int main(int argc, char* argv[])
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
info("TIME_MAX_ITER = %d", TIME_MAX_ITER);
// Load the mesh file.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements.
for (int i=0; i < INIT_GLOB_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(1, INIT_BDY_REF_NUM);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(BDY_DIRICHLET);
// Enter Dirichlet boudnary values.
BCValues bc_values;
bc_values.add_zero(BDY_DIRICHLET);
// Create H1 spaces with default shapesets.
H1Space space_T(&mesh, &bc_types, &bc_values, P_INIT);
H1Space space_phi(&mesh, &bc_types, &bc_values, P_INIT);
Hermes::Tuple<Space*> spaces(&space_T, &space_phi);
// Exact solutions for error evaluation.
ExactSolution T_exact_solution(&mesh, T_exact),
phi_exact_solution(&mesh, phi_exact);
// Initialize solution views (their titles will be2 updated in each time step).
ScalarView sview_T("", new WinGeom(0, 0, 500, 400));
sview_T.fix_scale_width(50);
ScalarView sview_phi("", new WinGeom(0, 500, 500, 400));
sview_phi.fix_scale_width(50);
ScalarView sview_T_exact("", new WinGeom(550, 0, 500, 400));
sview_T_exact.fix_scale_width(50);
ScalarView sview_phi_exact("", new WinGeom(550, 500, 500, 400));
sview_phi_exact.fix_scale_width(50);
char title[100]; // Character array to store the title for an actual view and time step.
// Solutions in the previous time step.
Solution T_prev_time, phi_prev_time;
Hermes::Tuple<MeshFunction*> time_iterates(&T_prev_time, &phi_prev_time);
// Solutions in the previous Newton's iteration.
Solution T_prev_newton, phi_prev_newton;
Hermes::Tuple<Solution*> newton_iterates(&T_prev_newton, &phi_prev_newton);
// Initialize the weak formulation.
WeakForm wf(2);
wf.add_matrix_form(0, 0, jac_TT, jac_TT_ord);
wf.add_matrix_form(0, 1, jac_Tphi, jac_Tphi_ord);
wf.add_vector_form(0, res_T, res_T_ord, HERMES_ANY, &T_prev_time);
wf.add_matrix_form(1, 0, jac_phiT, jac_phiT_ord);
wf.add_matrix_form(1, 1, jac_phiphi, jac_phiphi_ord);
wf.add_vector_form(1, res_phi, res_phi_ord, HERMES_ANY, &phi_prev_time);
// Set initial conditions.
T_prev_time.set_exact(&mesh, T_exact);
phi_prev_time.set_exact(&mesh, phi_exact);
// 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_MATRIX_REORDERING);
// Time stepping.
int t_step = 1;
do {
TIME += TAU;
info("---- Time step %d, t = %g s:", t_step, TIME); t_step++;
info("Projecting to obtain initial vector for the Newton's method.");
scalar* coeff_vec = new scalar[Space::get_num_dofs(spaces)];
OGProjection::project_global(spaces, time_iterates, coeff_vec, matrix_solver);
Solution::vector_to_solutions(coeff_vec, Hermes::Tuple<Space*>(&space_T, &space_phi),
Hermes::Tuple<Solution*>(&T_prev_newton, &phi_prev_newton));
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, spaces, is_linear);
// Perform Newton's iteration.
info("Newton's iteration...");
bool verbose = true;
if(!solve_newton(coeff_vec, &dp, solver, matrix, rhs, NEWTON_TOL, NEWTON_MAX_ITER, verbose))
error("Newton's iteration failed.");
// Translate the resulting coefficient vector into the Solution sln.
Solution::vector_to_solutions(coeff_vec, spaces, newton_iterates);
delete [] coeff_vec;
// Show the new time level solution.
sprintf(title, "Approx. solution for T, t = %g s", TIME);
sview_T.set_title(title);
sview_T.show(&T_prev_newton);
sprintf(title, "Approx. solution for phi, t = %g s", TIME);
sview_phi.set_title(title);
sview_phi.show(&phi_prev_newton);
// Exact solution for comparison with computational results.
