int main(int argc, char **args)
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
//CTUReader mloader;
H3DReader mloader;
info("Loading mesh...");
mloader.load("bridge.mesh3d", &mesh);
// Create H1 space with default shapeset.
H1Space 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(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>, HERMES_ANY_INT);
// Initialize discrete 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);
// Assemble stiffness matrix and load vector.
info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(&space));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution sln(&mesh);
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
// Output the solution for Paraview.
if (solution_output) out_fn_vtk(&sln, "sln");
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solutions and mesh with polynomial orders saved. Total running time: %g s",
cpu_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
return 0;
}
int main(int argc, char **args)
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
ExodusIIReader mloader;
mloader.load("brick_with_hole_hex.e", &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 H1 space with default shapeset for x-displacement component.
H1Space xdisp(&mesh, bc_types_x, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Create H1 space with default shapeset for y-displacement component.
H1Space ydisp(&mesh, bc_types_y, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Create H1 space with default shapeset for z-displacement component.
H1Space zdisp(&mesh, bc_types_z, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Initialize weak formulation.
WeakForm wf(3);
wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), HERMES_SYM);
wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), HERMES_SYM);
wf.add_matrix_form(0, 2, callback(bilinear_form_0_2), HERMES_SYM);
wf.add_vector_form_surf(0, callback(surf_linear_form_x), bdy_force);
wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), HERMES_SYM);
wf.add_matrix_form(1, 2, callback(bilinear_form_1_2), HERMES_SYM);
wf.add_vector_form_surf(1, callback(surf_linear_form_y), bdy_force);
wf.add_matrix_form(2, 2, callback(bilinear_form_2_2), HERMES_SYM);
wf.add_vector_form_surf(2, callback(surf_linear_form_z), bdy_force);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::Tuple<Space *>(&xdisp, &ydisp, &zdisp), 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 stiffness matrix and load vector.
info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(Hermes::Tuple<Space *>(&xdisp, &ydisp, &zdisp)));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution xsln(xdisp.get_mesh());
Solution ysln(ydisp.get_mesh());
Solution zsln(zdisp.get_mesh());
if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(),
Hermes::Tuple<Space *>(&xdisp, &ydisp, &zdisp), Hermes::Tuple<Solution *>(&xsln, &ysln, &zsln));
else error ("Matrix solver failed.\n");
// Output all components of the solution.
if (solution_output) out_fn_vtk(&xsln, &ysln, &zsln, "sln");
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solutions saved. Total running time: %g s.", cpu_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
return 0;
}
int main(int argc, char **args)
{
// Load the mesh.
Mesh mesh;
H3DReader mesh_loader;
mesh_loader.load("fichera-corner.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 H1 space with default shapeset.
H1Space 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(bilinear_form<double, double>, bilinear_form<Ord, Ord>, HERMES_SYM, HERMES_ANY);
wf.add_vector_form(linear_form<double, double>, linear_form<Ord, Ord>, HERMES_ANY);
// Set exact solution.
ExactSolution exact(&mesh, fndd);
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est, graph_dof_exact, graph_cpu_exact;
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Initialize the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
initialize_solution_environment(matrix_solver, argc, args);
// 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 , H3D_H3D_H3D_REFT_HEX_XYZ);
// 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);
// 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_H1_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, 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);
// Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
finalize_solution_environment(matrix_solver);
return 1;
}
int main (int argc, char* argv[]) {
// Load the mesh.
Mesh basemesh;
ExodusIIReader mesh_loader;
if (!mesh_loader.load("coarse_mesh_full.e", &basemesh))
error("Loading mesh file '%s' failed.\n", "coarse_mesh_full.e");
Mesh C_mesh, phi_mesh;
C_mesh.copy(basemesh);
phi_mesh.copy(basemesh);
H1Space C_space(&C_mesh, bc_types_C, essential_bc_values_C, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
H1Space phi_space(MULTIMESH ? &phi_mesh : &C_mesh, bc_types_phi, essential_bc_values_phi, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
Solution C_prev_time(&C_mesh);
C_prev_time.set_const(C0);
Solution phi_prev_time(MULTIMESH ? &phi_mesh : &C_mesh);
phi_prev_time.set_const(0.0);
WeakForm wf(2);
// Add the bilinear and linear forms.
