int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("square_2_elem.mesh", &mesh); // Perform initial mesh refinements. for(int i = 0; i < UNIFORM_REF_LEVEL; i++) mesh.refine_all_elements(); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_neumann(Hermes::vector<int>(BDY_LEFT_RIGHT, BDY_TOP_BOTTOM)); // Create an H1 space with default shapeset. H1Space space(&mesh, &bc_types, 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_vol)); wf.add_vector_form(callback(linear_form_vol)); wf.add_vector_form_surf(callback(linear_form_surf_right), 2); wf.add_vector_form_surf(callback(linear_form_surf_left), 2); Solution sln; // NON-ADAPTIVE VERSION // Initialize the linear problem. bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, &space, is_linear); // Select matrix solver. 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 rhs. dp->assemble(matrix, rhs); // Solve the linear system of the reference problem. If successful, obtain the solutions. if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), &space, &sln); else error ("Matrix solver failed.\n"); // Visualize the solution. ScalarView view("Solution", new WinGeom(0, 0, 440, 350)); view.show(&sln); // Calculate error wrt. exact solution. Solution sln_exact; sln_exact.set_exact(&mesh, exact); double err = calc_abs_error(&sln, &sln_exact, HERMES_H1_NORM); printf("err = %g, err_squared = %g\n\n", err, err*err); // 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("domain.mesh", &mesh); // Perform initial mesh refinements. mesh.refine_towards_vertex(3, CORNER_REF_LEVEL); // Create an H1 space with default shapeset. H1Space space(&mesh, bc_types, essential_bc_values, P_INIT); int ndof = 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_vector_form_surf(callback(linear_form_surf)); // Initialize the linear problem. LinearProblem lp(&wf, &space); // Select matrix solver. Matrix* mat; Vector* rhs; CommonSolver* solver; init_matrix_solver(matrix_solver, ndof, mat, rhs, solver); // Assemble stiffness matrix and rhs. lp.assemble(mat, rhs); // Solve the matrix problem. if (!solver->solve(mat, rhs)) error ("Matrix solver failed.\n"); // Convert coefficient vector into a Solution. Solution* sln = new Solution(&space, rhs); // Visualize the approximation. ScalarView view("Solution", new WinGeom(0, 0, 440, 350)); view.show(sln); // Compute and show gradient magnitude. // (Note that the gradient at the re-entrant // corner needs to be truncated for visualization purposes.) ScalarView gradview("Gradient", new WinGeom(450, 0, 400, 350)); MagFilter grad(Tuple<MeshFunction *>(sln, sln), Tuple<int>(H2D_FN_DX, H2D_FN_DY)); gradview.show(&grad); // Wait for the views to be closed. View::wait(); return 0; }
int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh; H2DReader mloader; if (ALIGN_MESH) mloader.load("oven_load_circle.mesh", &mesh); else mloader.load("oven_load_square.mesh", &mesh); // Perform initial mesh refinemets. for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(); // Create an Hcurl space. HcurlSpace space(&mesh, bc_types, essential_bc_values, P_INIT); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(callback(bilinear_form)); wf.add_vector_form_surf(callback(linear_form_surf)); // Initialize refinements selector. HcurlProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Initialize adaptivity parameters. double to_be_processed = 0; AdaptivityParamType apt(ERR_STOP, NDOF_STOP, THRESHOLD, STRATEGY, MESH_REGULARITY, to_be_processed, H2D_TOTAL_ERROR_REL, H2D_ELEMENT_ERROR_REL); // Geometry and position of visualization windows. WinGeom* sln_win_geom = new WinGeom(0, 355, 900, 300); WinGeom* mesh_win_geom = new WinGeom(0, 0, 900, 300); // Adaptivity loop. Solution *sln = new Solution(); Solution *ref_sln = new Solution(); bool verbose = true; // Print info during adaptivity. bool is_complex = true; solve_linear_adapt(&space, &wf, NULL, matrix_solver, H2D_HCURL_NORM, sln, ref_sln, Tuple<WinGeom *>(sln_win_geom), Tuple<WinGeom *>(mesh_win_geom), &selector, &apt, verbose, Tuple<ExactSolution *>(), is_complex); // Wait for all views 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("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 and next time level solutions. Solution* sln_time_prev = new Solution(&mesh, TEMP_INIT); Solution* sln_time_new = new Solution(&mesh); // Initialize weak formulation. WeakForm wf; wf.add_matrix_form(callback(stac_jacobian_vol)); wf.add_vector_form(callback(stac_residual_vol), HERMES_ANY, sln_time_prev); wf.add_matrix_form_surf(callback(stac_jacobian_surf), BDY_AIR, sln_time_prev); wf.add_vector_form_surf(callback(stac_residual_surf), BDY_AIR, sln_time_prev); // Initialize the FE problem. bool is_linear = false; DiscreteProblem dp(&wf, &space, is_linear); // Time stepping loop: double current_time = time_step; 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, &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); // Increase current time and time step counter. current_time += time_step; ts++; } while (current_time < T_FINAL); info("Coordinate (-2.0, 2.0) value = %lf", sln_time_new->get_pt_value(-2.0, 2.0)); info("Coordinate (-1.0, 2.0) value = %lf", sln_time_new->get_pt_value(-1.0, 2.0)); info("Coordinate ( 0.0, 2.0) value = %lf", sln_time_new->get_pt_value(0.0, 2.0)); info("Coordinate ( 1.0, 2.0) value = %lf", sln_time_new->get_pt_value(1.0, 2.0)); info("Coordinate ( 2.0, 2.0) value = %lf", sln_time_new->get_pt_value(2.0, 2.0)); bool success = true; if (fabs(sln_time_new->get_pt_value(-2.0, 2.0) - 9.999982) > 1E-6) success = false; if (fabs(sln_time_new->get_pt_value(-1.0, 2.0) - 10.000002) > 1E-6) success = false; if (fabs(sln_time_new->get_pt_value( 0.0, 2.0) - 9.999995) > 1E-6) success = false; if (fabs(sln_time_new->get_pt_value( 1.0, 2.0) - 10.000002) > 1E-6) success = false; if (fabs(sln_time_new->get_pt_value( 2.0, 2.0) - 9.999982) > 1E-6) success = false; if (success) { printf("Success!\n"); return ERR_SUCCESS; } else { printf("Failure!\n"); return ERR_FAILURE; } }