T_exact_solution.update(&mesh, T_exact);
phi_exact_solution.update(&mesh, phi_exact);
// Show exact solution.
sview_T_exact.show(&T_exact_solution);
sprintf(title, "Exact solution for T, t = %g s", TIME);
sview_T_exact.set_title(title);
sview_phi_exact.show(&phi_exact_solution);
sprintf(title, "Exact solution for phi, t = %g s", TIME);
sview_phi_exact.set_title(title);
// Calculate exact error.
info("Calculating error (exact).");
Hermes::Tuple<double> exact_errors;
Adapt adaptivity_exact(spaces, Hermes::Tuple<ProjNormType>(HERMES_H1_NORM, HERMES_H1_NORM));
bool solutions_for_adapt = false;
adaptivity_exact.calc_err_exact(Hermes::Tuple<Solution *>(&T_prev_newton, &phi_prev_newton), Hermes::Tuple<Solution *>(&T_exact_solution, &phi_exact_solution), solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL, &exact_errors);
double maxerr = std::max(exact_errors[0], exact_errors[1])*100;
info("Exact solution error for T (H1 norm): %g %%", exact_errors[0]*100);
info("Exact solution error for phi (H1 norm): %g %%", exact_errors[1]*100);
info("Exact solution error (maximum): %g %%", maxerr);
// Prepare previous time level solution for the next time step.
T_prev_time.copy(&T_prev_newton);
phi_prev_time.copy(&phi_prev_newton);
}
while (t_step <= TIME_MAX_ITER);
// Cleanup.
delete matrix;
delete rhs;
delete solver;
// 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();
info("TIME_MAX_ITER = %d", TIME_MAX_ITER);
// Load the mesh file.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Perform initial mesh refinements.
for (int i=0; i < INIT_GLOB_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(1, INIT_BDY_REF_NUM);
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(BDY_DIRICHLET);
// Enter Dirichlet boudnary values.
BCValues bc_values;
bc_values.add_zero(BDY_DIRICHLET);
// Create H1 spaces with default shapesets.
H1Space space_T(&mesh, &bc_types, &bc_values, P_INIT);
H1Space space_phi(&mesh, &bc_types, &bc_values, P_INIT);
Hermes::vector<Space*> spaces(&space_T, &space_phi);
// Exact solutions for error evaluation.
ExactSolution T_exact_solution(&mesh, T_exact),
phi_exact_solution(&mesh, phi_exact);
// Solutions in the previous time step.
Solution T_prev_time, phi_prev_time;
Hermes::vector<MeshFunction*> time_iterates(&T_prev_time, &phi_prev_time);
// Solutions in the previous Newton's iteration.
Solution T_prev_newton, phi_prev_newton;
Hermes::vector<Solution*> newton_iterates(&T_prev_newton, &phi_prev_newton);
// Initialize the weak formulation.
WeakForm wf(2);
wf.add_matrix_form(0, 0, jac_TT, jac_TT_ord);
wf.add_matrix_form(0, 1, jac_Tphi, jac_Tphi_ord);
wf.add_vector_form(0, res_T, res_T_ord, HERMES_ANY, &T_prev_time);
wf.add_matrix_form(1, 0, jac_phiT, jac_phiT_ord);
wf.add_matrix_form(1, 1, jac_phiphi, jac_phiphi_ord);
wf.add_vector_form(1, res_phi, res_phi_ord, HERMES_ANY, &phi_prev_time);
// Set initial conditions.
T_prev_time.set_exact(&mesh, T_exact);
phi_prev_time.set_exact(&mesh, phi_exact);
// 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_MATRIX_REORDERING);
// Time stepping.
int t_step = 1;
do {
TIME += TAU;
info("---- Time step %d, t = %g s:", t_step, TIME);
t_step++;
info("Projecting to obtain initial vector for the Newton's method.");
scalar* coeff_vec = new scalar[Space::get_num_dofs(spaces)];
OGProjection::project_global(spaces, time_iterates, coeff_vec, matrix_solver);
Solution::vector_to_solutions(coeff_vec, Hermes::vector<Space*>(&space_T, &space_phi),
Hermes::vector<Solution*>(&T_prev_newton, &phi_prev_newton));
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem dp(&wf, spaces, is_linear);
// Perform Newton's iteration.
info("Newton's iteration...");
bool verbose = false;
if(!solve_newton(coeff_vec, &dp, solver, matrix, rhs, NEWTON_TOL, NEWTON_MAX_ITER, verbose))
error("Newton's iteration failed.");
// Translate the resulting coefficient vector into the Solution sln.
Solution::vector_to_solutions(coeff_vec, spaces, newton_iterates);
delete [] coeff_vec;
// Exact solution for comparison with computational results.