if (TIME_DISCR == 1) { // Implicit Euler.
wf.add_matrix_form(0, 0, callback(J_euler_DFcDYc), HERMES_NONSYM);
wf.add_matrix_form(0, 1, callback(J_euler_DFcDYphi), HERMES_NONSYM);
wf.add_matrix_form(1, 0, callback(J_euler_DFphiDYc), HERMES_NONSYM);
wf.add_matrix_form(1, 1, callback(J_euler_DFphiDYphi), HERMES_NONSYM);
wf.add_vector_form(0, callback(Fc_euler), HERMES_ANY_INT,
Hermes::vector<MeshFunction*>(&C_prev_time, &phi_prev_time));
wf.add_vector_form(1, callback(Fphi_euler), HERMES_ANY,
Hermes::vector<MeshFunction*>(&C_prev_time, &phi_prev_time));
} else {
wf.add_matrix_form(0, 0, callback(J_cranic_DFcDYc), HERMES_NONSYM);
wf.add_matrix_form(0, 1, callback(J_cranic_DFcDYphi), HERMES_NONSYM);
wf.add_matrix_form(1, 0, callback(J_cranic_DFphiDYc), HERMES_NONSYM);
wf.add_matrix_form(1, 1, callback(J_cranic_DFphiDYphi), HERMES_NONSYM);
wf.add_vector_form(0, callback(Fc_cranic), HERMES_ANY,
Hermes::vector<MeshFunction*>(&C_prev_time, &phi_prev_time));
wf.add_vector_form(1, callback(Fphi_cranic), HERMES_ANY);
}
int ndof = Space::get_num_dofs(Hermes::vector<Space*>(&C_space, &phi_space));
Solution C_sln(C_space.get_mesh());
Solution phi_sln(phi_space.get_mesh());
info("Projecting initial condition to obtain initial vector for the Newton's method.");
scalar* coeff_vec_coarse = new scalar[ndof];
OGProjection::project_global(Hermes::vector<Space *>(&C_space, &phi_space),
Hermes::vector<MeshFunction *>(&C_prev_time, &phi_prev_time),
coeff_vec_coarse, matrix_solver);
bool is_linear = false;
DiscreteProblem dp_coarse(&wf, Hermes::vector<Space *>(&C_space, &phi_space), is_linear);
//Solution::vector_to_solutions(coeff_vec_coarse, dp_coarse.get_spaces(), Hermes::vector<Solution *>(&C_sln, &phi_sln), NULL);
// Set up the solver, matrix, and rhs for the coarse mesh according to the solver selection.
SparseMatrix* matrix_coarse = create_matrix(matrix_solver);
Vector* rhs_coarse = create_vector(matrix_solver);
Solver* solver_coarse = create_linear_solver(matrix_solver, matrix_coarse, rhs_coarse);
info("Solving on coarse mesh:");
bool verbose = true;
if (!solve_newton(coeff_vec_coarse, &dp_coarse, solver_coarse, matrix_coarse, rhs_coarse,
NEWTON_TOL_COARSE, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");
info("Solved!");
// Translate the resulting coefficient vector into the Solution sln.
Solution::vector_to_solutions(coeff_vec_coarse, Hermes::vector<Space *>(&C_space, &phi_space),
Hermes::vector<Solution *>(&C_sln, &phi_sln));
out_fn_vtk(&C_sln,"C_init_sln");
out_fn_vtk(&phi_sln,"phi_init_sln");
//out_fn_vtk(&sln, "sln", ts);
Solution *C_ref_sln, *phi_ref_sln;
PidTimestepController pid(T_FINAL, false, INIT_TAU);
TAU = pid.timestep;
info("Starting time iteration with the step %g", *TAU);
do {
pid.begin_step();
if (pid.get_timestep_number() > 1 && pid.get_timestep_number() % UNREF_FREQ == 0)
{
info("Global mesh derefinement.");
C_mesh.copy(basemesh);
if (MULTIMESH)
{
phi_mesh.copy(basemesh);
}
C_space.set_uniform_order(Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
phi_space.set_uniform_order(Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
}
bool done = false; int as = 1;
double err_est;
do {
info("Time step %d, adaptivity step %d:", pid.get_timestep_number(), as);
// Construct globally refined reference mesh
// and setup reference space.
