. fine mesh solution.
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_ABS) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d, space_err_est_rel: %g%%",
Space::get_num_dofs(&space), Space::get_num_dofs(ref_space), err_est_rel);
// Add entries to convergence graphs.
graph_time_err_est.add_values(ts*TAU, err_est_rel);
graph_time_err_est.save("time_error_est.dat");
graph_time_dof.add_values(ts*TAU, Space::get_num_dofs(&space));
graph_time_dof.save("time_dof.dat");
graph_time_cpu.add_values(ts*TAU, cpu_time.accumulated());
graph_time_cpu.save("time_cpu.dat");
// If space_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);
if (Space::get_num_dofs(&space) >= NDOF_STOP) {
done = true;
break;
}
as++;
}
// Cleanup.
delete [] coeff_vec;
delete solver;
delete matrix;
delete rhs;
delete adaptivity;
delete ref_space->get_mesh();
delete ref_space;
}
while (!done);
// Copy new time level solution into sln_prev_time.
sln_prev_time.copy(&ref_sln);
}
info("Coordinate ( 2, -2.0) value = %lf", sln_prev_time.get_pt_value( 2, -2.0));
info("Coordinate ( 2, -4.0) value = %lf", sln_prev_time.get_pt_value( 2, -4.0));
info("Coordinate ( 6, -2.0) value = %lf", sln_prev_time.get_pt_value( 6, -2.0));
info("Coordinate ( 6, -4.0) value = %lf", sln_prev_time.get_pt_value( 6, -4.0));
info("Coordinate ( 4, -3.0) value = %lf", sln_prev_time.get_pt_value( 4, -3.0));
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
double coor_x[5] = {2.0, 2.0, 6.0, 6.0, 4.0};
double coor_y[5] = {-2.0, -4.0, -2.0, -4.0, -3.0};
double value[5] = {-4.821844, -2.462673, -4.000754, -1.705534, -3.257146};
for (int i = 0; i < 5; i++)
{
if ((value[i] - sln_prev_time.get_pt_value(coor_x[i], coor_y[i])) < 1E-6)
{
}
else
{
printf("Failure!\n");
return ERROR_FAILURE;
}
}
printf("Success!\n");
return ERROR_SUCCESS;
}
int main(int argc, char* argv[])
{
// Time measurement
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("lshape3q.mesh", &mesh); // quadrilaterals
//mloader.load("lshape3t.mesh", &mesh); // triangles
// Perform initial mesh refinemets.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<int>(BDY_1, BDY_6));
bc_types.add_bc_newton(Hermes::vector<int>(BDY_2, BDY_3, BDY_4, BDY_5));
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_zero(Hermes::vector<int>(BDY_1, BDY_6));
// Create an Hcurl space with default shapeset.
HcurlSpace space(&mesh, &bc_types, &bc_values, P_INIT);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form), HERMES_SYM);
wf.add_matrix_form_surf(callback(bilinear_form_surf));
wf.add_vector_form_surf(linear_form_surf, linear_form_surf_ord);
// Initialize coarse and reference mesh solutions.
Solution sln, ref_sln;
// Initialize exact solution.
ExactSolution sln_exact(&mesh, exact);
// Initialize refinement selector.
HcurlProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize views.
VectorView v_view("Solution (magnitude)", new WinGeom(0, 0, 460, 350));
v_view.set_min_max_range(0, 1.5);
OrderView o_view("Polynomial orders", new WinGeom(470, 0, 400, 350));
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est,
graph_dof_exact, graph_cpu_exact;
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space);
// Initialize matrix solver.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Assemble the reference problem.
info("Solving on reference mesh.");
bool is_linear = true;
DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);
dp->assemble(matrix, rhs);
// Time measurement.
cpu_time.tick();
// Solve the linear system of the reference problem. If successful, obtain the solution.