T_exact_solution.update(&mesh, T_exact);
phi_exact_solution.update(&mesh, phi_exact);
// Calculate exact error.
info("Calculating error (exact).");
Hermes::vector<double> exact_errors;
Adapt adaptivity_exact(spaces);
bool solutions_for_adapt = false;
adaptivity_exact.calc_err_exact(Hermes::vector<Solution *>(&T_prev_newton, &phi_prev_newton), Hermes::vector<Solution *>(&T_exact_solution, &phi_exact_solution), &exact_errors, solutions_for_adapt);
double maxerr = std::max(exact_errors[0], exact_errors[1])*100;
info("Exact solution error for T (H1 norm): %g %%", exact_errors[0]*100);
info("Exact solution error for phi (H1 norm): %g %%", exact_errors[1]*100);
info("Exact solution error (maximum): %g %%", maxerr);
// Prepare previous time level solution for the next time step.
T_prev_time.copy(&T_prev_newton);
phi_prev_time.copy(&phi_prev_newton);
}
while (t_step <= TIME_MAX_ITER);
// Cleanup.
delete matrix;
delete rhs;
delete solver;
info("Coordinate ( 0, 0) T value = %lf", T_prev_time.get_pt_value(0.0, 0.0));
info("Coordinate ( 25, 25) T value = %lf", T_prev_time.get_pt_value(25.0, 25.0));
info("Coordinate ( 75, 25) T value = %lf", T_prev_time.get_pt_value(75.0, 25.0));
info("Coordinate ( 25, 75) T value = %lf", T_prev_time.get_pt_value(25.0, 75.0));
info("Coordinate ( 75, 75) T value = %lf", T_prev_time.get_pt_value(75.0, 75.0));
info("Coordinate ( 0, 0) phi value = %lf", phi_prev_time.get_pt_value(0.0, 0.0));
info("Coordinate ( 25, 25) phi value = %lf", phi_prev_time.get_pt_value(25.0, 25.0));
info("Coordinate ( 75, 25) phi value = %lf", phi_prev_time.get_pt_value(75.0, 25.0));
info("Coordinate ( 25, 75) phi value = %lf", phi_prev_time.get_pt_value(25.0, 75.0));
info("Coordinate ( 75, 75) phi value = %lf", phi_prev_time.get_pt_value(75.0, 75.0));
int success = 1;
double eps = 1e-5;
if (fabs(T_prev_time.get_pt_value(0.0, 0.0) - 0.000000) > eps) {
printf("Coordinate ( 0, 0) T value = %lf\n", T_prev_time.get_pt_value(0.0, 0.0));
success = 0;
}
if (fabs(T_prev_time.get_pt_value(25.0, 25.0) - 0.915885) > eps) {
printf("Coordinate ( 25, 25) T value = %lf\n", T_prev_time.get_pt_value(25.0, 25.0));
success = 0;
}
if (fabs(T_prev_time.get_pt_value(75.0, 25.0) - 0.915885) > eps) {
printf("Coordinate ( 75, 25) T value = %lf\n", T_prev_time.get_pt_value(75.0, 25.0));
success = 0;
}
if (fabs(T_prev_time.get_pt_value(25.0, 75.0) - 0.915885) > eps) {
printf("Coordinate ( 25, 75) T value = %lf\n", T_prev_time.get_pt_value(25.0, 75.0));
success = 0;
}
if (fabs(T_prev_time.get_pt_value(75.0, 75.0) - 0.915885) > eps) {
printf("Coordinate ( 75, 75) T value = %lf\n", T_prev_time.get_pt_value(75.0, 75.0));
success = 0;
}
if (fabs(phi_prev_time.get_pt_value(0.0, 0.0) - 0.000000) > eps) {
printf("Coordinate ( 0, 0) phi value = %lf\n", phi_prev_time.get_pt_value(0.0, 0.0));
success = 0;
}
if (fabs(phi_prev_time.get_pt_value(25.0, 25.0) - 0.071349) > eps) {
printf("Coordinate ( 25, 25) phi value = %lf\n", phi_prev_time.get_pt_value(25.0, 25.0));
success = 0;
}
if (fabs(phi_prev_time.get_pt_value(75.0, 25.0) - 0.214063) > eps) {
printf("Coordinate ( 75, 25) phi value = %lf\n", phi_prev_time.get_pt_value(75.0, 25.0));
success = 0;
}
if (fabs(phi_prev_time.get_pt_value(25.0, 75.0) - 0.214063) > eps) {
printf("Coordinate ( 25, 75) phi value = %lf\n", phi_prev_time.get_pt_value(25.0, 75.0));
success = 0;
}
if (fabs(phi_prev_time.get_pt_value(75.0, 75.0) - 0.642226) > eps) {
printf("Coordinate ( 75, 75) phi value = %lf\n", phi_prev_time.get_pt_value(75.0, 75.0));
success = 0;
}
if (success == 1) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}