int order_increase = 1;
Hermes::vector<Space *>* ref_spaces = construct_refined_spaces(Hermes::vector<Space *>(&C_space, &phi_space),
order_increase);
scalar* coeff_vec = new scalar[Space::get_num_dofs(*ref_spaces)];
DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces, is_linear);
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
if (as == 1 && pid.get_timestep_number() == 1) {
info("Projecting coarse mesh solution to obtain coefficient vector on new fine mesh.");
OGProjection::project_global(*ref_spaces, Hermes::vector<MeshFunction *>(&C_sln, &phi_sln),
coeff_vec, matrix_solver);
}
else {
info("Projecting previous fine mesh solution to obtain coefficient vector on new fine mesh.");
OGProjection::project_global(*ref_spaces, Hermes::vector<MeshFunction *>(C_ref_sln, phi_ref_sln),
coeff_vec, matrix_solver);
}
if (as > 1) {
// Now deallocate the previous mesh
info("Deallocating the previous mesh");
//delete C_ref_sln->get_mesh();
//delete phi_ref_sln->get_mesh();
//delete C_ref_sln;
//delete phi_ref_sln;
}
/*TODO TEMP */
if (pid.get_timestep_number() > 1) {
delete C_ref_sln;
delete phi_ref_sln;
}
info("Solving on fine mesh:");
if (!solve_newton(coeff_vec, dp, solver, matrix, rhs,
NEWTON_TOL_FINE, NEWTON_MAX_ITER, verbose)) error("Newton's iteration failed.");
// Store the result in ref_sln.
C_ref_sln = new Solution(ref_spaces->at(0)->get_mesh());
phi_ref_sln = new Solution(ref_spaces->at(1)->get_mesh());
Solution::vector_to_solutions(coeff_vec, *ref_spaces,
Hermes::vector<Solution *>(C_ref_sln, phi_ref_sln));
// Projecting reference solution onto the coarse mesh
info("Projecting fine mesh solution on coarse mesh.");
OGProjection::project_global(Hermes::vector<Space *>(&C_space, &phi_space),
Hermes::vector<Solution *>(C_ref_sln, phi_ref_sln),
Hermes::vector<Solution *>(&C_sln, &phi_sln),
matrix_solver);
info("Calculating error estimate.");
Adapt* adaptivity = new Adapt(Hermes::vector<Space *>(&C_space, &phi_space),
Hermes::vector<ProjNormType> (HERMES_H1_NORM, HERMES_H1_NORM));
Hermes::vector<double> err_est_rel;
bool solutions_for_adapt = true;
double err_est_rel_total = adaptivity->calc_err_est(Hermes::vector<Solution *>(&C_sln, &phi_sln),
Hermes::vector<Solution *>(C_ref_sln, phi_ref_sln), solutions_for_adapt,
HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_ABS, &err_est_rel) * 100;
// Report results.
info("ndof_coarse[0]: %d, ndof_fine[0]: %d",
C_space.get_num_dofs(), (*ref_spaces)[0]->get_num_dofs());
info("err_est_rel[0]: %g%%", err_est_rel[0]*100);
info("ndof_coarse[1]: %d, ndof_fine[1]: %d",
phi_space.get_num_dofs(), (*ref_spaces)[1]->get_num_dofs());
info("err_est_rel[1]: %g%%", err_est_rel[1]*100);
// Report results.
info("ndof_coarse_total: %d, ndof_fine_total: %d, err_est_rel: %g%%",
Space::get_num_dofs(Hermes::vector<Space *>(&C_space, &phi_space)),
Space::get_num_dofs(*ref_spaces), err_est_rel_total);
// If err_est too large, adapt the mesh.
