int main() { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Create space, set Dirichlet BC, enumerate basis functions. Space* space = new Space(A, B, NELEM, DIR_BC_LEFT, DIR_BC_RIGHT, P_INIT, NEQ, NEQ); // Enumerate basis functions, info for user. int ndof = Space::get_num_dofs(space); info("ndof: %d", ndof); // Initialize the weak formulation. WeakForm wf(2); wf.add_matrix_form(0, 0, jacobian_0_0); wf.add_matrix_form(0, 1, jacobian_0_1); wf.add_matrix_form(1, 0, jacobian_1_0); wf.add_matrix_form(1, 1, jacobian_1_1); wf.add_vector_form(0, residual_0); wf.add_vector_form(1, residual_1); // 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; bool success = false; 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(!(success = 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++; } info("Total running time: %g s", cpu_time.accumulated()); // Test variable. info("ndof = %d.", Space::get_num_dofs(space)); // Cleanup. for(unsigned i = 0; i < DIR_BC_LEFT.size(); i++) delete DIR_BC_LEFT[i]; DIR_BC_LEFT.clear(); for(unsigned i = 0; i < DIR_BC_RIGHT.size(); i++) delete DIR_BC_RIGHT[i]; DIR_BC_RIGHT.clear(); delete matrix; delete rhs; delete solver; delete[] coeff_vec; delete dp; delete space; if (success) { info("Success!"); return ERROR_SUCCESS; } else { info("Failure!"); return ERROR_FAILURE; } }
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(); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_dirichlet(BDY_DIRICHLET); bc_types.add_bc_neumann(BDY_NEUMANN_LEFT); // Enter Dirichlet boudnary values. BCValues bc_values; bc_values.add_function(BDY_DIRICHLET, essential_bc_values); // 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(linear_form, linear_form_ord); // 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, 420, 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 for each solution component. 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(); return 0; }
int main() { // Create space. // Transform input data to the format used by the "Space" constructor. SpaceData *md = new SpaceData(); Space* space = new Space(md->N_macroel, md->interfaces, md->poly_orders, md->material_markers, md->subdivisions, N_GRP, N_SLN); delete md; // Enumerate basis functions, info for user. int ndof = Space::get_num_dofs(space); info("ndof: %d", ndof); // Plot the space. space->plot("space.gp"); for (int g = 0; g < N_GRP; g++) { space->set_bc_left_dirichlet(g, flux_left_surf[g]); space->set_bc_right_dirichlet(g, flux_right_surf[g]); } // Initialize the weak formulation. WeakForm wf(2); wf.add_matrix_form(0, 0, jacobian_mat1_0_0, NULL, mat1); wf.add_matrix_form(0, 0, jacobian_mat2_0_0, NULL, mat2); wf.add_matrix_form(0, 0, jacobian_mat3_0_0, NULL, mat3); wf.add_matrix_form(0, 1, jacobian_mat1_0_1, NULL, mat1); wf.add_matrix_form(0, 1, jacobian_mat2_0_1, NULL, mat2); wf.add_matrix_form(0, 1, jacobian_mat3_0_1, NULL, mat3); wf.add_matrix_form(1, 0, jacobian_mat1_1_0, NULL, mat1); wf.add_matrix_form(1, 0, jacobian_mat2_1_0, NULL, mat2); wf.add_matrix_form(1, 0, jacobian_mat3_1_0, NULL, mat3); wf.add_matrix_form(1, 1, jacobian_mat1_1_1, NULL, mat1); wf.add_matrix_form(1, 1, jacobian_mat2_1_1, NULL, mat2); wf.add_matrix_form(1, 1, jacobian_mat3_1_1, NULL, mat3); wf.add_vector_form(0, residual_mat1_0, NULL, mat1); wf.add_vector_form(0, residual_mat2_0, NULL, mat2); wf.add_vector_form(0, residual_mat3_0, NULL, mat3); wf.add_vector_form(1, residual_mat1_1, NULL, mat1); wf.add_vector_form(1, residual_mat2_1, NULL, mat2); wf.add_vector_form(1, residual_mat3_1, NULL, mat3); // 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"); info("Done."); return 0; }
int main() { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Create coarse mesh, set Dirichlet BC, enumerate basis functions. Space* space = new Space(A, B, NELEM, DIR_BC_LEFT, DIR_BC_RIGHT, P_INIT, NEQ); // Enumerate basis functions, info for user. int ndof = Space::get_num_dofs(space); info("ndof: %d", ndof); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(jacobian); wf.add_vector_form(residual); // Initialize the FE problem. bool is_linear = false; DiscreteProblem *dp_coarse = new DiscreteProblem(&wf, space, is_linear); // Newton's loop on coarse mesh. // Fill vector coeff_vec using dof and coeffs arrays in elements. double *coeff_vec_coarse = new double[Space::get_num_dofs(space)]; get_coeff_vector(space, coeff_vec_coarse); // Set up the solver, matrix, and rhs according to the solver selection. SparseMatrix* matrix_coarse = create_matrix(matrix_solver); Vector* rhs_coarse = create_vector(matrix_solver); Solver* solver_coarse = create_linear_solver(matrix_solver, matrix_coarse, rhs_coarse); int it = 1; while (1) { // Obtain the number of degrees of freedom. int ndof_coarse = Space::get_num_dofs(space); // Assemble the Jacobian matrix and residual vector. dp_coarse->assemble(coeff_vec_coarse, matrix_coarse, rhs_coarse); // Calculate the l2-norm of residual vector. double res_l2_norm = get_l2_norm(rhs_coarse); // 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_COARSE && 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_coarse; i++) rhs_coarse->set(i, -rhs_coarse->get(i)); // Solve the linear system. if(!solver_coarse->solve()) error ("Matrix solver failed.\n"); // Add \deltaY^{n+1} to Y^n. for (int i = 0; i < ndof_coarse; i++) coeff_vec_coarse[i] += solver_coarse->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_coarse, space); it++; } // Cleanup. delete matrix_coarse; delete rhs_coarse; delete solver_coarse; delete [] coeff_vec_coarse; delete dp_coarse; // DOF and CPU convergence graphs. SimpleGraph graph_dof_est, graph_cpu_est; SimpleGraph 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); // Initialize the FE problem. bool is_linear = false; DiscreteProblem* dp = new DiscreteProblem(&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); // Newton's loop on the fine mesh. info("Solving on fine mesh:"); // Fill vector coeff_vec using dof and coeffs arrays in elements. double *coeff_vec = new double[Space::get_num_dofs(ref_space)]; get_coeff_vector(ref_space, coeff_vec); int it = 1; while (1) { // Obtain the number of degrees of freedom. int ndof = Space::get_num_dofs(ref_space); // Assemble the Jacobian matrix and residual vector. dp->assemble(coeff_vec, matrix, rhs); // Calculate the l2-norm of residual vector. double res_l2_norm = get_l2_norm(rhs); // Info for user. info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(ref_space), res_l2_norm); // If l2 norm of the residual vector is within tolerance, 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_REF && 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, ref_space); it++; } // Starting with second adaptivity step, obtain new coarse // mesh solution via projecting the fine mesh solution. if(as > 1) { info("Projecting the fine mesh solution onto the coarse mesh."); // Project the fine mesh solution (defined on space_ref) onto the coarse mesh (defined on space). OGProjection::project_global(space, ref_space, matrix_solver); } // Calculate element errors and total error estimate. info("Calculating error estimate."); double err_est_array[MAX_ELEM_NUM]; double err_est_rel = calc_err_est(NORM, space, ref_space, err_est_array) * 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(); // If exact solution available, also calculate exact error. if (EXACT_SOL_PROVIDED) { // Calculate element errors wrt. exact solution. double err_exact_rel = calc_err_exact(NORM, space, exact_sol, NEQ, A, B) * 100; // Info for user. info("Relative error (exact) = %g %%", err_exact_rel); // Add entry to DOF and CPU convergence graphs. graph_dof_exact.add_values(Space::get_num_dofs(space), err_exact_rel); graph_cpu_exact.add_values(cpu_time.accumulated(), 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_cpu_est.add_values(cpu_time.accumulated(), err_est_rel); // If err_est_rel too large, adapt the mesh. if (err_est_rel < NEWTON_TOL_REF) done = true; else { info("Adapting the coarse mesh."); adapt(NORM, ADAPT_TYPE, THRESHOLD, err_est_array, space, ref_space); } as++; // Plot meshes, results, and errors. adapt_plotting(space, ref_space, NORM, EXACT_SOL_PROVIDED, exact_sol); // Cleanup. delete solver; delete matrix; delete rhs; delete ref_space; delete dp; delete [] coeff_vec; } while (done == false); info("Total running time: %g s", cpu_time.accumulated()); // Save convergence graphs. graph_dof_est.save("conv_dof_est.dat"); graph_cpu_est.save("conv_cpu_est.dat"); graph_dof_exact.save("conv_dof_exact.dat"); graph_cpu_exact.save("conv_cpu_exact.dat"); return 0; }