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), ref_space, &ref_sln);
else error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver);
// View the coarse mesh solution and polynomial orders.
v_view.show(&sln);
o_view.show(&space);
// Calculate element errors and total error estimate.
info("Calculating error estimate and exact error.");
Adapt* adaptivity = new Adapt(&space);
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 100;
// Calculate exact error,
bool solutions_for_adapt = false;
double err_exact_rel = adaptivity->calc_err_exact(&sln, &sln_exact, solutions_for_adapt) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d",
Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
info("err_est_rel: %g%%, err_exact_rel: %g%%", err_est_rel, err_exact_rel);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.add_values(Space::get_num_dofs(&space), err_exact_rel);
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel);
graph_cpu_exact.save("conv_cpu_exact.dat");
// If err_est_rel 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(&space) >= NDOF_STOP) done = true;
// Clean up.
delete solver;
delete matrix;
delete rhs;
delete adaptivity;
if(done == false) delete ref_space->get_mesh();
delete ref_space;
delete dp;
}
while (done == false);
verbose("Total running time: %g s", cpu_time.accumulated());
// Show the reference solution - the final result.
v_view.set_title("Fine mesh solution (magnitude)");
v_view.show(&ref_sln);
// Wait for all views to be closed.
View::wait();
return 0;
}
int main() {
// Create space, set Dirichlet BC, enumerate basis functions.
Space* space = new Space(A, B, NELEM, P_INIT, NEQ);
info("N_dof = %d", Space::get_num_dofs(space));
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(jacobian_vol);
wf.add_vector_form(residual_vol);
wf.add_matrix_form_surf(jacobian_surf_left, BOUNDARY_LEFT);
wf.add_vector_form_surf(residual_surf_left, BOUNDARY_LEFT);
wf.add_matrix_form_surf(jacobian_surf_right, BOUNDARY_RIGHT);
wf.add_vector_form_surf(residual_surf_right, BOUNDARY_RIGHT);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem *dp = new DiscreteProblem(&wf, space, is_linear);
// Newton's loop.
// Fill vector coeff_vec using dof and coeffs arrays in elements.
double *coeff_vec = new double[Space::get_num_dofs(space)];
get_coeff_vector(space, coeff_vec);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
int it = 1;
while (1) {
// Obtain the number of degrees of freedom.
int ndof = Space::get_num_dofs(space);
// Assemble the Jacobian matrix and residual vector.
dp->assemble(matrix, rhs);
// Calculate the l2-norm of residual vector.
double res_l2_norm = get_l2_norm(rhs);
// Info for user.
info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(space), res_l2_norm);
// If l2 norm of the residual vector is within tolerance, then quit.
// NOTE: at least one full iteration forced
// here because sometimes the initial
// residual on fine mesh is too small.
if(res_l2_norm < NEWTON_TOL && it > 1) break;
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
for(int i=0; i<ndof; i++) rhs->set(i, -rhs->get(i));
// Solve the linear system.
if(!solver->solve())
error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof; i++) coeff_vec[i] += solver->get_solution()[i];
// If the maximum number of iteration has been reached, then quit.
if (it >= NEWTON_MAX_ITER) error ("Newton method did not converge.");
// Copy coefficients from vector y to elements.
set_coeff_vector(coeff_vec, space);
it++;
}
// Plot the solution.
Linearizer l(space);
l.plot_solution("solution.gp");
// Plot the resulting space.
space->plot("space.gp");
info("Done.");
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("lshape3q.mesh", &mesh); // quadrilaterals
//mloader.load("lshape3t.mesh", &mesh); // triangles
// Perform initial mesh refinemets.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Create an Hcurl space with default shapeset.
HcurlSpace space(&mesh, bc_types, essential_bc_values, P_INIT);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form), H2D_SYM);
wf.add_matrix_form_surf(callback(bilinear_form_surf));
wf.add_vector_form_surf(linear_form_surf, linear_form_surf_ord);
// Initialize views.
OrderView ordview("Coarse mesh", 600, 0, 600, 500);
VectorView vecview("Electric Field - VectorView", 0, 0, 600, 500);
/*
// View the basis functions.
VectorBaseView bview;
vbview.show(&space);
View::wait(H2DV_WAIT_KEYPRESS);
*/
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// Initialize refinement selector.
HcurlProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// Initialize the coarse mesh problem.
LinSystem ls(&wf, &space);
// Adaptivity loop:
int as = 1; bool done = false;
Solution sln_coarse, sln_fine;
do
{
info("---- Adaptivity step %d:", as);
// Assemble and solve the fine mesh problem.
info("Solving on fine mesh.");
RefSystem rs(&ls);
rs.assemble();
rs.solve(&sln_fine);
// Either solve on coarse mesh or project the fine mesh solution
// on the coarse mesh.
if (SOLVE_ON_COARSE_MESH) {
info("Solving on coarse mesh.");
ls.assemble();
ls.solve(&sln_coarse);
}
else {
info("Projecting fine mesh solution on coarse mesh.");
int proj_type = 2; // Hcurl projection.
ls.project_global(&sln_fine, &sln_coarse, proj_type);
}
// Time measurement.
cpu_time.tick();
// Calculate error wrt. exact solution.
info("Calculating error (exact).");
ExactSolution ex(&mesh, exact);
double err_exact = hcurl_error(&sln_coarse, &ex) * 100;
// Show real part of the solution and mesh.
ordview.show(&space);
RealFilter real(&sln_coarse);
vecview.set_min_max_range(0, 1);
vecview.show(&real, H2D_EPS_HIGH);
// Skip exact error calculation and visualization time.
cpu_time.tick(HERMES_SKIP);
// Calculate error estimate wrt. fine mesh solution.
info("Calculating error (est).");
HcurlAdapt hp(&ls);
hp.set_solutions(&sln_coarse, &sln_fine);
double err_est_adapt = hp.calc_error() * 100;
double err_est_hcurl = hcurl_error(&sln_coarse, &sln_fine) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d, err_est: %g%%, err_exact: %g%%",
ls.get_num_dofs(), rs.get_num_dofs(), err_est_hcurl, err_exact);
// Add entries to DOF convergence graphs.
graph_dof_exact.add_values(ls.get_num_dofs(), err_exact);
graph_dof_exact.save("conv_dof_exact.dat");
graph_dof_est.add_values(ls.get_num_dofs(), err_est_hcurl);
graph_dof_est.save("conv_dof_est.dat");
// Add entries to CPU convergence graphs.
graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact);
graph_cpu_exact.save("conv_cpu_exact.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_hcurl);
graph_cpu_est.save("conv_cpu_est.dat");
// If err_est_adapt too large, adapt the mesh.
if (err_est_adapt < ERR_STOP) done = true;
else {
info("Adapting coarse mesh.");
done = hp.adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY);
if (ls.get_num_dofs() >= NDOF_STOP) done = true;
}
as++;
}
while (!done);
verbose("Total running time: %g s", cpu_time.accumulated());
// Show the fine mesh solution - the final result
vecview.set_title("Final solution");
vecview.show(&sln_fine);
// Wait for all views to be closed.
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("lshape3q.mesh", &mesh); // quadrilaterals
//mloader.load("lshape3t.mesh", &mesh); // triangles
// Perform initial mesh refinemets.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Create an Hcurl space with default shapeset.
HcurlSpace space(&mesh, bc_types, essential_bc_values, P_INIT);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form), HERMES_SYM);
wf.add_matrix_form_surf(callback(bilinear_form_surf));
wf.add_vector_form_surf(linear_form_surf, linear_form_surf_ord);
// Initialize coarse and reference mesh solutions.
Solution sln, ref_sln;
// Initialize exact solution.
ExactSolution sln_exact(&mesh, exact);
// Initialize refinement selector.
HcurlProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER);
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est,
graph_dof_exact, graph_cpu_exact;
// Adaptivity loop:
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space);
// Assemble the reference problem.
info("Solving on reference mesh.");
bool is_linear = true;
DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
dp->assemble(matrix, rhs);
// Time measurement.
cpu_time.tick();
// Solve the linear system of the reference problem. If successful, obtain the solution.