int main(int argc, char* argv[]) { // 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); // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Solutions for the time stepping and the Newton's method. Solution u_prev_time, u_prev_newton; // Adapt mesh to represent initial condition with given accuracy. int proj_norm = 1; // H1 norm. bool verbose0 = true; bool visualization = false; double err_stop_init_cond = 0.1 * ERR_STOP; adapt_to_exact_function(&space, init_cond, &selector, THRESHOLD, STRATEGY, MESH_REGULARITY, ERR_STOP, NDOF_STOP, proj_norm, verbose0, visualization, &u_prev_time); // Initialize views. ScalarView sview("Solution", 0, 0, 500, 350); sview.set_min_max_range(-9.5, 2.2); OrderView oview("Mesh", 510, 0, 500, 350); // Initialize the weak formulation. WeakForm wf; if (TIME_INTEGRATION == 1) { wf.add_matrix_form(jac_form_vol_euler, jac_form_vol_ord, H2D_UNSYM, H2D_ANY, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); wf.add_matrix_form_surf(jac_form_surf_1_euler, jac_form_surf_1_ord, BDY_1, &u_prev_newton); wf.add_matrix_form_surf(jac_form_surf_4_euler, jac_form_surf_4_ord, BDY_4, &u_prev_newton); wf.add_matrix_form_surf(jac_form_surf_6_euler, jac_form_surf_6_ord, BDY_6, &u_prev_newton); wf.add_vector_form(res_form_vol_euler, res_form_vol_ord, H2D_ANY, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); wf.add_vector_form_surf(res_form_surf_1_euler, res_form_surf_1_ord, BDY_1, &u_prev_newton); wf.add_vector_form_surf(res_form_surf_4_euler, res_form_surf_4_ord, BDY_4, &u_prev_newton); wf.add_vector_form_surf(res_form_surf_6_euler, res_form_surf_6_ord, BDY_6, &u_prev_newton); } else { wf.add_matrix_form(jac_form_vol_cranic, jac_form_vol_ord, H2D_UNSYM, H2D_ANY, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); wf.add_matrix_form_surf(jac_form_surf_1_cranic, jac_form_surf_1_ord, BDY_1, &u_prev_newton); wf.add_matrix_form_surf(jac_form_surf_4_cranic, jac_form_surf_4_ord, BDY_4, &u_prev_newton); wf.add_matrix_form_surf(jac_form_surf_6_cranic, jac_form_surf_6_ord, BDY_6, &u_prev_newton); wf.add_vector_form(res_form_vol_cranic, res_form_vol_ord, H2D_ANY, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); wf.add_vector_form_surf(res_form_surf_1_cranic, res_form_surf_1_ord, BDY_1, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); wf.add_vector_form_surf(res_form_surf_4_cranic, res_form_surf_4_ord, BDY_4, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); wf.add_vector_form_surf(res_form_surf_6_cranic, res_form_surf_6_ord, BDY_6, Tuple<MeshFunction*>(&u_prev_newton, &u_prev_time)); } // Initialize the nonlinear system. NonlinSystem nls(&wf, &space); // Error estimate and discrete problem size as a function of physical time. SimpleGraph graph_time_err_est, graph_time_dof_est; // Calculating initial vector for Newton. info("Projecting initial condition to obtain coefficient vector for Newton on coarse mesh."); nls.project_global(&u_prev_time, &u_prev_newton); // Initial vector calculated here. // Newton's loop (one time step) on the coarse mesh. info("Solving on coarse mesh."); bool verbose = true; // Default is false. if (!nls.solve_newton(&u_prev_newton, NEWTON_TOL_COARSE, NEWTON_MAX_ITER, verbose)) error("Newton's method did not converge."); // Store the result in sln_coarse. Solution sln_coarse, sln_fine; sln_coarse.copy(&u_prev_newton); // Time stepping loop. int num_time_steps = (int)(T_FINAL/TAU + 0.5); for(int ts = 1; ts <= num_time_steps; ts++) { // Update time-dependent Dirichlet BC values. if (TIME <= STARTUP_TIME) space.update_essential_bc_values(); // Periodic global derefinements. if (ts > 1 && ts % UNREF_FREQ == 0) { info("Global mesh derefinement."); 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); // Project fine mesh solution on the globally derefined mesh. info("---- Time step %d:", ts); info("Projecting fine mesh solution on globally derefined mesh for error calculation."); nls.project_global(&sln_fine, &u_prev_newton); // Store the result in sln_coarse. sln_coarse.copy(&u_prev_newton); } // Adaptivity loop (in space): bool done = false; double space_err_est; int as = 1; do { info("---- Time step %d, adaptivity step %d:", ts, as); // Initialize reference nonlinear system. RefSystem rnls(&nls); // Set initial condition for the Newton's method on the fine mesh. if (as == 1) { info("Projecting coarse mesh solution to obtain initial vector on new fine mesh."); rnls.project_global(&sln_coarse, &u_prev_newton); } else { info("Projecting previous fine mesh solution to obtain initial vector on new fine mesh."); rnls.project_global(&sln_fine, &u_prev_newton); } // Newton's method (one time step) on fine mesh info("Solving on fine mesh."); if (!rnls.solve_newton(&u_prev_newton, NEWTON_TOL_FINE, NEWTON_MAX_ITER, verbose)) error("Newton's method did not converge."); // Store the result in sln_fine. sln_fine.copy(&u_prev_newton); // Calculate error estimate wrt. fine mesh solution. info("Calculating error (est)."); H1Adapt hp(&nls); hp.set_solutions(&sln_coarse, &sln_fine); space_err_est = hp.calc_error() * 100; info("ndof_coarse: %d, ndof_fine: %d, space_err_est: %g%%", nls.get_num_dofs(), rnls.get_num_dofs(), space_err_est); // If space_err_est too large, adapt the mesh. if (space_err_est < ERR_STOP) done = true; else { info("Adapting coarse mesh."); done = hp.adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY); if (nls.get_num_dofs() >= NDOF_STOP) { done = true; break; } // Project the fine mesh solution on the new coarse mesh. info("Projecting fine mesh solution on coarse mesh for error calculation."); nls.project_global(&sln_fine, &u_prev_newton); // Store the result in sln_coarse. sln_coarse.copy(&u_prev_newton); as++; } } while (!done); // Show the new time level solution. char title[100]; sprintf(title, "Solution, t = %g", TIME); sview.set_title(title); sview.show(&sln_coarse); sprintf(title, "Mesh, t = %g", TIME); oview.set_title(title); oview.show(&space); /* //Write solution data into file. bool compress = false ; char* filenamecoarse = new char[100]; sprintf(filenamecoarse, "coarse_%g.dat", TIME); sln_coarse.save( filenamecoarse, compress ); //char* filenamefine = new char[100]; //sprintf(filenamefine, "fine_%g.dat", TIME); //sln_fine.save(filenamefine , compress ); //char* filefinemesh = new char[100]; //sprintf(filefinemesh, "mesh_%g.dat", TIME); //mesh.save( filefinemesh ) ; */ // Add entries to convergence graphs. graph_time_err_est.add_values(ts*TAU, space_err_est); graph_time_err_est.save("time_error_est.dat"); graph_time_dof_est.add_values(ts*TAU, nls.get_num_dofs()); graph_time_dof_est.save("time_dof_est.dat"); // Copy new time level solution into u_prev_time. u_prev_time.copy(&sln_fine); TIME += TAU; } // 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, DIR_BC_LEFT, DIR_BC_RIGHT, P_INIT, NEQ); int ndof = Space::get_num_dofs(space); info("ndof: %d", ndof); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(jacobian_vol); wf.add_vector_form(residual_vol); wf.add_vector_form_surf(0, 