int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("lshape.mesh", &mesh); // quadrilaterals // 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); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(callback(bilinear_form), HERMES_SYM); wf.add_vector_form(callback(linear_form)); // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Set exact solution. ExactSolution exact(&mesh, fndd); // 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); // 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 for each solution component. 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()); int ndof = Space::get_num_dofs(&space); #define ERROR_SUCCESS 0 #define ERROR_FAILURE -1 int n_dof_allowed = 660; 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 ERROR_SUCCESS; } else { printf("Failure!\n"); return ERROR_FAILURE; } }
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); info("ndof = %d", Space::get_num_dofs(space)); // Initialize the weak formulation. WeakForm wf(4); wf.add_matrix_form(0, 0, jacobian_1_1); wf.add_matrix_form(0, 2, jacobian_1_3); wf.add_matrix_form(0, 3, jacobian_1_4); wf.add_matrix_form(1, 1, jacobian_2_2); wf.add_matrix_form(1, 2, jacobian_2_3); wf.add_matrix_form(1, 3, jacobian_2_4); wf.add_matrix_form(2, 0, jacobian_3_1); wf.add_matrix_form(2, 1, jacobian_3_2); wf.add_matrix_form(2, 2, jacobian_3_3); wf.add_matrix_form(3, 0, jacobian_4_1); wf.add_matrix_form(3, 1, jacobian_4_2); wf.add_matrix_form(3, 3, jacobian_4_4); wf.add_vector_form(0, residual_1); wf.add_vector_form(1, residual_2); wf.add_vector_form(2, residual_3); wf.add_vector_form(3, residual_4); wf.add_matrix_form_surf(0, 0, jacobian_surf_right_U_Re_Re, BOUNDARY_RIGHT); wf.add_matrix_form_surf(0, 2, jacobian_surf_right_U_Re_Im, BOUNDARY_RIGHT); wf.add_matrix_form_surf(1, 1, jacobian_surf_right_U_Im_Re, BOUNDARY_RIGHT); wf.add_matrix_form_surf(1, 3, jacobian_surf_right_U_Im_Im, BOUNDARY_RIGHT); // Initialize the FE problem. bool is_linear = false; DiscreteProblem *dp = new DiscreteProblem(&wf, space, is_linear); // Set zero initial condition. double *coeff_vec = new double[Space::get_num_dofs(space)]; set_zero(coeff_vec, Space::get_num_dofs(space)); // 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) { // 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 < Space::get_num_dofs(space); 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 < Space::get_num_dofs(space); 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."); it++; } // Plot the solution. Linearizer l(space); l.plot_solution("solution.gp"); // cleaning delete dp; delete rhs; delete solver; delete[] coeff_vec; delete space; delete bc_u_re_left; delete bc_u_im_left; delete matrix; info("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("../domain.mesh", &mesh); // Perform initial mesh refinements. for (int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(); // Initialize boundary conditions. DefaultEssentialBCConst bc_essential("Source", P_SOURCE); EssentialBCs bcs(&bc_essential); // Create an H1 space with default shapeset. H1Space space(&mesh, &bcs, P_INIT); int ndof = Space::get_num_dofs(&space); info("ndof = %d", ndof); // Initialize the weak formulation. CustomWeakFormAcoustics wf(BDY_NEWTON, RHO, SOUND_SPEED, OMEGA); // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Initialize views. //ScalarView sview("Solution", new WinGeom(0, 0, 330, 350)); //sview.show_mesh(false); //sview.fix_scale_width(50); //OrderView oview("Polynomial orders", new WinGeom(340, 0, 300, 350)); // DOF and CPU convergence graphs initialization. SimpleGraph graph_dof, graph_cpu; 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). } // 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 = 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); 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); // 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."); Adapt* adaptivity = new Adapt(&space); double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 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); } if (Space::get_num_dofs(&space) >= NDOF_STOP) done = true; delete adaptivity; if (done == false) delete ref_space->get_mesh(); delete ref_space; delete dp; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); // Clean up. delete solver; delete matrix; delete rhs; // Show the reference solution - the final result. //sview.set_title("Fine mesh solution"); //sview.show(&ref_sln); // Wait for all views to be closed. //View::wait(); //return 0; ndof = Space::get_num_dofs(&space); #define ERROR_SUCCESS 0 #define ERROR_FAILURE -1 int ndof_allowed = 460; printf("ndof allowed = %d\n", ndof_allowed); printf("ndof actual = %d\n", ndof); if (ndof < ndof_allowed) { // ndof was 454 when this test was created (04-05-2011). printf("Success!\n"); return ERROR_SUCCESS; } else { printf("Failure!\n"); return ERROR_FAILURE; } }
int main(int argc, char* argv[]) { // Load the mesh. Mesh u_mesh, v_mesh; H2DReader mloader; mloader.load("crack.mesh", &u_mesh); // Perform initial uniform mesh refinement. for (int i=0; i < INIT_REF_NUM; i++) u_mesh.refine_all_elements(); // Create initial mesh for the vertical displacement component. // This also initializes the multimesh hp-FEM. v_mesh.copy(&u_mesh); // Create H1 spaces with default shapesets. H1Space u_space(&u_mesh, bc_types_xy, essential_bc_values, P_INIT); H1Space v_space(MULTI ? &v_mesh : &u_mesh, bc_types_xy, essential_bc_values, P_INIT); // Initialize the weak formulation. WeakForm wf(2); wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), HERMES_SYM); wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), HERMES_SYM); wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), HERMES_SYM); wf.add_vector_form_surf(1, linear_form_surf_1, linear_form_surf_1_ord, BDY_TOP); // Initialize coarse and reference mesh solutions. Solution u_sln, v_sln, u_ref_sln, v_ref_sln; // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // DOF and CPU convergence graphs. SimpleGraph graph_dof_est, graph_cpu_est; // 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. Tuple<Space *>* ref_spaces = construct_refined_spaces(Tuple<Space *>(&u_space, &v_space)); // Assemble the reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces, is_linear); SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); dp->assemble(matrix, rhs); // Time measurement. cpu_time.tick(); // Solve the linear system of the reference problem. If successful, obtain the solutions. if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), *ref_spaces, Tuple<Solution *>(&u_ref_sln, &v_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(Tuple<Space *>(&u_space, &v_space), Tuple<Solution *>(&u_ref_sln, &v_ref_sln), Tuple<Solution *>(&u_sln, &v_sln), matrix_solver); // Calculate element errors. info("Calculating error estimate and exact error."); Adapt* adaptivity = new Adapt(Tuple<Space *>(&u_space, &v_space), Tuple<ProjNormType>(HERMES_H1_NORM, HERMES_H1_NORM)); adaptivity->set_error_form(0, 0, bilinear_form_0_0<scalar, scalar>, bilinear_form_0_0<Ord, Ord>); adaptivity->set_error_form(0, 1, bilinear_form_0_1<scalar, scalar>, bilinear_form_0_1<Ord, Ord>); adaptivity->set_error_form(1, 0, bilinear_form_1_0<scalar, scalar>, bilinear_form_1_0<Ord, Ord>); adaptivity->set_error_form(1, 1, bilinear_form_1_1<scalar, scalar>, bilinear_form_1_1<Ord, Ord>); // Calculate error estimate for each solution component and the total error estimate. Tuple<double> err_est_rel; bool solutions_for_adapt = true; double err_est_rel_total = adaptivity->calc_err_est(Tuple<Solution *>(&u_sln, &v_sln), Tuple<Solution *>(&u_ref_sln, &v_ref_sln), solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_ABS, &err_est_rel) * 100; // Time measurement. cpu_time.tick(); // Report