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), ref_space, &ref_sln);
else error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// Project the fine mesh solution onto the coarse mesh.
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver, HERMES_HCURL_NORM);
// Calculate element errors and total error estimate.
info("Calculating error estimate and exact error.");
Adapt* adaptivity = new Adapt(&space, HERMES_HCURL_NORM);
bool solutions_for_adapt = true;
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Calculate exact error,
solutions_for_adapt = false;
double err_exact_rel = adaptivity->calc_err_exact(&sln, &sln_exact, solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d",
Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
info("err_est_rel: %g%%, err_exact_rel: %g%%", err_est_rel, err_exact_rel);
// Time measurement.
cpu_time.tick();
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.add_values(Space::get_num_dofs(&space), err_exact_rel);
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel);
graph_cpu_exact.save("conv_cpu_exact.dat");
// If err_est_rel 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(&space) >= NDOF_STOP) done = true;
// Clean up.
delete solver;
delete matrix;
delete rhs;
delete adaptivity;
if(done == false) delete ref_space->get_mesh();
delete ref_space;
delete dp;
}
while (done == false);
verbose("Total running time: %g s", cpu_time.accumulated());
int ndof = Space::get_num_dofs(&space);
printf("ndof allowed = %d\n", 1400);
printf("ndof actual = %d\n", ndof);
if (ndof < 1400) { // ndofs was 1384 atthe time this test was created
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
int main(int argc, char **args) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &args, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
if (argc < 5) error("Not enough parameters");
sscanf(args[2], "%d", &m);
sscanf(args[3], "%d", &n);
sscanf(args[4], "%d", &o);
printf("* Loading mesh '%s'\n", args[1]);
Mesh mesh;
H3DReader mesh_loader;
if (!mesh_loader.load(args[1], &mesh)) error("Loading mesh file '%s'\n", args[1]);
H1ShapesetLobattoHex shapeset;
printf("* Setting the space up\n");
int mx = maxn(4, m, n, o, 4);
Ord3 order(mx, mx, mx);
// Ord3 order(1, 1, 1);
printf(" - Setting uniform order to (%d, %d, %d)\n", mx, mx, mx);
H1Space space(&mesh, bc_types, NULL, order);
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
printf("* Calculating a solution\n");
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoMatrix mat;
PardisoVector rhs;
PardisoLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, SYM);
wf.add_matrix_form_surf(bilinear_form_surf<double, scalar>, bilinear_form_surf<Ord, Ord>);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>);
wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<Ord, Ord>);
DiscreteProblem dp(&wf, &space, true);
// assemble stiffness matrix
printf(" - assembling... "); fflush(stdout);
Timer assemble_timer;
assemble_timer.start();
dp.assemble(&mat, &rhs);
assemble_timer.stop();
printf("%s (%lf secs)\n", assemble_timer.get_human_time(), assemble_timer.get_seconds());
// solve the stiffness matrix
printf(" - solving... "); fflush(stdout);
Timer solve_timer;
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