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(coeff_vec, 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[]) { // Load the mesh. Mesh mesh; H2DReader mloader; if (ALIGN_MESH) mloader.load("oven_load_circle.mesh", &mesh); else mloader.load("oven_load_square.mesh", &mesh); // 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(BDY_DIRICHLET); bc_types.add_bc_neumann(BDY_NEUMANN); // Enter Dirichlet boundary values. BCValues bc_values; bc_values.add_zero(BDY_DIRICHLET); // Create an Hcurl space. HcurlSpace space(&mesh, &bc_types, &bc_values, P_INIT); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(callback(bilinear_form)); wf.add_vector_form_surf(callback(linear_form_surf)); // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Initialize refinements selector. HcurlProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Initialize views. VectorView eview("Electric field", new WinGeom(0, 0, 580, 400)); OrderView oview("Polynomial orders", new WinGeom(590, 0, 550, 400)); // DOF and CPU convergence graphs initialization. SimpleGraph graph_dof, graph_cpu; // 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); // 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"); // 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); // Time measurement. cpu_time.tick(); // Show real part of the solution. AbsFilter abs(&sln); eview.set_min_max_range(0, 4e3); eview.show(&abs); oview.show(&space); // Skip visualization time. cpu_time.tick(HERMES_SKIP); // Calculate element errors and total error estimate. info("Calculating error estimate."); 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; // Report results. info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%", Space::get_num_dofs(&space), Space::get_num_dofs(ref_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(&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. eview.set_title("Fine mesh solution"); eview.show(&ref_sln); // Wait for all views to be closed. View::wait(); return 0; }
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 < 3) error("Not enough parameters"); HcurlShapesetLobattoHex shapeset; printf("* Loading mesh '%s'\n", argv[1]); Mesh mesh; Mesh3DReader mesh_loader; if (!mesh_loader.load(argv[1], &mesh)) error("Loading mesh file '%s'\n", argv[1]); printf("* Setting the space up\n"); HcurlSpace space(&mesh, &shapeset); space.set_bc_types(bc_types); int order; sscanf(argv[2], "%d", &order); int dir_x = order, dir_y = order, dir_z = order; order3_t o(dir_x, dir_y, dir_z); printf(" - Setting uniform order to (%d, %d, %d)\n", o.x, o.y ,o.z); space.set_uniform_order(o); 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; PardisoSolver 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_t, ord_t>, SYM); wf.add_matrix_form_surf(bilinear_form_surf<double, scalar>, bilinear_form_surf<ord_t, ord_t>); wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>); wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<ord_t, ord_t>); LinearProblem lp(&wf, &space); // assemble stiffness matrix Timer assemble_timer("Assembling stiffness matrix"); assemble_timer.start(); lp.assemble(&mat, &rhs); assemble_timer.stop(); // solve the stiffness matrix Timer solve_timer("Solving stiffness matrix"); solve_timer.start(); bool solved = solver.solve(); solve_timer.stop(); //#ifdef OUTPUT_DIR mat.dump(stdout, "a"); rhs.dump(stdout, "b"); //#endif if (solved) { scalar *s = solver.get_solution(); Solution sln(&mesh); sln.set_coeff_vector(&space, s); printf("* Solution:\n"); for (int i = 1; i <= ndofs; i++) { printf(" x[% 3d] = " SCALAR_FMT "\n", i, SCALAR(s[i])); } // output the measured values printf("%s: %s (%lf secs)\n", assemble_timer.get_name(), assemble_timer.get_human_time(), assemble_timer.get_seconds()); printf("%s: %s (%lf secs)\n", solve_timer.get_name(), solve_timer.get_human_time(), solve_timer.get_seconds()); // norm ExactSolution ex_sln(&mesh, exact_solution); double hcurl_sln_norm = hcurl_norm(&sln); double hcurl_err_norm = hcurl_error(&sln, &ex_sln); printf(" - Hcurl solution norm: % le\n", hcurl_sln_norm); printf(" - Hcurl error norm: % le\n", hcurl_err_norm); double l2_sln_norm = l2_norm_hcurl(&sln); double l2_err_norm = l2_error_hcurl(&sln, &ex_sln); printf(" - L2 solution norm: % le\n", l2_sln_norm); printf(" - L2 error norm: % le\n", l2_err_norm); if (hcurl_err_norm > EPS || l2_err_norm > EPS) { // calculated solution is not enough precise res = ERR_FAILURE; } #if 0 //def OUTPUT_DIR // output printf("starting output\n"); const char *of_name = OUTPUT_DIR "/solution.vtk"; FILE *ofile = fopen(of_name, "w"); if (ofile != NULL) { ExactSolution ex_sln(&mesh, exact_solution_0, exact_solution_1, exact_solution_2); RealPartFilter real_sln(&mesh, &sln, FN_VAL); ImagPartFilter imag_sln(&mesh, &sln, FN_VAL); DiffFilter eh(&mesh, &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); VtkOutputEngine output(ofile); output.out(&real_sln, "real_Uh", FN_VAL); output.out(&imag_sln, "imag_Uh", FN_VAL); output.out(&real_sln, "real_Uh_0", FN_VAL_0); output.out(&real_sln, "real_Uh_1", FN_VAL_1); output.out(&real_sln, "real_Uh_2", FN_VAL_2); output.out(&imag_sln, "imag_Uh_0", FN_VAL_0); output.out(&imag_sln, "imag_Uh_1", FN_VAL_1); output.out(&imag_sln, "imag_Uh_2", FN_VAL_2); fclose(ofile); } else { warning("Can not open '%s' for writing.", of_name); } #endif } #ifdef WITH_PETSC mat.free(); rhs.free(); PetscFinalize(); #endif return res; }
int main(int argc, char* argv[]) { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // 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(); // 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); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(bilinear_form, bilinear_form_ord, HERMES_SYM); wf.add_vector_form(linear_form, linear_form_ord); wf.add_vector_form_surf(linear_form_surf, linear_form_surf_ord, BDY_VERTICAL); // Initialize the FE problem. bool is_linear = true; DiscreteProblem dp(&wf, &space, is_linear); initialize_solution_environment(matrix_solver, argc, argv); SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); 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; finalize_solution_environment(matrix_solver); // View the solution and mesh. ScalarView sview("Solution", new WinGeom(0, 0, 440, 350)); sview.show(&sln); OrderView oview("Polynomial orders", new WinGeom(450, 0, 400, 350)); oview.show(&space); // Skip visualization time. cpu_time.tick(HERMES_SKIP); // Print timing information. 