if (err_est_rel_total < ERR_STOP) done = true;
else
{
info("Adapting the coarse mesh.");
adaptivity->adapt(THRESHOLD);
info("Adapted...");
if (Space::get_num_dofs(Hermes::vector<Space *>(&C_space, &phi_space)) >= NDOF_STOP)
done = true;
else
// Increase the counter of performed adaptivity steps.
as++;
}
//as++;
delete solver;
delete matrix;
delete rhs;
delete ref_spaces;
delete dp;
delete[] coeff_vec;
done = true;
} while (!done);
out_fn_vtk(C_ref_sln,"C_sln", pid.get_timestep_number());
out_fn_vtk(phi_ref_sln,"phi_sln", pid.get_timestep_number());
pid.end_step(Hermes::vector<Solution*> (C_ref_sln, phi_ref_sln), Hermes::vector<Solution*> (&C_prev_time, &phi_prev_time));
// Copy last reference solution into sln_prev_time.
C_prev_time.copy(C_ref_sln);
phi_prev_time.copy(phi_ref_sln);
} while (pid.has_next());
//View::wait();
return 0;
}
int main(int argc, char **args)
{
// Test variable.
int success_test = 1;
// Check the number of command-line parameters.
if (argc < 2) {
info("Use x, y, z, xy, xz, yz, or xyz as a command-line parameter.");
error("Not enough command-line parameters.");
}
// Determine anisotropy type from the command-line parameter.
ANISO_TYPE = parse_aniso_type(args[1]);
// Load the mesh.
Mesh mesh;
H3DReader mesh_loader;
mesh_loader.load("hex-0-1.mesh3d", &mesh);
// Assign the lowest possible directional polynomial degrees so that the problem's NDOF >= 1.
assign_poly_degrees();
// Create an H1 space with default shapeset.
info("Setting directional polynomial degrees %d, %d, %d.", P_INIT_X, P_INIT_Y, P_INIT_Z);
H1Space 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(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM, HERMES_ANY);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>, HERMES_ANY);
// Set exact solution.
ExactSolution exact(&mesh, fndd);
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// 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");
success_test = 0;
}
// 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);
// 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_H1_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, 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);
// 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);
// This is the actual test.
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
int ndof_allowed;
switch (ANISO_TYPE) {
case ANISO_X: ndof_allowed = 28; break;
case ANISO_Y: ndof_allowed = 28; break;
case ANISO_Z: ndof_allowed = 28; break;
case ANISO_X | ANISO_Y: ndof_allowed = 98; break;
case ANISO_X | ANISO_Z: ndof_allowed = 98; break;
case ANISO_Y | ANISO_Z: ndof_allowed = 98; break;
case ANISO_X | ANISO_Y | ANISO_Z: ndof_allowed = 343; break;
default: error("Admissible command-line options are x, y, x, xy, xz, yz, xyz.");
}
int ndof = Space::get_num_dofs(&space);
info("ndof_actual = %d", ndof);
info("ndof_allowed = %d", ndof_allowed);
if (ndof > ndof_allowed)
success_test = 0;
if (success_test) {
info("Success!");
return ERR_SUCCESS;
}
else {
info("Failure!");
return ERR_FAILURE;
}
}
int main(int argc, char **args)
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
ExodusIIReader mesh_loader;
if (!mesh_loader.load("cylinder2.e", &mesh))
error("Loading mesh file '%s' failed.\n", "cylinder2.e");
// Perform initial mesh refinement.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Create H1 space with default shapeset.
H1Space space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
info("Number of DOF: %d.", Space::get_num_dofs(&space));
// Initialize weak formulation.