printf("%s (%lf secs)\n", solve_timer.get_human_time(), solve_timer.get_seconds());
// mat.dump(stdout, "a");
// rhs.dump(stdout, "b");
if (solved) {
Solution sln(&mesh);
sln.set_coeff_vector(&space, solver.get_solution());
printf("* Solution:\n");
// double *s = solver.get_solution();
// for (int i = 1; i <= ndofs; i++) {
// printf(" x[% 3d] = % lf\n", i, s[i]);
// }
// norm
ExactSolution ex_sln(&mesh, exact_solution);
double h1_sln_norm = h1_norm(&sln);
double h1_err_norm = h1_error(&sln, &ex_sln);
printf(" - H1 solution norm: % le\n", h1_sln_norm);
printf(" - H1 error norm: % le\n", h1_err_norm);
double l2_sln_norm = l2_norm(&sln);
double l2_err_norm = l2_error(&sln, &ex_sln);
printf(" - L2 solution norm: % le\n", l2_sln_norm);
printf(" - L2 error norm: % le\n", l2_err_norm);
if (h1_err_norm > EPS || l2_err_norm > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
#ifdef OUTPUT_DIR
printf("* Output\n");
// output
const char *of_name = OUTPUT_DIR "/solution.pos";
FILE *ofile = fopen(of_name, "w");
if (ofile != NULL) {
ExactSolution ex_sln(&mesh, exact_solution);
// DiffFilter eh(&sln, &ex_sln);
// DiffFilter eh_dx(mesh, &sln, &ex_sln, FN_DX, FN_DX);
// DiffFilter eh_dy(mesh, &sln, &ex_sln, FN_DY, FN_DY);
// DiffFilter eh_dz(mesh, &sln, &ex_sln, FN_DZ, FN_DZ);
GmshOutputEngine output(ofile);
output.out(&sln, "Uh");
// output.out(&sln, "Uh dx", FN_DX_0);
// output.out(&sln, "Uh dy", FN_DY_0);
// output.out(&sln, "Uh dz", FN_DZ_0);
// output.out(&eh, "Eh");
// output.out(&eh_dx, "Eh dx");
// output.out(&eh_dy, "Eh dy");
// output.out(&eh_dz, "Eh dz");
output.out(&ex_sln, "U");
// output.out(&ex_sln, "U dx", FN_DX_0);
// output.out(&ex_sln, "U dy", FN_DY_0);
// output.out(&ex_sln, "U dz", FN_DZ_0);
fclose(ofile);
}
else {
warning("Can not open '%s' for writing.", of_name);
}
#endif
}
else
res = ERR_FAILURE;
#ifdef WITH_PETSC
mat.free();
rhs.free();
PetscFinalize();
#endif
return res;
}
int main(int argc, char **args)
{
// Test variable.
int success_test = 1;
// Initialize the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
initialize_solution_environment(matrix_solver, argc, args);
for (int i = 0; i < 48; i++) {
for (int j = 0; j < 48; j++) {
info("Config: %d, %d ", i, j);
Mesh mesh;
for (unsigned int k = 0; k < countof(vtcs); k++)
mesh.add_vertex(vtcs[k].x, vtcs[k].y, vtcs[k].z);
unsigned int h1[] = {
hexs[0][i][0] + 1, hexs[0][i][1] + 1, hexs[0][i][2] + 1, hexs[0][i][3] + 1,
hexs[0][i][4] + 1, hexs[0][i][5] + 1, hexs[0][i][6] + 1, hexs[0][i][7] + 1 };
mesh.add_hex(h1);
unsigned int h2[] = {
hexs[1][j][0] + 1, hexs[1][j][1] + 1, hexs[1][j][2] + 1, hexs[1][j][3] + 1,
hexs[1][j][4] + 1, hexs[1][j][5] + 1, hexs[1][j][6] + 1, hexs[1][j][7] + 1 };
mesh.add_hex(h2);
// bc
for (unsigned int k = 0; k < countof(bnd); k++) {
unsigned int facet_idxs[Quad::NUM_VERTICES] = { bnd[k][0] + 1, bnd[k][1] + 1, bnd[k][2] + 1, bnd[k][3] + 1 };
mesh.add_quad_boundary(facet_idxs, bnd[k][4]);
}
mesh.ugh();
// Initialize the space.
H1Space space(&mesh, bc_types, essential_bc_values);
#ifdef XM_YN_ZO
Ord3 ord(4, 4, 4);
#elif defined XM_YN_ZO_2
Ord3 ord(4, 4, 4);
#elif defined X2_Y2_Z2
Ord3 ord(2, 2, 2);
#endif
space.set_uniform_order(ord);
// Initialize the weak formulation.