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); // 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); // Initialize views. ScalarView Tview("Temperature", new WinGeom(0, 0, 450, 600)); char title[100]; sprintf(title, "Time %3.5f, exterior temperature %3.5f", TIME, temp_ext(TIME)); Tview.set_min_max_range(0,20); Tview.set_title(title); Tview.fix_scale_width(3); // 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); // Update the time variable. TIME += TAU; // Visualize the solution. sprintf(title, "Time %3.2f, exterior temperature %3.5f", TIME, temp_ext(TIME)); Tview.set_title(title); Tview.show(&tsln); } // 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 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[]) { // Load the mesh. Mesh mesh; H2DReader mloader; if (ALIGN_MESH) mloader.load("oven_load_circle.mesh", &mesh); else mloader.load("oven_load_square.mesh", &mesh); // Perform initial mesh refinemets. for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(); // Create an Hcurl space. HcurlSpace space(&mesh, bc_types, essential_bc_values, P_INIT); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(callback(bilinear_form)); wf.add_vector_form_surf(callback(linear_form_surf)); // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Initialize refinements selector. HcurlProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // DOF and CPU convergence graphs initialization. SimpleGraph graph_dof, graph_cpu; // 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); // 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"); // 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); // Time measurement. cpu_time.tick(); // Calculate element errors and total error estimate. info("Calculating error estimate."); 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; // Report results. info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%", Space::get_num_dofs(&space), Space::get_num_dofs(ref_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(&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); int n_dof_allowed = 1300; printf("n_dof_actual = %d\n", ndof); printf("n_dof_allowed = %d\n", n_dof_allowed); if (ndof <= n_dof_allowed) { printf("Success!\n"); return ERR_SUCCESS; } else { printf("Failure!\n"); return ERR_FAILURE; } }
int main(int argc, char **args) { // Test variable. int success_test = 1; 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; } } 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); for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_dirichlet(BDY_HORIZONTAL); bc_types.add_bc_neumann(BDY_VERTICAL); BCValues bc_values; bc_values.add_function(BDY_HORIZONTAL, essential_bc_values); // 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(bilinear_form, bilinear_form_ord, HERMES_SYM); wf.add_vector_form(linear_form, linear_form_ord); wf.add_vector_form_surf(linear_form_surf, linear_form_surf_ord, BDY_VERTICAL); // 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 - 1.72173) > 1e-2) success = 0; if (p_init == 2 && fabs(sum - 0.639908) > 1e-2) success = 0; if (p_init == 3 && fabs(sum - 0.826367) > 1e-2) success = 0; if (p_init == 4 && fabs(sum - 0.629395) > 1e-2) success = 0; if (p_init == 5 && fabs(sum - 0.574235) > 1e-2) success = 0; if (p_init == 6 && fabs(sum - 0.62792) > 1e-2) success = 0; if (p_init == 7 && fabs(sum - 0.701982) > 1e-2) success = 0; if (p_init == 8 && fabs(sum - 0.7982) > 1e-2) success = 0; if (p_init == 9 && fabs(sum - 0.895069) > 1e-2) success = 0; if (p_init == 10 && fabs(sum - 1.03031) > 1e-2) success = 0; } if (success == 1) { printf("Success!\n"); return ERR_SUCCESS; } else { printf("Failure!\n"); return ERR_FAILURE; } }
int main() { // Three macroelements are defined above via the interfaces[] array. // poly_orders[]... initial poly degrees of macroelements. // material_markers[]... material markers of macroelements. // subdivisions[]... equidistant subdivision of macroelements. int poly_orders[N_MAT] = {P_init_inner, P_init_outer, P_init_reflector }; int material_markers[N_MAT] = {Marker_inner, Marker_outer, Marker_reflector }; int subdivisions[N_MAT] = {N_subdiv_inner, N_subdiv_outer, N_subdiv_reflector }; // Create space. Space* space = new Space(N_MAT, interfaces, poly_orders, material_markers, subdivisions, N_GRP, N_SLN); // Enumerate basis functions, info for user. info("N_dof = %d", Space::get_num_dofs(space)); // Initial approximation: u = 1. double K_EFF_old; double init_val = 1.0; set_vertex_dofs_constant(space, init_val, 0); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(jacobian_vol_inner, NULL, Marker_inner); wf.add_matrix_form(jacobian_vol_outer, NULL, Marker_outer); wf.add_matrix_form(jacobian_vol_reflector, NULL, Marker_reflector); wf.add_vector_form(residual_vol_inner, NULL, Marker_inner); wf.add_vector_form(residual_vol_outer, NULL, Marker_outer); wf.add_vector_form(residual_vol_reflector, NULL, Marker_reflector); 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); // Source iteration (power method). for (int i = 0; i < Max_SI; i++) { // Obtain fission source. int current_solution = 0, previous_solution = 1; copy_dofs(current_solution, previous_solution, space); // Obtain the number of degrees of freedom. int ndof = Space::get_num_dofs(space); // Fill vector coeff_vec using dof and coeffs arrays in elements. double *coeff_vec = new double[Space::get_num_dofs(space)]; solution_to_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_norm = 0; for(int i=0; i<ndof; i++) res_norm += rhs->get(i)*rhs->get(i); res_norm = sqrt(res_norm); // Info for user. info("---- Newton iter %d, residual norm: %.15f", it, res_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_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. vector_to_solution(coeff_vec, space); it++; } // Cleanup. delete matrix; delete rhs; delete solver; delete [] coeff_vec; // Update the eigenvalue. K_EFF_old = K_EFF; K_EFF = calc_fission_yield(space); info("K_EFF_%d = %f", i, K_EFF); if (fabs(K_EFF - K_EFF_old)/K_EFF < TOL_SI) break; } // Plot the critical (i.e. steady-state) neutron flux. Linearizer l(space); l.plot_solution("solution.gp"); // Normalize so that the absolute neutron flux generates 320 Watts of energy // (note that, using the symmetry condition at the origin, we've solved for // flux only in the right half of the reactor). normalize_to_power(space, 320/2.); // Plot the solution and space. l.plot_solution("solution_320W.gp"); space->plot("space.gp"); info("K_EFF = %f", K_EFF); info("Done."); return 1; }