WeakForm wf;
wf.add_matrix_form(callback(bilinear_form1), HERMES_SYM, 1);
wf.add_matrix_form(callback(bilinear_form2), HERMES_SYM, 2);
wf.add_vector_form(callback(linear_form), HERMES_ANY);
// Initialize discrete 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 stiffness amtrix and load vector.
info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(&space));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution sln(space.get_mesh());
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
// Output solution and the boundary condition.
if (solution_output)
{
out_fn_vtk(&sln, "sln");
out_bc_vtk(&mesh, "bc");
}
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solution and the boundary condition saved. Total running time: %g s", cpu_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
// Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
finalize_solution_environment(matrix_solver);
return 0;
}
int main(int argc, char **args)
{
// Test variable.
int success_test = 1;
// Load the initial mesh.
Mesh mesh;
H3DReader mesh_loader;
mesh_loader.load("../hexahedron.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 H1 space with default shapeset.
H1Space space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Construct initial solution and set it to zero.
Solution sln_prev(&mesh);
sln_prev.set_zero();
// Initialize weak formulation.
WeakForm wf;
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>, HERMES_ANY_INT, &sln_prev);
// Initialize discrete 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).
}
// Exact error for testing purposes.
double err_exact;
// Time stepping.
int nsteps = (int) (FINAL_TIME/TAU + 0.5);
for (int ts = 0; ts < nsteps; ts++)
{
info("---- Time step %d, time %3.5f.", ts, TIME);
// Assemble the linear problem.
info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(&space));
if (ts == 0) dp.assemble(matrix, rhs);
else dp.assemble(NULL, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution sln(space.get_mesh());
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
// Output solution.
if (solution_output)
out_fn_vtk(&sln, "sln", ts);
// Calculate exact error.
ExactSolution esln(&mesh, fndd);
info("Calculating exact error.");
Adapt *adaptivity = new Adapt(&space, HERMES_H1_NORM);
bool solutions_for_adapt = false;
err_exact = adaptivity->calc_err_exact(&sln, &esln, solutions_for_adapt, HERMES_TOTAL_ERROR_ABS) * 100;
info("Err. exact: %g%%.", err_exact);
// Next time step.
sln_prev = sln;
TIME += TAU;
// Cleanup.
delete adaptivity;
}
if(err_exact > 3.00)
success_test = 0;
// Clean up.
delete matrix;
delete rhs;
delete solver;
if (success_test) {
info("Success!");
return ERR_SUCCESS;
}
else {
info("Failure!");
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
if (argc < 2) error("Not enough parameters.");
printf("* Loading mesh '%s'\n", args[1]);
Mesh mesh1;
H3DReader mesh_loader;
if (!mesh_loader.load(args[1], &mesh1)) error("Loading mesh file '%s'\n", args[1]);
#if defined RHS2
Ord3 order(P_INIT_X, P_INIT_Y, P_INIT_Z);
printf(" - Setting uniform order to (%d, %d, %d)\n", order.x, order.y, order.z);
// Create an H1 space with default shapeset.
printf("* Setting the space up\n");
H1Space space(&mesh1, bc_types, essential_bc_values, order);
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
printf("* Calculating a solution\n");
// duplicate the mesh
Mesh mesh2;
mesh2.copy(mesh1);
// do some changes
mesh2.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
mesh2.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Solution fsln(&mesh2);
fsln.set_const(-6.0);
#else
// duplicate the mesh
Mesh mesh2;
mesh2.copy(mesh1);
Mesh mesh3;
mesh3.copy(mesh1);
// change meshes
mesh1.refine_all_elements(H3D_REFT_HEX_X);
mesh2.refine_all_elements(H3D_REFT_HEX_Y);
mesh3.refine_all_elements(H3D_REFT_HEX_Z);
printf("* Setup spaces\n");
Ord3 o1(2, 2, 2);
printf(" - Setting uniform order to (%d, %d, %d)\n", o1.x, o1.y, o1.z);