WeakForm wf;
#ifdef DIRICHLET
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>);
#elif defined NEWTON
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form_surf(bilinear_form_surf<double, scalar>, bilinear_form_surf<Ord, Ord>);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>);
wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<Ord, Ord>);
#endif
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Assemble the linear problem.
info("Assembling (ndof: %d).", Space::get_num_dofs(&space));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving.");
Solution sln(space.get_mesh());
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
ExactSolution ex_sln(&mesh, exact_solution);
// Calculate exact error.
info("Calculating exact error.");
Adapt *adaptivity = new Adapt(&space, HERMES_H1_NORM);
bool solutions_for_adapt = false;
double err_exact = adaptivity->calc_err_exact(&sln, &ex_sln, solutions_for_adapt, HERMES_TOTAL_ERROR_ABS);
if (err_exact > EPS)
{
// Calculated solution is not precise enough.
success_test = 0;
info("failed, error:%g", err_exact);
}
else
info("passed");
// Clean up.
delete matrix;
delete rhs;
delete solver;
delete adaptivity;
}
}
// Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
finalize_solution_environment(matrix_solver);
if (success_test) {
info("Success!");
return ERR_SUCCESS;
}
else {
info("Failure!");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Choose a Butcher's table or define your own.
ButcherTable bt(butcher_table_type);
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(BDY_AIR, INIT_REF_NUM_BDY);
mesh.refine_towards_boundary(BDY_GROUND, INIT_REF_NUM_BDY);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::vector<std::string>(BDY_GROUND));
bc_types.add_bc_newton(BDY_AIR);
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_const(BDY_GROUND, TEMP_INIT);
// Initialize an H1 space with default shapeset.
H1Space space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(&space);
info("ndof = %d.", ndof);
// Previous time level solution (initialized by the external temperature).
Solution u_prev_time(&mesh, TEMP_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(stac_jacobian));
wf.add_vector_form(callback(stac_residual));
wf.add_matrix_form_surf(callback(bilinear_form_surf), BDY_AIR);
wf.add_vector_form_surf(callback(linear_form_surf), BDY_AIR);
// Project the initial condition on the FE space to obtain initial solution coefficient vector.
info("Projecting initial condition to translate initial condition into a vector.");
scalar* coeff_vec = new scalar[ndof];
OGProjection::project_global(&space, &u_prev_time, coeff_vec, matrix_solver);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, &space, is_linear);
// Time stepping loop:
double current_time = 0.0; int ts = 1;
do
{
// Perform one Runge-Kutta time step according to the selected Butcher's table.
info("Runge-Kutta time step (t = %g, tau = %g, stages: %d).",
current_time, time_step, bt.get_size());
bool verbose = true;
if (!rk_time_step(current_time, time_step, &bt, coeff_vec, &dp, matrix_solver,
verbose, NEWTON_TOL, NEWTON_MAX_ITER)) {
error("Runge-Kutta time step failed, try to decrease time step size.");
}
// Convert coeff_vec into a new time level solution.
Solution::vector_to_solution(coeff_vec, &space, &u_prev_time);
// Update time.
current_time += time_step;
// Increase counter of time steps.
ts++;
}
while (current_time < time_step*5);
double sum = 0;
for (int i = 0; i < ndof; i++)
sum += coeff_vec[i];
printf("sum = %g\n", sum);
int success = 1;
if (fabs(sum - 3617.55) > 1e-1) success = 0;
// Cleanup.
delete [] coeff_vec;
if (success == 1) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("square.mesh", &mesh);
// Perform initial mesh refinements.
for (int i=0; i<INIT_REF; i++) mesh.refine_all_elements();
// Create an L2 space with default shapeset.
L2Space space(&mesh, bc_types, NULL, Ord2(P_H, P_V));
int ndof = Space::get_num_dofs(&space);
info("ndof = %d", ndof);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form));
wf.add_vector_form(callback(linear_form));
wf.add_matrix_form_surf(callback(bilinear_form_boundary), H2D_DG_BOUNDARY_EDGE);
wf.add_vector_form_surf(callback(linear_form_boundary), H2D_DG_BOUNDARY_EDGE);
wf.add_matrix_form_surf(callback(bilinear_form_interface), H2D_DG_INNER_EDGE);
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Initialize the solution.
Solution sln;
// Assemble the stiffness matrix and right-hand side vector.