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("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_vol)); wf.add_vector_form(callback(stac_residual_vol)); wf.add_matrix_form_surf(callback(stac_jacobian_surf), BDY_AIR); wf.add_vector_form_surf(callback(stac_residual_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 = new ButcherTable(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()); // Turn off adaptive time stepping if R-K method is not embedded. if (bt->is_embedded() == false && ADAPTIVE_TIME_STEP_ON == true) { warn("R-K method not embedded, turning off adaptive time stepping."); ADAPTIVE_TIME_STEP_ON = false; } // Load the mesh. Mesh mesh, basemesh; H2DReader mloader; mloader.load("wall.mesh", &basemesh); // Perform initial mesh refinements. for(int i = 0; i < INIT_REF_NUM; i++) basemesh.refine_all_elements(); basemesh.refine_towards_boundary(BDY_BOTTOM, INIT_REF_NUM_BDY); mesh.copy(&basemesh); // 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); // Convert initial condition into a Solution. Solution* sln_prev_time = new Solution(&mesh, TEMP_INIT); // Initialize weak formulation. WeakForm wf; wf.add_matrix_form(stac_jacobian_vol, stac_jacobian_vol_ord, HERMES_NONSYM, HERMES_ANY, sln_prev_time); wf.add_vector_form(stac_residual_vol, stac_residual_vol_ord, HERMES_ANY, sln_prev_time); wf.add_matrix_form_surf(stac_jacobian_bottom, stac_jacobian_bottom_ord, BDY_BOTTOM, sln_prev_time); wf.add_vector_form_surf(stac_residual_bottom, stac_residual_bottom_ord, BDY_BOTTOM, sln_prev_time); wf.add_matrix_form_surf(stac_jacobian_top, stac_jacobian_top_ord, BDY_TOP, sln_prev_time); wf.add_vector_form_surf(stac_residual_top, stac_residual_top_ord, BDY_TOP, sln_prev_time); // Initialize the FE problem. bool is_linear = true; DiscreteProblem dp(&wf, &space, is_linear); // Create a refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Visualize initial condition. char title[100]; ScalarView sln_view("Initial condition", new WinGeom(0, 0, 1500, 360)); OrderView ordview("Initial mesh", new WinGeom(0, 410, 1500, 360)); ScalarView time_error_view("Temporal error", new WinGeom(0, 800, 1500, 360)); time_error_view.fix_scale_width(40); ScalarView space_error_view("Spatial error", new WinGeom(0, 1220, 1500, 360)); space_error_view.fix_scale_width(40); sln_view.show(sln_prev_time, HERMES_EPS_VERYHIGH); ordview.show(&space); // Graph for time step history. SimpleGraph time_step_graph; if (ADAPTIVE_TIME_STEP_ON) info("Time step history will be saved to file time_step_history.dat."); // Time stepping loop: double current_time = 0; int ts = 1; do { info("Begin time step %d.", ts); // Periodic global derefinement. if (ts > 1 && ts % UNREF_FREQ == 0) { info("Global mesh derefinement."); if (UNREF_LEVEL == 1) mesh.unrefine_all_elements(); else mesh.copy(&basemesh); space.set_uniform_order(P_INIT); ndof = Space::get_num_dofs(&space); } // Spatial adaptivity loop. Note: sln_prev_time must not be // changed during spatial adaptivity. Solution ref_sln; Solution* time_error_fn; if (bt->is_embedded() == true) time_error_fn = new Solution(&mesh); else time_error_fn = NULL; bool done = false; int as = 1; double err_est; do { // Construct globally refined reference mesh and setup reference space. Space* ref_space = construct_refined_space(&space); // Initialize discrete problem on reference mesh. DiscreteProblem* ref_dp = new DiscreteProblem(&wf, ref_space); // Runge-Kutta step on the fine mesh. info("Runge-Kutta time step on fine mesh (t = %g s, tau = %g s, stages: %d).", current_time, time_step, bt->get_size()); bool verbose = true; bool is_linear = false; if (!rk_time_step(current_time, time_step, bt, sln_prev_time, &ref_sln, time_error_fn, ref_dp, matrix_solver, verbose, is_linear, NEWTON_TOL_FINE, NEWTON_MAX_ITER)) { error("Runge-Kutta time step failed, try to decrease time step size."); } /* If ADAPTIVE_TIME_STEP_ON == true, estimate temporal error. If too large or too small, then adjust it and restart the time step. */ double rel_err_time; if (bt->is_embedded() == true) { info("Calculating temporal error estimate."); // Show temporal error. char title[100]; sprintf(title, "Temporal error est, spatial adaptivity step %d", as); time_error_view.set_title(title); time_error_view.show_mesh(false); time_error_view.show(time_error_fn, HERMES_EPS_VERYHIGH); rel_err_time = calc_norm(time_error_fn, HERMES_H1_NORM) / calc_norm(&ref_sln, HERMES_H1_NORM) * 100; if (ADAPTIVE_TIME_STEP_ON == false) info("rel_err_time: %g%%", rel_err_time); } if (ADAPTIVE_TIME_STEP_ON) { if (rel_err_time > TIME_ERR_TOL_UPPER) { info("rel_err_time %g%% is above upper limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER); info("Decreasing tau from %g to %g s and restarting time step.", time_step, time_step * TIME_STEP_DEC_RATIO); time_step *= TIME_STEP_DEC_RATIO; delete ref_space; delete ref_dp; continue; } else if (rel_err_time < TIME_ERR_TOL_LOWER) { info("rel_err_time = %g%% is below lower limit %g%%", rel_err_time, TIME_ERR_TOL_UPPER); info("Increasing tau from %g to %g s.", time_step, time_step * TIME_STEP_INC_RATIO); time_step *= TIME_STEP_INC_RATIO; } else { info("rel_err_time = %g%% is in acceptable interval (%g%%, %g%%)", rel_err_time, TIME_ERR_TOL_LOWER, TIME_ERR_TOL_UPPER); } // Add entry to time step history graph. time_step_graph.add_values(current_time, time_step); time_step_graph.save("time_step_history.dat"); } /* Estimate spatial errors and perform mesh refinement */ info("Spatial adaptivity step %d.", as); // Project the fine mesh solution onto the coarse mesh. Solution sln; info("Projecting fine mesh solution on coarse mesh for error estimation."); OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver); // Show spatial error. sprintf(title, "Spatial error est, spatial adaptivity step %d", as); DiffFilter* space_error_fn = new DiffFilter(Hermes::vector<MeshFunction*>(&ref_sln, &sln)); space_error_view.set_title(title); space_error_view.show_mesh(false); AbsFilter abs_sef(space_error_fn); space_error_view.show(&abs_sef, HERMES_EPS_VERYHIGH); // Calculate element errors and spatial error estimate. info("Calculating spatial error estimate."); Adapt* adaptivity = new Adapt(&space); double err_rel_space = adaptivity->calc_err_est(&sln, &ref_sln) * 100; // Report results. info("ndof: %d, ref_ndof: %d, err_rel_space: %g%%", Space::get_num_dofs(&space), Space::get_num_dofs(ref_space), err_rel_space); // If err_est too large, adapt the mesh. if (err_rel_space < SPACE_ERR_TOL) done = true; else { info("Adapting the coarse mesh."); done = adaptivity->adapt(&selector, THRESHOLD, STRATEGY, MESH_REGULARITY); if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true; else // Increase the counter of performed adaptivity steps. as++; } // Clean up. delete adaptivity; delete ref_space; delete ref_dp; delete space_error_fn; } while (done == false); // Clean up. if (time_error_fn != NULL) delete time_error_fn; // Visualize the solution and mesh. char title[100]; sprintf(title, "Solution, time %g s", current_time); sln_view.set_title(title); sln_view.show_mesh(false); sln_view.show(&ref_sln, HERMES_EPS_VERYHIGH); sprintf(title, "Mesh, time %g s", current_time); ordview.set_title(title); ordview.show(&space); // Copy last reference solution into sln_prev_time. sln_prev_time->copy(&ref_sln); // Increase current time and counter of time steps. current_time += time_step; ts++; } while (current_time < T_FINAL); // Clean up. delete sln_prev_time; delete bt; // 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("domain.mesh", &mesh); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_dirichlet(BDY_BOTTOM); bc_types.add_bc_neumann(Hermes::Tuple<int>(BDY_TOP_NE, BDY_TOP_NW)); bc_types.add_bc_neumann(Hermes::Tuple<std::string>(BDY_VERTICAL_SE, BDY_VERTICAL_NE, BDY_VERTICAL_NW, BDY_VERTICAL_SW)); // Enter Dirichlet boundary values. BCValues bc_values; bc_values.add_zero(BDY_BOTTOM); // Create an H1 space with default shapeset. H1Space space(&mesh, &bc_types, &bc_values, P_INIT); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(callback(bilinear_form_vol_SE), HERMES_UNSYM, SOUTH_EAST); wf.add_matrix_form(callback(bilinear_form_vol_NE), HERMES_UNSYM, NORTH_EAST); wf.add_matrix_form(callback(bilinear_form_vol_NW), HERMES_UNSYM, NORTH_WEST); wf.add_matrix_form(callback(bilinear_form_vol_SW), HERMES_UNSYM, SOUTH_WEST); wf.add_vector_form(callback(linear_form_vol)); wf.add_vector_form_surf(callback(linear_form_surf_VERTICAL_SE), BDY_VERTICAL_SE); wf.add_vector_form_surf(callback(linear_form_surf_VERTICAL_NE), BDY_VERTICAL_NE); wf.add_vector_form_surf(callback(linear_form_surf_VERTICAL_NW), BDY_VERTICAL_NW); wf.add_vector_form_surf(callback(linear_form_surf_VERTICAL_SW), BDY_VERTICAL_SW); wf.add_vector_form_surf(callback(linear_form_surf_TOP_NE), BDY_TOP_NE); wf.add_vector_form_surf(callback(linear_form_surf_TOP_NW), BDY_TOP_NW); // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // DOF and CPU convergence graphs. SimpleGraph graph_dof, graph_cpu; // 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); // 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. Solution ref_sln; 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. Solution sln; info("Projecting reference solution on the coarse mesh."); OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver); // Calculate element errors and total error estimate. info("Calculating error estimate."); 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, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_REL) * 100; // Report results. info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%", Space::get_num_dofs(&space), Space::get_num_dofs(ref_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(&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", 210); printf("ndof actual = %d\n", ndof); if (ndof < 210) { // ndofs was 208 at the time this test was created printf("Success!\n"); return ERR_SUCCESS; } else { printf("Failure!\n"); return ERR_FAILURE; } }
int main(int argc, char* argv[]) { // 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 = 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, u_prev_time; // Adapt mesh to represent initial condition with given accuracy. int proj_norm = 1; // H1 norm. bool verbose = false; double err_stop_init_cond = 0.1 * ERR_STOP; adapt_to_exact_function(&space, proj_norm, init_cond, &selector, THRESHOLD, STRATEGY, MESH_REGULARITY, ERR_STOP, NDOF_STOP, verbose, &u_prev_time); // Assign initial condition to mesh. u_prev_time.set_exact(&mesh, init_cond); Vector *coeff_vec = new AVector(ndof); // Calculating initial vector for Newton. info("Projecting initial condition to obtain coefficient vector for Newton on coarse mesh."); project_global(&space, H2D_H1_NORM, &u_prev_time, &u_prev_time, coeff_vec); // Initialize the weak formulation. WeakForm wf; if (TIME_INTEGRATION == 1) { wf.add_matrix_form(jac_form_vol_euler, jac_form_vol_ord, H2D_UNSYM, H2D_ANY, Tuple<MeshFunction*>(&u_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, H2D_ANY, Tuple<MeshFunction*>(&u_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, H2D_UNSYM, H2D_ANY, Tuple<MeshFunction*>(&u_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, H2D_ANY, Tuple<MeshFunction*>(&u_prev_time)); wf.add_vector_form_surf(res_form_surf_1_cranic, res_form_surf_1_ord, BDY_1, Tuple<MeshFunction*>( &u_prev_time)); wf.add_vector_form_surf(res_form_surf_4_cranic, res_form_surf_4_ord, BDY_4, Tuple<MeshFunction*>(&u_prev_time)); wf.add_vector_form_surf(res_form_surf_6_cranic, res_form_surf_6_ord, BDY_6, Tuple<MeshFunction*>(&u_prev_time)); } // Initialize adaptivity parameters. AdaptivityParamType apt(ERR_STOP, NDOF_STOP, THRESHOLD, STRATEGY, MESH_REGULARITY); // Time stepping loop. int num_time_steps = (int)(T_FINAL/TAU + 0.5); for(int ts = 1; ts <= num_time_steps; ts++) { 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); } // Update the coefficient vector and u_prev_time. info("Projecting to obtain coefficient vector on coarse mesh."); project_global(&space, H2D_H1_NORM, &u_prev_time, &u_prev_time, coeff_vec); bool verbose = false; // Print info during adaptivity. info("Projecting coarse mesh solution to obtain initial vector on new fine mesh."); // The NULL pointers mean that we are not interested in visualization during the Newton's loop. solve_newton_adapt(&space, &wf, coeff_vec, matrix_solver, H2D_H1_NORM, &sln, &ref_sln, Tuple<WinGeom *>(), Tuple<WinGeom *>(), &selector, &apt, NEWTON_TOL_COARSE, NEWTON_TOL_FINE, NEWTON_MAX_ITER, verbose); // Copy new time level reference solution into u_prev_time. u_prev_time.set_coeff_vector(&space, coeff_vec); } // Waiting for test. }