H1Space space1(&mesh1, bc_types_1, essential_bc_values_1, o1);
Ord3 o2(2, 2, 2);
printf(" - Setting uniform order to (%d, %d, %d)\n", o2.x, o2.y, o2.z);
H1Space space2(&mesh2, bc_types_2, essential_bc_values_2, o2);
Ord3 o3(1, 1, 1);
printf(" - Setting uniform order to (%d, %d, %d)\n", o3.x, o3.y, o3.z);
H1Space space3(&mesh3, bc_types_3, essential_bc_values_3, o3);
int ndofs = 0;
ndofs += space1.assign_dofs();
ndofs += space2.assign_dofs(ndofs);
ndofs += space3.assign_dofs(ndofs);
printf(" - Number of DOFs: %d\n", ndofs);
#endif
#if defined WITH_UMFPACK
MatrixSolverType matrix_solver = SOLVER_UMFPACK;
#elif defined WITH_PETSC
MatrixSolverType matrix_solver = SOLVER_PETSC;
#elif defined WITH_MUMPS
MatrixSolverType matrix_solver = SOLVER_MUMPS;
#endif
#ifdef RHS2
WeakForm wf;
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>, HERMES_ANY_INT, &fsln);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
#elif defined SYS3
WeakForm wf(3);
wf.add_matrix_form(0, 0, biform_1_1<double, scalar>, biform_1_1<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form(0, 1, biform_1_2<double, scalar>, biform_1_2<Ord, Ord>, HERMES_NONSYM);
wf.add_vector_form(0, liform_1<double, scalar>, liform_1<Ord, Ord>);
wf.add_matrix_form(1, 1, biform_2_2<double, scalar>, biform_2_2<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form(1, 2, biform_2_3<double, scalar>, biform_2_3<Ord, Ord>, HERMES_NONSYM);
wf.add_vector_form(1, liform_2<double, scalar>, liform_2<Ord, Ord>);
wf.add_matrix_form(2, 2, biform_3_3<double, scalar>, biform_3_3<Ord, Ord>, HERMES_SYM);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::vector<Space *>(&space1, &space2, &space3), is_linear);
#endif
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// 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 stiffness matrix and load vector.
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
bool solved = solver->solve();
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solution and mesh with polynomial orders saved. Total running time: %g s", cpu_time.accumulated());
// Time measurement.
TimePeriod sln_time;
sln_time.tick();
if (solved) {
#ifdef RHS2
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution sln(&mesh1);
Solution::vector_to_solution(solver->get_solution(), &space, &sln);
// Set exact solution.
ExactSolution ex_sln(&mesh1, exact_solution);
// Norm.
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;
}
#elif defined SYS3
// Solution 1.
Solution sln1(&mesh1);
Solution sln2(&mesh2);
Solution sln3(&mesh3);
Solution::vector_to_solution(solver->get_solution(), &space1, &sln1);
Solution::vector_to_solution(solver->get_solution(), &space2, &sln2);
Solution::vector_to_solution(solver->get_solution(), &space3, &sln3);
ExactSolution esln1(&mesh1, exact_sln_fn_1);
ExactSolution esln2(&mesh2, exact_sln_fn_2);
ExactSolution esln3(&mesh3, exact_sln_fn_3);
// Norm.
double h1_err_norm1 = h1_error(&sln1, &esln1);
double h1_err_norm2 = h1_error(&sln2, &esln2);
double h1_err_norm3 = h1_error(&sln3, &esln3);
double l2_err_norm1 = l2_error(&sln1, &esln1);
double l2_err_norm2 = l2_error(&sln2, &esln2);
double l2_err_norm3 = l2_error(&sln3, &esln3);
printf(" - H1 error norm: % le\n", h1_err_norm1);
printf(" - L2 error norm: % le\n", l2_err_norm1);
if (h1_err_norm1 > EPS || l2_err_norm1 > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
printf(" - H1 error norm: % le\n", h1_err_norm2);
printf(" - L2 error norm: % le\n", l2_err_norm2);
if (h1_err_norm2 > EPS || l2_err_norm2 > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
printf(" - H1 error norm: % le\n", h1_err_norm3);
printf(" - L2 error norm: % le\n", l2_err_norm3);
if (h1_err_norm3 > EPS || l2_err_norm3 > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
#endif
#ifdef RHS2
out_fn_vtk(&sln, "solution");
#elif defined SYS3
out_fn_vtk(&sln1, "sln1");
out_fn_vtk(&sln2, "sln2");
out_fn_vtk(&sln3, "sln3");
#endif
}
else
res = ERR_FAILURE;
// Print timing information.
