int main(int argc, char **argv) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &argv, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
if (argc < 5) error("Not enough parameters.");
H1ShapesetLobattoHex shapeset;
printf("* Loading mesh '%s'\n", argv[1]);
Mesh mesh;
Mesh3DReader mloader;
if (!mloader.load(argv[1], &mesh)) error("Loading mesh file '%s'\n", argv[1]);
printf("* Setting the space up\n");
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
int o[3] = { 0, 0, 0 };
sscanf(argv[2], "%d", o + 0);
sscanf(argv[3], "%d", o + 1);
sscanf(argv[4], "%d", o + 2);
order3_t order(o[0], o[1], o[2]);
printf(" - Setting uniform order to (%d, %d, %d)\n", order.x, order.y, order.z);
space.set_uniform_order(order);
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<ord_t, ord_t>, SYM, ANY);
wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>, ANY);
LinearProblem lp(&wf);
lp.set_space(&space);
bool done = false;
int iter = 0;
do {
Timer assemble_timer("Assembling stiffness matrix");
Timer solve_timer("Solving stiffness matrix");
printf("\n=== Iter #%d ================================================================\n", iter);
printf("\nSolution\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
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
// assemble stiffness matrix
printf(" - Assembling... "); fflush(stdout);
assemble_timer.reset();
assemble_timer.start();
lp.assemble(&mat, &rhs);
assemble_timer.stop();
printf("done in %s (%lf secs)\n", assemble_timer.get_human_time(), assemble_timer.get_seconds());
// solve the stiffness matrix
printf(" - Solving... "); fflush(stdout);
solve_timer.reset();
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
if (solved)
printf("done in %s (%lf secs)\n", solve_timer.get_human_time(), solve_timer.get_seconds());
else {
res = ERR_FAILURE;
printf("failed\n");
break;
}
printf("Reference solution\n");
#if defined WITH_UMFPACK
UMFPackLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_PETSC
PetscLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsSolver rsolver(&mat, &rhs);
#endif
Mesh rmesh;
rmesh.copy(mesh);
rmesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Space *rspace = space.dup(&rmesh);
rspace->copy_orders(space, 1);
LinearProblem rlp(&wf);
rlp.set_space(rspace);
int rndofs = rspace->assign_dofs();
printf(" - Number of DOFs: %d\n", rndofs);
printf(" - Assembling... "); fflush(stdout);
assemble_timer.reset();
assemble_timer.start();
rlp.assemble(&mat, &rhs);
assemble_timer.stop();
printf("done in %s (%lf secs)\n", assemble_timer.get_human_time(), assemble_timer.get_seconds());
printf(" - Solving... "); fflush(stdout);
solve_timer.reset();
solve_timer.start();
bool rsolved = rsolver.solve();
solve_timer.stop();
if (rsolved)
printf("done in %s (%lf secs)\n", solve_timer.get_human_time(), solve_timer.get_seconds());
else {
res = ERR_FAILURE;
printf("failed\n");
break;
}
Solution sln(&mesh);
sln.set_coeff_vector(&space, solver.get_solution());
Solution rsln(&rmesh);
rsln.set_coeff_vector(rspace, rsolver.get_solution());
printf("Adaptivity:\n");
H1Adapt hp(&space);
double tol = hp.calc_error(&sln, &rsln) * 100;
printf(" - tolerance: "); fflush(stdout);
printf("% lf\n", tol);
if (tol < TOLERANCE) {
printf("\nDone\n");
ExactSolution ex_sln(&mesh, 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;
}
break;
}
Timer t("");
printf(" - adapting... "); fflush(stdout);
t.start();
hp.adapt(THRESHOLD);
t.stop();
printf("done in %lf secs (refined %d element(s))\n", t.get_seconds(), hp.get_num_refined_elements());
iter++;
} while (!done);
#ifdef WITH_PETSC
PetscFinalize();
#endif
return res;
}
/***********************************************************************************
* main program *
************************************************************************************/
int main(int argc, char **args)
{
#ifdef WITH_PETSC
PetscInitialize(NULL, NULL, PETSC_NULL, PETSC_NULL);
PetscPushErrorHandler(PetscIgnoreErrorHandler, PETSC_NULL); // Disable PETSc error handler.
#endif
// Load the inital mesh.
Mesh mesh;
Mesh3DReader mesh_loader;
mesh_loader.load("hexahedron.mesh3d", &mesh);
// Initial uniform mesh refinements.
printf("Performing %d initial mesh refinements.\n", INIT_REF_NUM);
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Word_t (nelem) = mesh.get_num_elements();
printf("New number of elements is %d.\n", nelem);
//Initialize the shapeset and the cache.