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[]) { // 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)); wf.add_matrix_form_surf(callback(bilinear_form_surf), BDY_BOTTOM); wf.add_vector_form_surf(callback(linear_form_surf), BDY_BOTTOM); // 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."); 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"); // Visualize the solution. ScalarView view("Solution", new WinGeom(0, 0, 440, 350)); view.show(&sln); // Compute and show gradient magnitude. // (Note that the gradient at the re-entrant // corner needs to be truncated for visualization purposes.) ScalarView gradview("Gradient", new WinGeom(450, 0, 400, 350)); MagFilter grad(Hermes::vector<MeshFunction *>(&sln, &sln), Hermes::vector<int>(H2D_FN_DX, H2D_FN_DY)); gradview.show(&grad); // Wait for all views to be closed. View::wait(); // Clean up. delete solver; delete matrix; delete rhs; 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); // 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[]) { // 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::Tuple<int>(BDY_1, BDY_6)); bc_types.add_bc_newton(Hermes::Tuple<int>(BDY_2, BDY_3, BDY_4, BDY_5)); // Enter Dirichlet boundary values. BCValues bc_values; bc_values.add_zero(Hermes::Tuple<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); // 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); // 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()); 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* 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(2, 5); // Initialize an H1 space. H1Space space(&mesh, bc_types, essential_bc_values, P_INIT); // 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>, marker_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>, marker_air); // Initialize linear system. LinSystem ls(&wf, &space); // time stepping int nsteps = (int)(FINAL_TIME/TAU + 0.5); bool rhsonly = false; for(int n = 1; n <= nsteps; n++) { info("---- Time step %d, time %3.5f, ext_temp %g", ts, TIME, temp_ext(TIME)); // Assemble and solve. ls.assemble(rhsonly); rhsonly = true; ls.solve(&tsln); // Update the time variable. TIME += TAU; } scalar *sol_vector; int n_dof; ls.get_solution_vector(sol_vector, n_dof); printf("n_dof = %d\n", n_dof); double sum = 0; for (int i=0; i < n_dof; i++) sum += sol_vector[i]; printf("coefficient sum = %g\n", sum); // Actual test. The value of 'sum' depend on the // current shapeset. If you change the shapeset, // you need to correct this number. int success = 1; if (fabs(sum - 8508.36) > 1e-1) success = 0; #define ERROR_SUCCESS 0 #define ERROR_FAILURE -1 if (success == 1) { printf("Success!\n"); return ERROR_SUCCESS; } else { printf("Failure!\n"); return ERROR_FAILURE; } }
int main(int argc, char **args) { // Test variable. int success_test = 1; if (argc < 2) 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. int mx = 2; Ord3 order(mx, mx, mx); H1Space space(&mesh, bc_types, NULL, order); #if defined LIN_DIRICHLET || defined NLN_DIRICHLET space.set_essential_bc_values(essential_bc_values); #endif // Initialize the weak formulation. WeakForm wf; wf.add_vector_form(form_0<double, scalar>, form_0<Ord, Ord>); #if defined LIN_NEUMANN || defined LIN_NEWTON wf.add_vector_form_surf(form_0_surf<double, scalar>, form_0_surf<Ord, Ord>); #endif #if defined LIN_DIRICHLET || defined NLN_DIRICHLET // preconditioner wf.add_matrix_form(precond_0_0<double, scalar>, precond_0_0<Ord, Ord>, HERMES_SYM); #endif // Initialize the FE problem. DiscreteProblem fep(&wf, &space); #if defined LIN_DIRICHLET || defined NLN_DIRICHLET // use ML preconditioner to speed-up things MlPrecond pc("sa"); pc.set_param("max levels", 6); pc.set_param("increasing or decreasing", "decreasing"); pc.set_param("aggregation: type", "MIS"); pc.set_param("coarse: type", "Amesos-KLU"); #endif NoxSolver solver(&fep); #if defined LIN_DIRICHLET || defined NLN_DIRICHLET // solver.set_precond(&pc); #endif info("Solving."); Solution sln(&mesh); if(solver.solve()) Solution::vector_to_solution(solver.get_solution(), &space, &sln); else error ("Matrix solver failed.\n"); Solution ex_sln(&mesh); ex_sln.set_exact(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; 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 set_verbose(false); TRACE_START("trace.txt"); DEBUG_OUTPUT_ON; SET_VERBOSE_LEVEL(0); 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; Mesh3DReader mloader; if (!mloader.load(args[1], &mesh)) error("Loading mesh file '%s'\n", args[1]); H1ShapesetLobattoHex shapeset; printf("* Setting the space up\n"); H1Space space(&mesh, &shapeset); space.set_bc_types(bc_types); int mx = maxn(4, m, n, o, 4); order3_t order(mx, mx, mx); // order3_t order(1, 1, 1); // order3_t order(m, n, o); printf(" - Setting uniform order to (%d, %d, %d)\n", mx, mx, mx); space.set_uniform_order(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_t, ord_t>, SYM); wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>); wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<ord_t, ord_t>); LinearProblem lp(&wf, &space); // assemble stiffness matrix printf(" - assembling...\n"); fflush(stdout); Timer assemble_timer; assemble_timer.start(); lp.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]); // } 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; } #if 0 //def 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 TRACE_END; return res; }
int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("domain.mesh", &mesh); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_dirichlet(BDY_BOTTOM); bc_types.add_bc_neumann(Hermes::Tuple<int>(BDY_RIGHT, BDY_TOP, BDY_LEFT)); // Enter Dirichlet boudnary values. BCValues bc_values; bc_values.add_zero(BDY_BOTTOM); // Create an H1 space with default shapeset. H1Space 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_vector_form(callback(linear_form)); wf.add_vector_form_surf(callback(linear_form_surf), BDY_TOP); // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Set exact solution. ExactSolution exact(&mesh, fndd); // Initialize views. ScalarView sview("Solution", new WinGeom(0, 0, 440, 350)); sview.show_mesh(false); OrderView oview("Polynomial orders", new WinGeom(450, 0, 400, 350)); // DOF and CPU convergence graphs. SimpleGraph graph_dof, graph_cpu, graph_dof_exact, graph_cpu_exact; // 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); // 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. Solution ref_sln; 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. Solution sln; info("Projecting reference solution on coarse mesh."); OGProjection::project_global(&space, &ref_sln, &sln, matrix_solver); // View the coarse mesh solution and polynomial orders. sview.show(&sln); oview.show(&space); // 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, 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, &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.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"); 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 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()); // Wait for all views to be closed. View::wait(); }