info("Solution and mesh with polynomial orders saved. Total running time: %g s", sln_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
return res;
}
int main(int argc, char* argv[])
{
info("Desired number of eigenvalues: %d.", NUMBER_OF_EIGENVALUES);
// Load the mesh.
info("Loading and refining mesh...");
Mesh mesh;
H3DReader mloader;
mloader.load("hexahedron.mesh3d", &mesh);
// Perform initial mesh refinements (optional).
for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Create an H1 space with default shapeset.
H1Space space(&mesh, bc_types, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
int ndof = Space::get_num_dofs(&space);
info("ndof: %d.", ndof);
// Initialize the weak formulation for the left hand side, i.e., H.
info("Initializing weak form...");
WeakForm wf_left, wf_right;
wf_left.add_matrix_form(bilinear_form_left, bilinear_form_left_ord, HERMES_SYM, HERMES_ANY );
wf_right.add_matrix_form(callback(bilinear_form_right), HERMES_SYM, HERMES_ANY );
// Initialize matrices and matrix solver.
SparseMatrix* matrix_left = create_matrix(matrix_solver);
SparseMatrix* matrix_right = create_matrix(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix_left);
// Assemble the matrices.
info("Assembling matrices...");
bool is_linear = true;
DiscreteProblem dp_left(&wf_left, &space, is_linear);
dp_left.assemble(matrix_left);
DiscreteProblem dp_right(&wf_right, &space, is_linear);
dp_right.assemble(matrix_right);
// Write matrix_left in MatrixMarket format.
write_matrix_mm("mat_left.mtx", matrix_left);
// Write matrix_right in MatrixMarket format.
write_matrix_mm("mat_right.mtx", matrix_right);
// Calling Python eigensolver. Solution will be written to "eivecs.dat".
info("Using eigensolver...");
char call_cmd[255];
sprintf(call_cmd, "python solveGenEigenFromMtx.py mat_left.mtx mat_right.mtx %g %d %g %d",
TARGET_VALUE, NUMBER_OF_EIGENVALUES, TOL, MAX_ITER);
system(call_cmd);
// Initializing solution vector, solution and ScalarView.
info("Initializing solution vector...");
double* coeff_vec = new double[ndof];
Solution sln(space.get_mesh());
// Reading solution vectors from file and visualizing.
info("Reading solution vectors from file and saving as solutions in paraview format...");
FILE *file = fopen("eivecs.dat", "r");
char line [64]; // Maximum line size.
fgets(line, sizeof line, file); // ndof
int n = atoi(line);
if (n != ndof) error("Mismatched ndof in the eigensolver output file.");
fgets(line, sizeof line, file); // Number of eigenvectors in the file.
int neig = atoi(line);
if (neig != NUMBER_OF_EIGENVALUES) error("Mismatched number of eigenvectors in the eigensolver output file.");
for (int ieig = 0; ieig < neig; ieig++) {
// Get next eigenvector from the file.
for (int i = 0; i < ndof; i++) {
fgets(line, sizeof line, file);
coeff_vec[i] = atof(line);
}
// Convert coefficient vector into a Solution.
Solution::vector_to_solution(coeff_vec, &space, &sln);
out_fn_vtk(&sln, "sln", ieig );
}
fclose(file);
delete [] coeff_vec;
return 0;
};
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);
// Initialize discrete 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 stiffness matrix and load vector.
info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(&space));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution sln(space.get_mesh());
if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln);
else error ("Matrix solver failed.\n");
// Output solution and mesh with polynomial orders.
if (solution_output)
{
out_fn_vtk(&sln, "sln");
out_orders_vtk(&space, "order");
}
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solution and mesh with polynomial orders saved. Total running time: %g s", cpu_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
// Properly terminate the solver in the case of SOLVER_PETSC or SOLVER_MUMPS.
finalize_solution_environment(matrix_solver);
return 0;
}