results. info("ndof_coarse[0]: %d, ndof_fine[0]: %d, err_est_rel[0]: %g%%", u_space.Space::get_num_dofs(), (*ref_spaces)[0]->Space::get_num_dofs(), err_est_rel[0]*100); info("ndof_coarse[1]: %d, ndof_fine[1]: %d, err_est_rel[1]: %g%%", v_space.Space::get_num_dofs(), (*ref_spaces)[1]->Space::get_num_dofs(), err_est_rel[1]*100); info("ndof_coarse_total: %d, ndof_fine_total: %d, err_est_rel_total: %g%%", Space::get_num_dofs(Tuple<Space *>(&u_space, &v_space)), Space::get_num_dofs(*ref_spaces), err_est_rel_total); // Add entry to DOF and CPU convergence graphs. graph_dof_est.add_values(Space::get_num_dofs(Tuple<Space *>(&u_space, &v_space)), err_est_rel_total); graph_dof_est.save("conv_dof_est.dat"); graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total); graph_cpu_est.save("conv_cpu_est.dat"); // If err_est too large, adapt the mesh. if (err_est_rel_total < ERR_STOP) done = true; else { info("Adapting coarse mesh."); done = adaptivity->adapt(Tuple<RefinementSelectors::Selector *>(&selector, &selector), MULTI ? THRESHOLD_MULTI:THRESHOLD_SINGLE, STRATEGY, MESH_REGULARITY); } if (Space::get_num_dofs(Tuple<Space *>(&u_space, &v_space)) >= NDOF_STOP) done = true; // Clean up. delete solver; delete matrix; delete rhs; delete adaptivity; if(done == false) for(int i = 0; i < ref_spaces->size(); i++) delete (*ref_spaces)[i]->get_mesh(); delete ref_spaces; delete dp; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); int ndof = Space::get_num_dofs(Tuple<Space *>(&u_space, &v_space)); int ndof_allowed = 920; printf("ndof actual = %d\n", ndof); printf("ndof allowed = %d\n", ndof_allowed); if (ndof <= ndof_allowed) { // ndofs was 908 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[]) { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("domain.mesh", &mesh); // Perform initial mesh refinements. mesh.refine_all_elements(); // Initialize boundary conditions. CustomEssentialBCNonConst bc_essential(BDY_HORIZONTAL); EssentialBCs bcs(&bc_essential); // Create an H1 space with default shapeset. H1Space space(&mesh, &bcs, P_INIT); int ndof = space.get_num_dofs(); info("ndof = %d", ndof); // Initialize the weak formulation. CustomWeakFormGeneral wf; // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // 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 initialization. SimpleGraph graph_dof, graph_cpu; // 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 = Space::construct_refined_space(&space); // Initialize matrix solver. SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); // Assemble reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear); 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); // 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."); Adapt* adaptivity = new Adapt(&space); double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 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_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); } 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; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); // Show the reference solution - the final result. sview.set_title("Fine mesh solution"); sview.show(&ref_sln); // Wait for all views to be closed. View::wait(); return 0; }
int main(int argc, char* argv[]) { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Load the mesh. Mesh u1_mesh, u2_mesh; H2DReader mloader; mloader.load("../bracket.mesh", &u1_mesh); // Initial mesh refinements. u1_mesh.refine_element_id(1); u1_mesh.refine_element_id(4); // Create initial mesh for the vertical displacement component. // This also initializes the multimesh hp-FEM. u2_mesh.copy(&u1_mesh); // Initialize boundary conditions. DefaultEssentialBCConst zero_disp(BDY_RIGHT, 0.0); EssentialBCs bcs(&zero_disp); // Create x- and y- displacement space using the default H1 shapeset. H1Space u1_space(&u1_mesh, &bcs, P_INIT); H1Space u2_space(&u2_mesh, &bcs, P_INIT); info("ndof = %d.", Space::get_num_dofs(Hermes::vector<Space *>(&u1_space, &u2_space))); // Initialize the weak formulation. CustomWeakForm wf(E, nu, rho*g1, BDY_TOP, f0, f1); // Initialize the FE problem. bool is_linear = true; DiscreteProblem dp(&wf, Hermes::vector<Space *>(&u1_space, &u2_space), is_linear); // Initialize coarse and reference mesh solutions. Solution u1_sln, u2_sln, u1_ref_sln, u2_ref_sln; // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Initialize views. //ScalarView s_view_0("Solution (x-displacement)", new WinGeom(0, 0, 400, 350)); //s_view_0.show_mesh(false); //ScalarView s_view_1("Solution (y-displacement)", new WinGeom(760, 0, 400, 350)); //s_view_1.show_mesh(false); //OrderView o_view_0("Mesh (x-displacement)", new WinGeom(410, 0, 340, 350)); //OrderView o_view_1("Mesh (y-displacement)", new WinGeom(1170, 0, 340, 350)); //ScalarView mises_view("Von Mises stress [Pa]", new WinGeom(0, 405, 400, 350)); // DOF and CPU convergence graphs. SimpleGraph graph_dof_est, graph_cpu_est; // Adaptivity loop: int as = 1; bool done = false; do { info("---- Adaptivity step %d:", as); // Construct globally refined reference mesh and setup reference space. Hermes::vector<Space *>* ref_spaces = Space::construct_refined_spaces(Hermes::vector<Space *>(&u1_space, &u2_space)); // Initialize matrix solver. SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); // Assemble the reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces, is_linear); dp->assemble(matrix, rhs); // Time measurement. cpu_time.tick(); // Solve the linear system of the reference problem. If successful, obtain the solutions. if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), *ref_spaces, Hermes::vector<Solution *>(&u1_ref_sln, &u2_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(Hermes::vector<Space *>(&u1_space, &u2_space), Hermes::vector<Solution *>(&u1_ref_sln, &u2_ref_sln), Hermes::vector<Solution *>(&u1_sln, &u2_sln), matrix_solver); // View the coarse mesh solution and polynomial orders. //s_view_0.show(&u1_sln); //o_view_0.show(&u1_space); //s_view_1.show(&u2_sln); //o_view_1.show(&u2_space); // For von Mises stress Filter. //double lambda = (E * nu) / ((1 + nu) * (1 - 2*nu)); //double mu = E / (2*(1 + nu)); //VonMisesFilter stress(Hermes::vector<MeshFunction *>(&u1_sln, &u2_sln), lambda, mu); //mises_view.show(&stress, HERMES_EPS_HIGH, H2D_FN_VAL_0, &u1_sln, &u2_sln, 1e4); // Skip visualization time. cpu_time.tick(HERMES_SKIP); // Initialize adaptivity. Adapt* adaptivity = new Adapt(Hermes::vector<Space *>(&u1_space, &u2_space)); /* // Register custom forms for error calculation. adaptivity->set_error_form(0, 0, bilinear_form_0_0<scalar, scalar>, bilinear_form_0_0<Ord, Ord>); adaptivity->set_error_form(0, 1, bilinear_form_0_1<scalar, scalar>, bilinear_form_0_1<Ord, Ord>); adaptivity->set_error_form(1, 0, bilinear_form_1_0<scalar, scalar>, bilinear_form_1_0<Ord, Ord>); adaptivity->set_error_form(1, 1, bilinear_form_1_1<scalar, scalar>, bilinear_form_1_1<Ord, Ord>); */ // Calculate error estimate for each solution component and the total error estimate. info("Calculating error estimate and exact error."); Hermes::vector<double> err_est_rel; double err_est_rel_total = adaptivity->calc_err_est(Hermes::vector<Solution *>(&u1_sln, &u2_sln), Hermes::vector<Solution *>(&u1_ref_sln, &u2_ref_sln), &err_est_rel) * 100; // Time measurement. cpu_time.tick(); // Report results. info("ndof_coarse[0]: %d, ndof_fine[0]: %d, err_est_rel[0]: %g%%", u1_space.Space::get_num_dofs(), Space::get_num_dofs((*ref_spaces)[0]), err_est_rel[0]*100); info("ndof_coarse[1]: %d, ndof_fine[1]: %d, err_est_rel[1]: %g%%", u2_space.Space::get_num_dofs(), Space::get_num_dofs((*ref_spaces)[1]), err_est_rel[1]*100); info("ndof_coarse_total: %d, ndof_fine_total: %d, err_est_rel_total: %g%%", Space::get_num_dofs(Hermes::vector<Space *>(&u1_space, &u2_space)), Space::get_num_dofs(*ref_spaces), err_est_rel_total); // Add entry to DOF and CPU convergence graphs. graph_dof_est.add_values(Space::get_num_dofs(Hermes::vector<Space *>(&u1_space, &u2_space)), err_est_rel_total); graph_dof_est.save("conv_dof_est.dat"); graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total); graph_cpu_est.save("conv_cpu_est.dat"); // If