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else
error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// Clean up.
delete solver;
delete matrix;
delete rhs;
info("ndof = %d", ndof);
info("Coordinate ( 0.1, 0.1) value = %lf", sln.get_pt_value(0.1, 0.1));
info("Coordinate ( 0.3, 0.3) value = %lf", sln.get_pt_value(0.3, 0.3));
info("Coordinate ( 0.5, 0.5) value = %lf", sln.get_pt_value(0.5, 0.5));
info("Coordinate ( 0.7, 0.7) value = %lf", sln.get_pt_value(0.7, 0.7));
double coor_xy[4] = {0.1, 0.3, 0.5, 0.7};
double value[4] = {0.999885, 0.844340, 0.000000, 0.000000};
for (int i = 0; i < 4; i++)
{
if ((value[i] - sln.get_pt_value(coor_xy[i], coor_xy[i])) < 1E-6)
{
printf("Success!\n");
}
else
{
printf("Failure!\n");
return ERR_FAILURE;
}
}
return ERR_SUCCESS;
}
int main(int argc, char **args)
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
H3DReader mloader;
mloader.load("lshape_hex.mesh3d", &mesh);
// Perform initial mesh refinement.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Create an Hcurl space with default shapeset.
HcurlSpace space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(biform<double, scalar>, biform<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form_surf(biform_surf, biform_surf_ord);
wf.add_vector_form_surf(liform_surf, liform_surf_ord);
// Set exact solution.
ExactSolution exact_sol(&mesh, exact);
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est, graph_dof_exact, graph_cpu_exact;
// Adaptivity loop.
int as = 1;
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(&space, 1);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, ref_space, is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Assemble the reference problem.
info("Assembling on reference mesh (ndof: %d).", Space::get_num_dofs(ref_space));
dp.assemble(matrix, rhs);
// Time measurement.
cpu_time.tick();
// Solve the linear system on reference mesh. If successful, obtain the solution.
info("Solving on reference mesh.");
Solution ref_sln(ref_space->get_mesh());
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), ref_space, &ref_sln);
else error ("Matrix solver failed.\n");
// Time measurement.
cpu_time.tick();
// Project the reference solution on the coarse mesh.
Solution sln(space.get_mesh());
info("Projecting reference solution on coarse mesh.");
OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver, HERMES_HCURL_NORM);
// Time measurement.
cpu_time.tick();
// Output solution and mesh with polynomial orders.
if (solution_output)
{
out_fn_vtk(&sln, "sln", as);
out_orders_vtk(&space, "order", as);
}
// Skip the visualization time.
cpu_time.tick(HERMES_SKIP);
// Calculate element errors and total error estimate.
info("Calculating error estimate and exact error.");
Adapt *adaptivity = new Adapt(&space, HERMES_HCURL_NORM);
bool solutions_for_adapt = true;
double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln, solutions_for_adapt) * 100;
// Calculate exact error.
solutions_for_adapt = false;
double err_exact_rel = adaptivity->calc_err_exact(&sln, &exact_sol, solutions_for_adapt) * 100;
// Report results.
info("ndof_coarse: %d, ndof_fine: %d.", Space::get_num_dofs(&space), Space::get_num_dofs(ref_space));
info("err_est_rel: %g%%, err_exact_rel: %g%%.", err_est_rel, err_exact_rel);
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(&space), err_est_rel);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel);
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.add_values(Space::get_num_dofs(&space), err_exact_rel);
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel);
graph_cpu_exact.save("conv_cpu_exact.dat");
// If err_est_rel is too large, adapt the mesh.
if (err_est_rel < ERR_STOP) done = true;
else
{
info("Adapting coarse mesh.");
adaptivity->adapt(THRESHOLD);
}
if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true;
// Clean up.
delete ref_space->get_mesh();
delete ref_space;
delete matrix;
delete rhs;
delete solver;
delete adaptivity;
// Increase the counter of performed adaptivity steps.
as++;
} while (!done);
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("cathedral.mesh", &mesh);
// Perform initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(bdy_air, INIT_REF_NUM_BDY);
// Initialize an H1 space with default shepeset.