int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("square_quad.mesh", &mesh); // Perform initial mesh refinement. for (int i=0; i<INIT_REF_NUM; i++) mesh.refine_all_elements(); mesh.refine_towards_boundary(BOUNDARY_LAYER, INIT_BDY_REF_NUM); //mesh.refine_towards_boundary(NONZERO_DIRICHLET, INIT_BDY_REF_NUM/2); // Create a space and refinement selector appropriate for the selected discretization method. Space *space; ProjBasedSelector *selector; ProjNormType norm; if (method != DG) { space = new H1Space(&mesh, bc_types, essential_bc_values, P_INIT); selector = new L2ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); norm = HERMES_L2_NORM; // WARNING: In order to compare the errors with DG, L2 norm should be here. } else { space = new L2Space(&mesh, bc_types, NULL, Ord2(P_INIT)); selector = new L2ProjBasedSelector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); norm = HERMES_L2_NORM; // Disable weighting of refinement candidates. selector->set_error_weights(1, 1, 1); } // Initialize the weak formulation. info("Discretization method: %s", method_names[method].c_str()); if (method != CG && method != DG) { if (STRATEGY > -1 && CAND_LIST != H2D_H_ISO && CAND_LIST != H2D_H_ANISO) error("The %s method may be used only with h-refinement.", method_names[method].c_str()); int eff_order = (STRATEGY == -1) ? P_INIT : P_INIT + ORDER_INCREASE; if (method != CG_STAB_GLS) { if (eff_order > 1) error("The %s method may be used only with at most 1st order elements.", method_names[method].c_str()); } else { if (eff_order > 2) error("The %s method may be used only with at most 2nd order elements.", method_names[method].c_str()); } } WeakForm wf; switch(method) { case CG: wf.add_matrix_form(callback(cg_biform)); break; case CG_STAB_SUPG: wf.add_matrix_form(callback(cg_biform)); wf.add_matrix_form(callback(stabilization_biform_supg)); break; case CG_STAB_GLS: wf.add_matrix_form(callback(cg_biform)); wf.add_matrix_form(callback(stabilization_biform_gls)); break; case CG_STAB_SGS: wf.add_matrix_form(callback(cg_biform)); wf.add_matrix_form(callback(stabilization_biform_sgs)); break; case CG_STAB_SGS_ALT: wf.add_matrix_form(callback(cg_biform)); wf.add_matrix_form(callback(stabilization_biform_sgs_alt)); break; case DG: wf.add_matrix_form(callback(dg_volumetric_biform_advection)); wf.add_matrix_form(callback(dg_volumetric_biform_diffusion)); wf.add_matrix_form_surf(callback(dg_interface_biform_advection), H2D_DG_INNER_EDGE); wf.add_matrix_form_surf(callback(dg_interface_biform_diffusion), H2D_DG_INNER_EDGE); wf.add_matrix_form_surf(callback(dg_boundary_biform_advection)); wf.add_matrix_form_surf(callback(dg_boundary_biform_diffusion)); wf.add_vector_form_surf(callback(dg_boundary_liform_advection)); wf.add_vector_form_surf(callback(dg_boundary_liform_diffusion)); break; } // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Set exact solution. ExactSolution exact(&mesh, exact_sln); // Initialize views. ScalarView sview("Solution", new WinGeom(0, 0, 440, 350)); sview.fix_scale_width(50); sview.show_mesh(false); OrderView oview("Polynomial orders", new WinGeom(450, 0, 400, 350)); // DOF and CPU convergence graphs initialization. SimpleGraph graph_dof, graph_cpu, graph_dof_exact, graph_cpu_exact; // 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); // Adaptivity loop: int as = 1; bool done = false; Space* actual_sln_space; do { info("---- Adaptivity step %d:", as); if (STRATEGY == -1) actual_sln_space = space; else // Construct globally refined reference mesh and setup reference space. actual_sln_space = Space::construct_refined_space(space, ORDER_INCREASE); // Assemble the reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, actual_sln_space, is_linear); dp->assemble(matrix, rhs); // Solve the linear system of the reference problem. // If successful, obtain the solution. if(solver->solve()) Solution::vector_to_solution(solver->get_solution(), actual_sln_space, &ref_sln); else error ("Matrix solver failed.\n"); // Instantiate adaptivity and error calculation driver. Space is used only for adaptivity, it is ignored when // STRATEGY == -1 and only the exact error is calculated by this object. Adapt* adaptivity = new Adapt(space, norm); // Calculate exact error. bool solutions_for_adapt = false; double err_exact_rel = calc_rel_error(&sln, &exact, HERMES_H1_NORM) * 100; info("ndof_fine: %d, err_exact_rel: %g%%", Space::get_num_dofs(actual_sln_space), err_exact_rel); // Time measurement. cpu_time.tick(); // View the fine mesh solution and polynomial orders. sview.show(&ref_sln); oview.show(actual_sln_space); // Skip visualization time. cpu_time.tick(HERMES_SKIP); if (STRATEGY == -1) done = true; // Do not adapt. else { // 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, norm); // Calculate element errors and total error estimate. info("Calculating error estimate."); 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; // Report results. info("ndof_coarse: %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"); 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"); // Skip graphing time. cpu_time.tick(HERMES_SKIP); // If err_est too large, adapt the mesh. if (err_exact_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; if(done == false) { delete actual_sln_space->get_mesh(); delete actual_sln_space; } } // Clean up. delete adaptivity; delete dp; } while (done == false); if (space != actual_sln_space) { delete space; delete actual_sln_space->get_mesh(); } delete actual_sln_space; delete solver; delete matrix; delete rhs; delete selector; 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 **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 = 4; sscanf(args[2], "%d", &o); H1Space space(&mesh, bc_types, NULL, o); // Initialize the weak formulation. WeakForm wf; 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>); // 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(&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; // Clean up. delete matrix; delete rhs; delete solver; delete adaptivity; 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("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; }