err_est too large, adapt the mesh. if (err_est_rel_total < ERR_STOP) done = true; else { info("Adapting coarse mesh."); done = adaptivity->adapt(Hermes::vector<RefinementSelectors::Selector *>(&selector, &selector), THRESHOLD, STRATEGY, MESH_REGULARITY); } if (Space::get_num_dofs(Hermes::vector<Space *>(&u1_space, &u2_space)) >= NDOF_STOP) done = true; // Clean up. delete solver; delete matrix; delete rhs; delete adaptivity; if(done == false) for(unsigned int i = 0; i < ref_spaces->size(); i++) delete (*ref_spaces)[i]->get_mesh(); delete ref_spaces; delete dp; // Increase counter. as++; } while (done == false); int ndof = Space::get_num_dofs(Hermes::vector<Space *>(&u1_space, &u2_space)); int ndof_allowed = 1420; printf("ndof actual = %d\n", ndof); printf("ndof allowed = %d\n", ndof_allowed); if (ndof <= ndof_allowed) { // ndofs was 1414 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[]) { // Instantiate a class with global functions. Hermes2D hermes2d; // Load the mesh. Mesh u_mesh, v_mesh; H2DReader mloader; mloader.load("../square.mesh", &u_mesh); if (MULTI == false) u_mesh.refine_towards_boundary("Outer", INIT_REF_BDY); // Create initial mesh (master mesh). v_mesh.copy(&u_mesh); // Initial mesh refinements in the v_mesh towards the boundary. if (MULTI == true) v_mesh.refine_towards_boundary("Outer", INIT_REF_BDY); // Set exact solutions. ExactSolutionFitzHughNagumo1 exact_u(&u_mesh); ExactSolutionFitzHughNagumo2 exact_v(&v_mesh, K); // Define right-hand sides. CustomRightHandSide1 rhs_1(K, D_u, SIGMA); CustomRightHandSide2 rhs_2(K, D_v); // Initialize the weak formulation. WeakFormFitzHughNagumo wf(&rhs_1, &rhs_2); // Initialize boundary conditions DefaultEssentialBCConst bc_u("Outer", 0.0); EssentialBCs bcs_u(&bc_u); DefaultEssentialBCConst bc_v("Outer", 0.0); EssentialBCs bcs_v(&bc_v); // Create H1 spaces with default shapeset for both displacement components. H1Space u_space(&u_mesh, &bcs_u, P_INIT_U); H1Space v_space(MULTI ? &v_mesh : &u_mesh, &bcs_v, P_INIT_V); // Initialize coarse and reference mesh solutions. Solution u_sln, v_sln, u_ref_sln, v_ref_sln; // Initialize refinement selector. H1ProjBasedSelector 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; // 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. Hermes::vector<Space *>* ref_spaces = Space::construct_refined_spaces(Hermes::vector<Space *>(&u_space, &v_space)); int ndof_ref = Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)); // Initialize matrix solver. SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); // Initialize reference problem. info("Solving on reference mesh."); DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces); dp->assemble(matrix, rhs); // Time measurement. cpu_time.tick(); // Initial coefficient vector for the Newton's method. scalar* coeff_vec = new scalar[ndof_ref]; memset(coeff_vec, 0, ndof_ref * sizeof(scalar)); // Perform Newton's iteration. if (!hermes2d.solve_newton(coeff_vec, dp, solver, matrix, rhs)) error("Newton's iteration failed."); // Translate the resulting coefficient vector into the Solution sln. Solution::vector_to_solutions(coeff_vec, *ref_spaces, Hermes::vector<Solution *>(&u_ref_sln, &v_ref_sln)); // Project the fine mesh solution onto the coarse mesh. info("Projecting reference solution on coarse mesh."); OGProjection::project_global(Hermes::vector<Space *>(&u_space, &v_space), Hermes::vector<Solution *>(&u_ref_sln, &v_ref_sln), Hermes::vector<Solution *>(&u_sln, &v_sln), matrix_solver); // Calculate element errors. info("Calculating error estimate and exact error."); Adapt* adaptivity = new Adapt(Hermes::vector<Space *>(&u_space, &v_space)); // Calculate error estimate for each solution component and the total error estimate. Hermes::vector<double> err_est_rel; double err_est_rel_total = adaptivity->calc_err_est(Hermes::vector<Solution *>(&u_sln, &v_sln), Hermes::vector<Solution *>(&u_ref_sln, &v_ref_sln), &err_est_rel) * 100; // Calculate exact error for each solution component and the total exact error. Hermes::vector<double> err_exact_rel; bool solutions_for_adapt = false; double err_exact_rel_total = adaptivity->calc_err_exact(Hermes::vector<Solution *>(&u_sln, &v_sln), Hermes::vector<Solution *>(&exact_u, &exact_v), &err_exact_rel, solutions_for_adapt) * 100; // Time measurement. cpu_time.tick(); // Report results. info("ndof_coarse[0]: %d, ndof_fine[0]: %d", u_space.Space::get_num_dofs(), (*ref_spaces)[0]->Space::get_num_dofs()); info("err_est_rel[0]: %g%%, err_exact_rel[0]: %g%%", err_est_rel[0]*100, err_exact_rel[0]*100); info("ndof_coarse[1]: %d, ndof_fine[1]: %d", v_space.Space::get_num_dofs(), (*ref_spaces)[1]->Space::get_num_dofs()); info("err_est_rel[1]: %g%%, err_exact_rel[1]: %g%%", err_est_rel[1]*100, err_exact_rel[1]*100); info("ndof_coarse_total: %d, ndof_fine_total: %d", Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)), Space::get_num_dofs(*ref_spaces)); info("err_est_rel_total: %g%%, err_est_exact_total: %g%%", err_est_rel_total, err_exact_rel_total); // Add entry to DOF and CPU convergence graphs. graph_dof_est.add_values(Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)), err_est_rel_total); graph_dof_est.save("conv_dof_est.dat"); graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total); graph_cpu_est.save("conv_cpu_est.dat"); graph_dof_exact.add_values(Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)), err_exact_rel_total); graph_dof_exact.save("conv_dof_exact.dat"); graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel_total); graph_cpu_exact.save("conv_cpu_exact.dat"); // If err_est too large, adapt the mesh. if (err_est_rel_total < ERR_STOP) done = true; else { info("Adapting coarse mesh."); done = adaptivity->adapt(Hermes::vector<RefinementSelectors::Selector *>(&selector, &selector), THRESHOLD, STRATEGY, MESH_REGULARITY); } if (Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)) >= NDOF_STOP) done = true; // Clean up. delete [] coeff_vec; delete solver; delete matrix; delete rhs; delete adaptivity; if(done == false) for(unsigned int i = 0; i < ref_spaces->size(); i++) delete (*ref_spaces)[i]->get_mesh(); delete ref_spaces; delete dp; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); int ndof = Space::get_num_dofs(Hermes::vector<Space *>(&u_space, &v_space)); printf("ndof allowed = %d\n", 580); printf("ndof actual = %d\n", ndof); if (ndof < 580) { // ndofs was 574 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 u_mesh, v_mesh; H2DReader mloader; mloader.load("square.mesh", &u_mesh); if (MULTI == false) u_mesh.refine_towards_boundary(1, INIT_REF_BDY); // Create initial mesh (master mesh). v_mesh.copy(&u_mesh); // Initial mesh refinements in the v_mesh towards the boundary. if (MULTI == true) v_mesh.refine_towards_boundary(1, INIT_REF_BDY); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_dirichlet(OUTER_BDY); // Enter Dirichlet boundary values. BCValues bc_values; bc_values.add_zero(OUTER_BDY); // Create H1 spaces with default shapeset for both displacement components. H1Space u_space(&u_mesh, &bc_types, &bc_values, P_INIT_U); H1Space v_space(MULTI ? &v_mesh : &u_mesh, &bc_types, &bc_values, P_INIT_V); // Initialize the weak formulation. WeakForm wf(2); wf.add_matrix_form(0, 0, callback(bilinear_form_0_0)); wf.add_matrix_form(0, 1, callback(bilinear_form_0_1)); wf.add_matrix_form(1, 0, callback(bilinear_form_1_0)); wf.add_matrix_form(1, 1, callback(bilinear_form_1_1)); wf.add_vector_form(0, linear_form_0, linear_form_0_ord); wf.add_vector_form(1, linear_form_1, linear_form_1_ord); // Initialize coarse and reference mesh solutions. Solution u_sln, v_sln, u_ref_sln, v_ref_sln; // Initialize exact solutions. ExactSolution u_exact(&u_mesh, uexact); ExactSolution v_exact(&v_mesh, vexact); // Initialize refinement selector. H1ProjBasedSelector 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; // 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. Hermes::Tuple<Space *>* ref_spaces = construct_refined_spaces(Hermes::Tuple<Space *>(&u_space, &v_space)); // Assemble the reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces, is_linear); SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); dp->assemble(matrix, rhs); // Time