H1Space space(&mesh, bc_types, essential_bc_values, P_INIT);
int ndof = get_num_dofs(&space);
info("ndof = %d.", ndof);
// Set initial condition.
Solution tsln;
tsln.set_const(&mesh, T_INIT);
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, double>, bilinear_form<Ord, Ord>);
wf.add_matrix_form_surf(bilinear_form_surf<double, double>, bilinear_form_surf<Ord, Ord>, bdy_air);
wf.add_vector_form(linear_form<double, double>, linear_form<Ord, Ord>, H2D_ANY, &tsln);
wf.add_vector_form_surf(linear_form_surf<double, double>, linear_form_surf<Ord, Ord>, bdy_air);
// Initialize the linear problem.
LinearProblem lp(&wf, &space);
// Initialize matrix solver.
Matrix* mat; Vector* rhs; CommonSolver* solver;
init_matrix_solver(matrix_solver, ndof, mat, rhs, solver);
// Time stepping:
int nsteps = (int)(FINAL_TIME/TAU + 0.5);
bool rhsonly = false;
for(int ts = 1; ts <= nsteps; ts++)
{
info("---- Time step %d, time %3.5f, ext_temp %g", ts, TIME, temp_ext(TIME));
// Assemble stiffness matrix and rhs.
lp.assemble(mat, rhs, rhsonly);
rhsonly = true;
// Solve the matrix problem.
if (!solver->solve(mat, rhs)) error ("Matrix solver failed.\n");
// Update tsln.
tsln.set_fe_solution(&space, rhs);
if (ts % OUTPUT_FREQUENCY == 0) {
Linearizer lin;
int item = H2D_FN_VAL_0;
double eps = H2D_EPS_NORMAL;
double max_abs = -1.0;
MeshFunction* xdisp = NULL;
MeshFunction* ydisp = NULL;
double dmult = 1.0;
lin.process_solution(&tsln, item, eps, max_abs, xdisp, ydisp, dmult);
char* filename = new char[100];
sprintf(filename, "tsln_%d.lin", ts);
// Save Linearizer data.
lin.save_data(filename);
info("Linearizer data saved to file %s.", filename);
// Save complete Solution.
sprintf(filename, "tsln_%d.dat", ts);
bool compress = false; // Gzip compression not used as it only works on Linux.
tsln.save(filename, compress);
info("Complete Solution saved to file %s.", filename);
}
// Update the time variable.
TIME += TAU;
}
info("Let's assume that the remote computation has finished and you fetched the *.lin files.");
info("Visualizing Linearizer data from file tsln_40.lin.");
// First use ScalarView to read and show the Linearizer data.
WinGeom* win_geom_1 = new WinGeom(0, 0, 450, 600);
ScalarView sview_1("Saved Linearizer data", win_geom_1);
sview_1.lin.load_data("tsln_40.lin");
sview_1.set_min_max_range(0,20);
sview_1.fix_scale_width(3);
sview_1.show_linearizer_data();
info("Visualizing Solution from file tsln_60.dat.");
Solution sln_from_file;
sln_from_file.load("tsln_60.dat");
WinGeom* win_geom_2 = new WinGeom(460, 0, 450, 600);
ScalarView sview_2("Saved Solution data", win_geom_2);
sview_2.set_min_max_range(0,20);
sview_2.fix_scale_width(3);
sview_2.show(&sln_from_file);
info("Visualizing Mesh and Orders extracted from the Solution.");
int p_init = 1;
// The NULLs are for bc_types() and essential_bc_values().
H1Space space_from_file(sln_from_file.get_mesh(), NULL, NULL, p_init);
space_from_file.set_element_orders(sln_from_file.get_element_orders());
WinGeom* win_geom_3 = new WinGeom(920, 0, 450, 600);
OrderView oview("Saved Solution -> Space", win_geom_3);
oview.show(&space_from_file);
// Wait for the view to be closed.
View::wait();
return 0;
}