H1ShapesetLobattoHex shapeset;
//Matrix solver.
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver 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
// Graphs of DOF convergence.
GnuplotGraph graph;
graph.set_captions("", "Degrees of Freedom", "Error [%]");
graph.set_log_y();
graph.add_row("Total error", "k", "-", "O");
// Create H1 space to setup the problem.
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
space.set_uniform_order(order3_t(P_INIT, P_INIT, P_INIT));
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(biform<double, double>, biform<ord_t, ord_t>, SYM, ANY);
wf.add_vector_form(liform<double, double>, liform<ord_t, ord_t>, ANY);
// Initialize the coarse mesh problem.
LinProblem lp(&wf);
lp.set_space(&space);
// Adaptivity loop.
int as = 0;
bool done = false;
do {
printf("\n---- Adaptivity step %d:\n", as);
printf("\nSolving on coarse mesh:\n");
// Procedures for coarse mesh problem.
// Assign DOF.
int ndof = space.assign_dofs();
printf(" - Number of DOF: %d\n", ndof);
// Assemble stiffness matrix and rhs.
printf(" - Assembling... ");
fflush(stdout);
if (lp.assemble(&mat, &rhs))
printf("done in %lf secs.\n", lp.get_time());
else
error("failed!");
// Solve the system.
printf(" - Solving... ");
fflush(stdout);
bool solved = solver.solve();
if (solved)
printf("done in %lf secs.\n", solver.get_time());
else
{
printf("Failed.\n");
break;
}
// Construct a solution.
Solution sln(&mesh);
sln.set_fe_solution(&space, solver.get_solution());
// Output the orders and the solution.
if (do_output)
{
out_orders(&space, "order", as);
out_fn(&sln, "sln", as);
}
// Solving fine mesh problem.
printf("Solving on fine mesh:\n");
// Matrix solver.
#if defined WITH_UMFPACK
UMFPackLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_PETSC
PetscLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsSolver rsolver(&mat, &rhs);
#endif
// Construct the refined mesh for reference(refined) solution.
Mesh rmesh;
rmesh.copy(mesh);
rmesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Setup space for the reference (globally refined) solution.
Space *rspace = space.dup(&rmesh);
rspace->copy_orders(space, 1);
// Initialize the mesh problem for reference solution.
LinProblem rlp(&wf);
rlp.set_space(rspace);
// Assign DOF.
int rndof = rspace->assign_dofs();
printf(" - Number of DOF: %d\n", rndof);
// Assemble stiffness matric and rhs.
printf(" - Assembling... ");
fflush(stdout);
if (rlp.assemble(&mat, &rhs))
printf("done in %lf secs.\n", rlp.get_time());
else
error("failed!");
// Solve the system.
printf(" - Solving... ");
fflush(stdout);
bool rsolved = rsolver.solve();
if (rsolved)
printf("done in %lf secs.\n", rsolver.get_time());
else
{
printf("failed.\n");
break;
}
// Construct the reference(refined) solution.
Solution rsln(&rmesh);
rsln.set_fe_solution(rspace, rsolver.get_solution());
// Compare coarse and fine mesh.
// Calculate the error estimate wrt. refined mesh solution.
double err = h1_error(&sln, &rsln);
printf(" - H1 error: % lf\n", err * 100);
// Save it to the graph.
graph.add_value(0, ndof, err * 100);
if (do_output)
graph.save("conv.gp");
// Calculate error estimates for adaptivity.
printf("Adaptivity\n");
printf(" - calculating error: ");
fflush(stdout);
H1Adapt hp(&space);
double err_est = hp.calc_error(&sln, &rsln) * 100;
printf("% lf %%\n", err_est);
// If error is too large, adapt the mesh.
if (err_est < ERR_STOP)
{
printf("\nDone\n");
break;
}
printf(" - adapting... ");
fflush(stdout);
hp.adapt(THRESHOLD);
printf("done in %lf secs (refined %d element(s)).\n", hp.get_adapt_time(), hp.get_num_refined_elements());
if (rndof >= NDOF_STOP)
{
printf("\nDone.\n");
break;
}
// Clean up.
delete rspace;
// Next adaptivity step.
as++;
mat.free();
rhs.free();
} while (!done);
#ifdef WITH_PETSC
PetscFinalize();
#endif
return 1;
}