measurement. cpu_time.tick(); // Solve the linear system of the reference problem. If successful, obtain the solutions. if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), *ref_spaces, Hermes::Tuple<Solution *>(&u_ref_sln, &v_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(Hermes::Tuple<Space *>(&u_space, &v_space), Hermes::Tuple<Solution *>(&u_ref_sln, &v_ref_sln), Hermes::Tuple<Solution *>(&u_sln, &v_sln), matrix_solver); // Calculate element errors. info("Calculating error estimate and exact error."); Adapt* adaptivity = new Adapt(Hermes::Tuple<Space *>(&u_space, &v_space), Hermes::Tuple<ProjNormType>(HERMES_H1_NORM, HERMES_H1_NORM)); // Calculate error estimate for each solution component and the total error estimate. Hermes::Tuple<double> err_est_rel; bool solutions_for_adapt = true; double err_est_rel_total = adaptivity->calc_err_est(Hermes::Tuple<Solution *>(&u_sln, &v_sln), Hermes::Tuple<Solution *>(&u_ref_sln, &v_ref_sln), solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_ABS, &err_est_rel) * 100; // Calculate exact error for each solution component and the total exact error. Hermes::Tuple<double> err_exact_rel; solutions_for_adapt = false; double err_exact_rel_total = adaptivity->calc_err_exact(Hermes::Tuple<Solution *>(&u_sln, &v_sln), Hermes::Tuple<Solution *>(&u_exact, &v_exact), solutions_for_adapt, HERMES_TOTAL_ERROR_REL, &err_exact_rel) * 100; // Time measurement. cpu_time.tick(); // Report results. info("ndof_coarse[0]: %d, ndof_fine[0]: %d", u_space.Space::get_num_dofs(), (*ref_spaces)[0]->Space::get_num_dofs()); info("err_est_rel[0]: %g%%, err_exact_rel[0]: %g%%", err_est_rel[0]*100, err_exact_rel[0]*100); info("ndof_coarse[1]: %d, ndof_fine[1]: %d", v_space.Space::get_num_dofs(), (*ref_spaces)[1]->Space::get_num_dofs()); info("err_est_rel[1]: %g%%, err_exact_rel[1]: %g%%", err_est_rel[1]*100, err_exact_rel[1]*100); info("ndof_coarse_total: %d, ndof_fine_total: %d", Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space)), Space::get_num_dofs(*ref_spaces)); info("err_est_rel_total: %g%%, err_est_exact_total: %g%%", err_est_rel_total, err_exact_rel_total); // Add entry to DOF and CPU convergence graphs. graph_dof_est.add_values(Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space)), err_est_rel_total); graph_dof_est.save("conv_dof_est.dat"); graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total); graph_cpu_est.save("conv_cpu_est.dat"); graph_dof_exact.add_values(Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space)), err_exact_rel_total); graph_dof_exact.save("conv_dof_exact.dat"); graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel_total); graph_cpu_exact.save("conv_cpu_exact.dat"); // If err_est too large, adapt the mesh. if (err_est_rel_total < ERR_STOP) done = true; else { info("Adapting coarse mesh."); done = adaptivity->adapt(Hermes::Tuple<RefinementSelectors::Selector *>(&selector, &selector), THRESHOLD, STRATEGY, MESH_REGULARITY); } if (Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space)) >= NDOF_STOP) done = true; // Clean up. delete solver; delete matrix; delete rhs; delete adaptivity; if(done == false) for(unsigned int i = 0; i < ref_spaces->size(); i++) delete (*ref_spaces)[i]->get_mesh(); delete ref_spaces; delete dp; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); int ndof = Space::get_num_dofs(Hermes::Tuple<Space *>(&u_space, &v_space)); printf("ndof allowed = %d\n", 1040); printf("ndof actual = %d\n", ndof); if (ndof < 1040) { // ndofs was 1030 at the time this test was created printf("Success!\n"); return ERR_SUCCESS; } else { printf("Failure!\n"); return ERR_FAILURE; } }
int main() { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Create coarse mesh, set Dirichlet BC, enumerate basis functions. Space* space = new Space(A, B, NELEM, DIR_BC_LEFT, DIR_BC_RIGHT, P_INIT, NEQ); // Enumerate basis functions, info for user. int ndof = Space::get_num_dofs(space); info("ndof: %d", ndof); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(jacobian); wf.add_vector_form(residual); double elem_errors[MAX_ELEM_NUM]; // This array decides what // elements will be refined. ElemPtr2 ref_elem_pairs[MAX_ELEM_NUM]; // To store element pairs from the // FTR solution. Decides how // elements will be hp-refined. for (int i=0; i < MAX_ELEM_NUM; i++) { ref_elem_pairs[i][0] = new Element(); ref_elem_pairs[i][1] = new Element(); } // DOF and CPU convergence graphs. SimpleGraph graph_dof_exact, graph_cpu_exact; /// Adaptivity loop: int as = 1; bool done = false; do { info("---- Adaptivity step %d:", as); // Initialize the FE problem. bool is_linear = false; DiscreteProblem *dp_coarse = new DiscreteProblem(&wf, space, is_linear); // Newton's loop on coarse mesh. // Fill vector coeff_vec using dof and coeffs arrays in elements. double *coeff_vec_coarse = new double[Space::get_num_dofs(space)]; get_coeff_vector(space, coeff_vec_coarse); // Set up the solver, matrix, and rhs according to the solver selection. SparseMatrix* matrix_coarse = create_matrix(matrix_solver); Vector* rhs_coarse = create_vector(matrix_solver); Solver* solver_coarse = create_linear_solver(matrix_solver, matrix_coarse, rhs_coarse); int it = 1; while (1) { // Obtain the number of degrees of freedom. int ndof_coarse = Space::get_num_dofs(space); // Assemble the Jacobian matrix and residual vector. dp_coarse->assemble(coeff_vec_coarse, matrix_coarse, rhs_coarse); // Calculate the l2-norm of residual vector. double res_l2_norm = get_l2_norm(rhs_coarse); // 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_COARSE && 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_coarse; i++) rhs_coarse->set(i, -rhs_coarse->get(i)); // Solve the linear system. if(!solver_coarse->solve()) error ("Matrix solver failed.\n"); // Add \deltaY^{n+1} to Y^n. for (int i = 0; i < ndof_coarse; i++) coeff_vec_coarse[i] += solver_coarse->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_coarse, space); it++; } // Cleanup. delete matrix_coarse; delete rhs_coarse; delete solver_coarse; delete [] coeff_vec_coarse; delete dp_coarse; // For every element perform its fast trial refinement (FTR), // calculate the norm of the difference between the FTR // solution and the coarse space solution, and store the // error in the elem_errors[] array. int n_elem = space->get_n_active_elem(); for (int i=0; i < n_elem; i++) { info("=== Starting FTR of Elem [%d].", i); // Replicate coarse space including solution. Space *space_ref_local = space->replicate(); // Perform FTR of element 'i' space_ref_local->reference_refinement(i, 1); info("Elem [%d]: fine space created (%d DOF).", i, space_ref_local->assign_dofs()); // Initialize the FE problem. bool is_linear = false; DiscreteProblem* dp = new DiscreteProblem(&wf, space_ref_local, 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); // Newton's loop on the FTR space. // Fill vector coeff_vec using dof and coeffs arrays in elements. double *coeff_vec = new double[Space::get_num_dofs(space_ref_local)]; get_coeff_vector(space_ref_local, coeff_vec); memset(coeff_vec, 0, Space::get_num_dofs(space_ref_local)*sizeof(double)); int it = 1; while (1) { // Obtain the number of degrees of freedom. int ndof = Space::get_num_dofs(space_ref_local); // 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_ref_local), 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_REF && 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_ref_local); it++; } // Cleanup. delete matrix; delete rhs; delete solver; delete dp; delete [] coeff_vec; // Print FTR solution (enumerated). Linearizer *lxx = new Linearizer(space_ref_local); char out_filename[255]; sprintf(out_filename, "solution_ref_%d.gp", i); lxx->plot_solution(out_filename); delete lxx; // Calculate norm of the difference between the coarse space // and FTR solutions. // NOTE: later we want to look at the difference in some quantity // of interest rather than error in global norm. double err_est_array[MAX_ELEM_NUM]; elem_errors[i] = calc_err_est(NORM, space, space_ref_local, err_est_array) * 100; info("Elem [%d]: absolute error (est) = %g%%", i, elem_errors[i]); // Copy the reference element pair for element 'i'. // into the ref_elem_pairs[i][] array Iterator *I = new Iterator(space); Iterator *I_ref = new Iterator(space_ref_local); Element *e, *e_ref; while (1) { e = I->next_active_element(); e_ref = I_ref->next_active_element(); if (e->id == i) { e_ref->copy_into(ref_elem_pairs[e->id][0]); // coarse element 'e' was split in space. if (e->level != e_ref->level) { e_ref = I_ref->next_active_element(); e_ref->copy_into(ref_elem_pairs[e->id][1]); } break; } } delete I; delete I_ref; delete space_ref_local; } // Time measurement. cpu_time.tick(); // If exact solution available, also calculate exact error. if (EXACT_SOL_PROVIDED) { // Calculate element errors wrt. exact solution. double err_exact_rel = calc_err_exact(NORM, space, exact_sol, NEQ, A, B) * 100; // Info for user. info("Relative error (exact) = %g %%", err_exact_rel); // Add entry to DOF and CPU convergence graphs. graph_dof_exact.add_values(Space::get_num_dofs(space), err_exact_rel); graph_cpu_exact.add_values(cpu_time.accumulated(), err_exact_rel); } // Calculate max FTR error. double max_ftr_error = 0; for (int i=0; i < space->get_n_active_elem(); i++) { if (elem_errors[i] > max_ftr_error) max_ftr_error = elem_errors[i]; } info("Max FTR error = %g%%.", max_ftr_error); // Decide whether the max. FTR error is sufficiently small. if(max_ftr_error < TOL_ERR_FTR) break; // debug //if (as >= 1) break; // Returns updated coarse space with the last solution on it. adapt(NORM, ADAPT_TYPE, THRESHOLD, elem_errors, space, ref_elem_pairs); // Plot spaces, results, and errors. adapt_plotting(space, ref_elem_pairs, NORM, EXACT_SOL_PROVIDED, exact_sol); as++; } while (done == false); info("Total running time: %g s", cpu_time.accumulated()); // Save convergence graphs. graph_dof_exact.save("conv_dof_exact.dat"); graph_cpu_exact.save("conv_cpu_exact.dat"); // Test variable. bool success = true; info("ndof = %d.", Space::get_num_dofs(space)); if (Space::get_num_dofs(space) > 35) success = false; if (success) { info("Success!"); return ERROR_SUCCESS; } else { info("Failure!"); return ERROR_FAILURE; } }
int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh, basemesh; H2DReader mloader; mloader.load("GAMM-channel.mesh", &basemesh); // Perform initial mesh refinements. for (int i = 0; i < INIT_REF_NUM; i++) basemesh.refine_all_elements(); basemesh.refine_by_criterion(criterion, 4); mesh.copy(&basemesh); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_neumann(Hermes::Tuple<int>(BDY_SOLID_WALL, BDY_INLET_OUTLET)); // Create L2 spaces with default shapesets. L2Space space_rho(&mesh, &bc_types, P_INIT); L2Space space_rho_v_x(&mesh, &bc_types, P_INIT); L2Space space_rho_v_y(&mesh, &bc_types, P_INIT); L2Space space_e(&mesh, &bc_types, P_INIT); // Initialize solutions, set initial conditions. Solution sln_rho, sln_rho_v_x, sln_rho_v_y, sln_e, prev_rho, prev_rho_v_x, prev_rho_v_y, prev_e; Solution rsln_rho, rsln_rho_v_x, rsln_rho_v_y, rsln_e; sln_rho.set_exact(&mesh, ic_density); sln_rho_v_x.set_exact(&mesh, ic_density_vel_x); sln_rho_v_y.set_exact(&mesh, ic_density_vel_y); sln_e.set_exact(&mesh, ic_energy); prev_rho.set_exact(&mesh, ic_density); prev_rho_v_x.set_exact(&mesh, ic_density_vel_x); prev_rho_v_y.set_exact(&mesh, ic_density_vel_y); prev_e.set_exact(&mesh, ic_energy); // Initialize weak formulation. WeakForm wf(4); // Bilinear forms coming from time discretization by explicit Euler's method. wf.add_matrix_form(0,0,callback(bilinear_form_0_0_time)); wf.add_matrix_form(1,1,callback(bilinear_form_1_1_time)); wf.add_matrix_form(2,2,callback(bilinear_form_2_2_time)); wf.add_matrix_form(3,3,callback(bilinear_form_3_3_time)); // Volumetric linear forms. // Linear forms coming from the linearization by taking the Eulerian fluxes' Jacobian matrices from the previous time step. // First flux. /* wf.add_vector_form(0,callback(linear_form_0_1), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho_v_x)); wf.add_vector_form(1, callback(linear_form_1_0_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_1_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_2_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_3_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(2, callback(linear_form_2_0_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(2, callback(linear_form_2_1_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(2, callback(linear_form_2_2_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(2, callback(linear_form_2_3_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_0_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_1_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_2_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_3_first_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); // Second flux. wf.add_vector_form(0,callback(linear_form_0_2),HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_0_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_1_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_2_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(1, callback(linear_form_1_3_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(2, callback(linear_form_2_0_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(2, callback(linear_form_2_1_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(2, callback(linear_form_2_2_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y)); wf.add_vector_form(2, callback(linear_form_2_3_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_0_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_1_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_2_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, callback(linear_form_3_3_second_flux), HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); */ // Volumetric linear forms coming from the time discretization. #ifdef HERMES_USE_VECTOR_VALUED_FORMS wf.add_vector_form(0, linear_form_vector, linear_form_order, HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(1, linear_form_vector, linear_form_order, HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(2, linear_form_vector, linear_form_order, HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form(3, linear_form_vector, linear_form_order, HERMES_ANY, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #else wf.add_vector_form(0,linear_form, linear_form_order, HERMES_ANY, &prev_rho); wf.add_vector_form(1,linear_form, linear_form_order, HERMES_ANY, &prev_rho_v_x); wf.add_vector_form(2,linear_form, linear_form_order, HERMES_ANY, &prev_rho_v_y); wf.add_vector_form(3,linear_form, linear_form_order, HERMES_ANY, &prev_e); #endif // Surface linear forms - inner edges coming from the DG formulation. #ifdef HERMES_USE_VECTOR_VALUED_FORMS wf.add_vector_form_surf(0, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(1, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(2, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(3, linear_form_interface_vector, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #else wf.add_vector_form_surf(0, linear_form_interface_0, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(1, linear_form_interface_1, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(2, linear_form_interface_2, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(3, linear_form_interface_3, linear_form_order, H2D_DG_INNER_EDGE, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #endif // Surface linear forms - inlet / outlet edges. #ifdef HERMES_USE_VECTOR_VALUED_FORMS wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_vector, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #else wf.add_vector_form_surf(0, bdy_flux_inlet_outlet_comp_0, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(1, bdy_flux_inlet_outlet_comp_1, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(2, bdy_flux_inlet_outlet_comp_2, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(3, bdy_flux_inlet_outlet_comp_3, linear_form_order, BDY_INLET_OUTLET, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #endif // Surface linear forms - Solid wall edges. #ifdef HERMES_USE_VECTOR_VALUED_FORMS wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_vector, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #else wf.add_vector_form_surf(0, bdy_flux_solid_wall_comp_0, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(1, bdy_flux_solid_wall_comp_1, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(2, bdy_flux_solid_wall_comp_2, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); wf.add_vector_form_surf(3, bdy_flux_solid_wall_comp_3, linear_form_order, BDY_SOLID_WALL, Hermes::Tuple<MeshFunction*>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e)); #endif // Filters for visualization of pressure and the two components of velocity. SimpleFilter pressure(calc_pressure_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e)); SimpleFilter u(calc_u_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e)); SimpleFilter w(calc_w_func, Hermes::Tuple<MeshFunction*>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e)); // Initialize refinement selector. L2ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Disable weighting of refinement candidates. selector.set_error_weights(1, 1, 1); //VectorView vview("Velocity", new WinGeom(0, 0, 600, 300)); //ScalarView sview("Pressure", new WinGeom(700, 0, 600, 300)); ScalarView s1("w1", new WinGeom(0, 0, 620, 300)); s1.fix_scale_width(80); ScalarView s2("w2", new WinGeom(625, 0, 600, 300)); s2.fix_scale_width(50); ScalarView s3("w3", new WinGeom(0, 350, 620, 300)); s3.fix_scale_width(80); ScalarView s4("w4", new WinGeom(625, 350, 600, 300)); s4.fix_scale_width(50); // Iteration number. int iteration = 0; // For calculation of the time derivative of the norm of the solution approximation. // Not used yet in the adaptive version. double difference; double *difference_values = new double[Space::get_num_dofs(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e))]; double *last_values = new double[Space::get_num_dofs(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e))]; for(int i = 0; i < Space::get_num_dofs(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e)); i++) last_values[i] = 0.; // Output of the approximate time derivative. // Not used yet in the adaptive version. std::ofstream time_der_out("time_der"); for(t = 0.0; t < 10; t += TAU) { info("---- Time step %d, time %3.5f.", iteration, t); iteration++; // Periodic global derefinements. if (iteration > 1 && iteration % UNREF_FREQ == 0 && REFINEMENT_COUNT > 0) { REFINEMENT_COUNT = 0; info("Global mesh derefinement."); mesh.unrefine_all_elements(); space_rho.set_uniform_order(P_INIT); space_rho_v_x.set_uniform_order(P_INIT); space_rho_v_y.set_uniform_order(P_INIT); space_e.set_uniform_order(P_INIT); } // Adaptivity loop: int as = 1; bool done = false; do { info("---- Adaptivity step %d:", as); // Construct globally refined reference mesh and setup reference space. // Global polynomial order increase = 0; int order_increase = 0; Hermes::Tuple<Space *>* ref_spaces = construct_refined_spaces(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), order_increase); // Project the previous time level solution onto the new fine mesh. info("Projecting the previous time level solution onto the new fine mesh."); OGProjection::project_global(*ref_spaces, Hermes::Tuple<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), Hermes::Tuple<Solution *>(&prev_rho, &prev_rho_v_x, &prev_rho_v_y, &prev_e), matrix_solver, Hermes::Tuple<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM)); if(as > 1) { delete rsln_rho.get_mesh(); delete rsln_rho_v_x.get_mesh(); delete rsln_rho_v_y.get_mesh(); delete rsln_e.get_mesh(); } // Assemble the reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces, is_linear); SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); // The FE problem is in fact a FV problem. dp->set_fvm(); #ifdef HERMES_USE_VECTOR_VALUED_FORMS dp->use_vector_valued_forms(); #endif dp->assemble(matrix, rhs); // Solve the linear system of the reference problem. If successful, obtain the solutions. if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), *ref_spaces, Hermes::Tuple<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e)); 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(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), Hermes::Tuple<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), Hermes::Tuple<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), matrix_solver, Hermes::Tuple<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM)); // Calculate element errors and total error estimate. info("Calculating error estimate."); Adapt* adaptivity = new Adapt(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), Hermes::Tuple<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM)); bool solutions_for_adapt = true; // Error components. Hermes::Tuple<double> *error_components = new Hermes::Tuple<double>(4); double err_est_rel_total = adaptivity->calc_err_est(Hermes::Tuple<Solution *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), Hermes::Tuple<Solution *>(&rsln_rho, &rsln_rho_v_x, &rsln_rho_v_y, &rsln_e), solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_ABS, error_components) * 100; // Report results. info("ndof_coarse: %d, ndof_fine: %d, err_est_rel: %g%%", Space::get_num_dofs(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e)), Space::get_num_dofs(*ref_spaces), err_est_rel_total); // Determine the time step. double *solution_vector = new double[Space::get_num_dofs(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e))]; OGProjection::project_global(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e), Hermes::Tuple<MeshFunction *>(&sln_rho, &sln_rho_v_x, &sln_rho_v_y, &sln_e), solution_vector, matrix_solver, Hermes::Tuple<ProjNormType>(HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM, HERMES_L2_NORM)); double min_condition = 0; Element *e; for (int _id = 0, _max = mesh.get_max_element_id(); _id < _max; _id++) \ if (((e) = mesh.get_element_fast(_id))->used) \ if ((e)->active) { AsmList al; space_rho.get_element_assembly_list(e, &al); double rho = solution_vector[al.dof[0]]; space_rho_v_x.get_element_assembly_list(e, &al); double v1 = solution_vector[al.dof[0]] / rho; space_rho_v_y.get_element_assembly_list(e, &al); double v2 = solution_vector[al.dof[0]] / rho; space_e.get_element_assembly_list(e, &al); double energy = solution_vector[al.dof[0]]; double condition = e->get_area() / (std::sqrt(v1*v1 + v2*v2) + calc_sound_speed(rho, rho*v1, rho*v2, energy)); if(condition < min_condition || min_condition == 0.) min_condition = condition; } if(TAU > min_condition) TAU = min_condition; if(TAU < min_condition * 0.9) TAU = min_condition; delete [] solution_vector; // Visualization. s1.show(&sln_rho); s2.show(&sln_rho_v_x); s3.show(&sln_rho_v_y); s4.show(&sln_e); // If err_est too large, adapt the mesh. if (err_est_rel_total < ERR_STOP && (*error_components)[1] * 100 < ERR_STOP_VEL_X) done = true; else { info("Adapting coarse mesh."); done = adaptivity->adapt(Hermes::Tuple<RefinementSelectors::Selector *>(&selector, &selector, &selector, &selector), THRESHOLD, STRATEGY, MESH_REGULARITY); REFINEMENT_COUNT++; if (Space::get_num_dofs(Hermes::Tuple<Space *>(&space_rho, &space_rho_v_x, &space_rho_v_y, &space_e)) >= NDOF_STOP) done = true; else // Increase the counter of performed adaptivity steps. as++; } // We have to empty the cache of NeighborSearch class instances. NeighborSearch::empty_main_caches(); // If used, we need to clean the vector valued form caches. #ifdef HERMES_USE_VECTOR_VALUED_FORMS DiscreteProblem::empty_form_caches(); #endif // Clean up. delete solver; delete matrix; delete rhs; delete adaptivity; for(unsigned int i = 0; i < ref_spaces->size(); i++) delete (*ref_spaces)[i]; delete dp; } while (done == false); // Debugging. /* std::ofstream out("matrix"); for(int i = 0; i < matrix->get_size(); i++) for(int j = 0; j < matrix->get_size(); j++) if(std::abs(matrix->get(i,j)) != 0) out << '(' << i << ',' << j << ')' << ':' << matrix->get(i,j) << std::endl; out.close(); out.open("rhs"); for(int j = 0; j < matrix->get_size(); j++) if(std::abs(rhs->get(j)) != 0) out << '(' << j << ')' << ':' << rhs->get(j) << std::endl; out.close(); out.open("sol"); for(int