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 an H1 space for the initial coarse mesh solution.
H1Space init_space(&basemesh, bc_types, essential_bc_values, P_INIT);
// 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:");
// Initialize views.
char title_init[200];
sprintf(title_init, "Projection of initial condition");
ScalarView* view_init = new ScalarView(title_init, new WinGeom(0, 0, 410, 300));
sprintf(title_init, "Initial mesh");
OrderView* ordview_init = new OrderView(title_init, new WinGeom(420, 0, 350, 300));
view_init->fix_scale_width(80);
int as = 1; bool done = false;
do
{
// Setup space for the reference solution.
Space *rspace = construct_refined_space(&init_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(&init_space, &ref_sln, &sln_prev_time, matrix_solver);
// Calculate element errors and total error estimate.
Adapt adaptivity(&init_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(&init_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(&init_space) >= NDOF_STOP) done = true;
view_init->show(&sln_prev_time);
char title_init[100];
sprintf(title_init, "Initial mesh, step %d", as);
ordview_init->set_title(title_init);
ordview_init->show(&init_space);
}
as++;
}
while (done == false);
// 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;
// Visualize the projection and mesh.
ScalarView view("Initial condition", new WinGeom(0, 0, 440, 350));
OrderView ordview("Initial mesh", new WinGeom(450, 0, 400, 350));
view.show(&sln_prev_time);
ordview.show(&space);
// 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);
}
// 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_prev_time, 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);
delete ref_sln.get_mesh();
}
// 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.
info("Solving nonlinear problem:");
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 actual solutions.
Solution::vector_to_solution(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;
}
while (!done);
// Visualize the solution and mesh.
char title[100];
sprintf(title, "Solution, time level %d", ts);
view.set_title(title);
view.show(&sln);
sprintf(title, "Mesh, time level %d", ts);
ordview.set_title(title);
ordview.show(&space);
// Copy new time level solution into sln_prev_time.
sln_prev_time.copy(&ref_sln);
}
// 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, 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;
}