j = 0; j < matrix->get_size(); j++) out << '(' << j << ')' << ':' << solver->get_solution()[j] << std::endl; out.close(); */ // Copy the solutions into the previous time level ones. prev_rho.copy(&rsln_rho); prev_rho_v_x.copy(&rsln_rho_v_x); prev_rho_v_y.copy(&rsln_rho_v_y); prev_e.copy(&rsln_e); delete rsln_rho.get_mesh(); delete rsln_rho_v_x.get_mesh(); delete rsln_rho_v_y.get_mesh(); delete rsln_e.get_mesh(); // Visualization. /* pressure.reinit(); u.reinit(); w.reinit(); sview.show(&pressure); vview.show(&u,&w); */ } time_der_out.close(); 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); wf.add_vector_form(residual); // Initialize the FE problem. DiscreteProblem *dp = new DiscreteProblem(&wf, space); // Allocate coefficient vector. double *coeff_vec = new double[ndof]; memset(coeff_vec, 0, ndof*sizeof(double)); // 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); // Time stepping loop. double current_time = 0.0; while (current_time < T_FINAL) { // Newton's loop. // Fill vector coeff_vec using dof and coeffs arrays in elements. get_coeff_vector(space, coeff_vec); int it = 1; while (true) { // 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); char filename[100]; sprintf(filename, "solution_%g.gp", current_time); l.plot_solution(filename); info("Solution %s written.", filename); current_time += TAU; } // Plot the resulting space. space->plot("space.gp"); // Cleaning delete dp; delete rhs; delete solver; delete[] coeff_vec; delete space; delete matrix; info("Done."); return 0; }
int main(int argc, char* argv[]) { // Instantiate a class with global functions. Hermes2D hermes2d; // 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(); // Set exact solution. CustomExactSolution exact(&mesh, ALPHA); // Define right-hand side. CustomRightHandSide rhs(ALPHA); // Initialize the weak formulation. CustomWeakForm wf(&rhs); // Initialize boundary conditions DefaultEssentialBCNonConst bc(BDY_DIRICHLET, &exact); EssentialBCs bcs(&bc); // Create an H1 space with default shapeset. H1Space space(&mesh, &bcs, P_INIT); // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // 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 = Space::construct_refined_space(&space); SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); // Assemble the reference problem. info("Solving on reference mesh."); DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space); 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); // 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. double err_exact_rel = hermes2d.calc_rel_error(&sln, &exact, HERMES_H1_NORM) * 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()); int ndof = Space::get_num_dofs(&space); int n_dof_allowed = 270; 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* argv[]) { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Load the mesh. Mesh xmesh, ymesh, tmesh; H2DReader mloader; mloader.load("domain.mesh", &xmesh); // Master mesh. // Initialize multimesh hp-FEM. ymesh.copy(&xmesh); // Ydisp will share master mesh with xdisp. tmesh.copy(&xmesh); // Temp will share master mesh with xdisp. // Enter boundary markers. BCTypes bc_types_x_y; bc_types_x_y.add_bc_dirichlet(BDY_BOTTOM); bc_types_x_y.add_bc_neumann(Hermes::Tuple<int>(BDY_SIDES, BDY_TOP, BDY_HOLES)); BCTypes bc_types_t; bc_types_t.add_bc_dirichlet(BDY_HOLES); bc_types_t.add_bc_neumann(Hermes::Tuple<int>(BDY_SIDES, BDY_TOP, BDY_BOTTOM)); // Enter Dirichlet boundary values. BCValues bc_values_x_y; bc_values_x_y.add_zero(BDY_BOTTOM); BCValues bc_values_t; bc_values_t.add_const(BDY_HOLES, TEMP_INNER); // Create H1 spaces with default shapesets. H1Space xdisp(&xmesh, &bc_types_x_y, &bc_values_x_y, P_INIT_DISP); H1Space ydisp(MULTI ? &ymesh : &xmesh, &bc_types_x_y, &bc_values_x_y, P_INIT_DISP); H1Space temp(MULTI ? &tmesh : &xmesh, &bc_types_t, &bc_values_t, P_INIT_TEMP); // Initialize the weak formulation. WeakForm wf(3); wf.add_matrix_form(0, 0, callback(bilinear_form_0_0)); wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), HERMES_SYM); wf.add_matrix_form(0, 2, callback(bilinear_form_0_2)); wf.add_matrix_form(1, 1, callback(bilinear_form_1_1)); wf.add_matrix_form(1, 2, callback(bilinear_form_1_2)); wf.add_matrix_form(2, 2, callback(bilinear_form_2_2)); wf.add_vector_form(1, callback(linear_form_1)); wf.add_vector_form(2, callback(linear_form_2)); wf.add_vector_form_surf(2, callback(linear_form_surf_2)); // Initialize coarse and reference mesh solutions. Solution xdisp_sln, ydisp_sln, temp_sln, ref_xdisp_sln, ref_ydisp_sln, ref_temp_sln; // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // Initialize views. ScalarView s_view_0("Solution[xdisp]", new WinGeom(0, 0, 450, 350)); s_view_0.show_mesh(false); ScalarView s_view_1("Solution[ydisp]", new WinGeom(460, 0, 450, 350)); s_view_1.show_mesh(false); ScalarView s_view_2("Solution[temp]", new WinGeom(920, 0, 450, 350)); s_view_1.show_mesh(false); OrderView o_view_0("Mesh[xdisp]", new WinGeom(0, 360, 450, 350)); OrderView o_view_1("Mesh[ydisp]", new WinGeom(460, 360, 450, 350)); OrderView o_view_2("Mesh[temp]", new WinGeom(920, 360, 450, 350)); // DOF and CPU convergence graphs. SimpleGraph graph_dof_est, graph_cpu_est; // Adaptivity loop: int as = 1; bool done = false; do { info("---- Adaptivity step %d:", as); // Construct globally refined reference mesh and setup reference space. Hermes::Tuple<Space *>* ref_spaces = construct_refined_spaces(Hermes::Tuple<Space *>(&xdisp, &ydisp, &temp)); // Assemble the reference problem. info("Solving on reference mesh."); bool is_linear = true; DiscreteProblem* dp = new DiscreteProblem(&wf, *ref_spaces, is_linear); SparseMatrix* matrix = create_matrix(matrix_solver); Vector* rhs = create_vector(matrix_solver); Solver* solver = create_linear_solver(matrix_solver, matrix, rhs); dp->assemble(matrix, rhs); // Time measurement. cpu_time.tick(); // Solve the linear system of the reference problem. If successful, obtain the solutions. if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(), *ref_spaces, Hermes::Tuple<Solution *>(&ref_xdisp_sln, &ref_ydisp_sln, &ref_temp_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(Hermes::Tuple<Space *>(&xdisp, &ydisp, &temp), Hermes::Tuple<Solution *>(&ref_xdisp_sln, &ref_ydisp_sln, &ref_temp_sln), Hermes::Tuple<Solution *>(&xdisp_sln, &ydisp_sln, &temp_sln), matrix_solver); // View the coarse mesh solution and polynomial orders. s_view_0.show(&xdisp_sln); o_view_0.show(&xdisp); s_view_1.show(&ydisp_sln); o_view_1.show(&ydisp); s_view_2.show(&temp_sln); o_view_2.show(&temp); // Skip visualization time. cpu_time.tick(HERMES_SKIP); // Calculate element errors. info("Calculating error estimate and exact error."); Adapt* adaptivity = new Adapt(Hermes::Tuple<Space *>(&xdisp, &ydisp, &temp), Hermes::Tuple<ProjNormType>(HERMES_H1_NORM, HERMES_H1_NORM, HERMES_H1_NORM)); adaptivity->set_error_form(0, 0, bilinear_form_0_0<scalar, scalar>, bilinear_form_0_0<Ord, Ord>); adaptivity->set_error_form(0, 1, bilinear_form_0_1<scalar, scalar>, bilinear_form_0_1<Ord, Ord>); adaptivity->set_error_form(0, 2, bilinear_form_0_2<scalar, scalar>, bilinear_form_0_2<Ord, Ord>); adaptivity->set_error_form(1, 0, bilinear_form_1_0<scalar, scalar>, bilinear_form_1_0<Ord, Ord>); adaptivity->set_error_form(1, 1, bilinear_form_1_1<scalar, scalar>, bilinear_form_1_1<Ord, Ord>); adaptivity->set_error_form(1, 2, bilinear_form_1_2<scalar, scalar>, bilinear_form_1_2<Ord, Ord>); adaptivity->set_error_form(2, 2, bilinear_form_2_2<scalar, scalar>, bilinear_form_2_2<Ord, Ord>); // Calculate error estimate for each solution component and the total error estimate. Hermes::Tuple<double> err_est_rel; bool solutions_for_adapt = true; double err_est_rel_total = adaptivity->calc_err_est(Hermes::Tuple<Solution *>(&xdisp_sln, &ydisp_sln, &temp_sln), Hermes::Tuple<Solution *>(&ref_xdisp_sln, &ref_ydisp_sln, &ref_temp_sln), solutions_for_adapt, HERMES_TOTAL_ERROR_REL | HERMES_ELEMENT_ERROR_ABS, &err_est_rel) * 100; // Time measurement. cpu_time.tick(); // Report results. info("ndof_coarse[xdisp]: %d, ndof_fine[xdisp]: %d, err_est_rel[xdisp]: %g%%", xdisp.Space::get_num_dofs(), Space::get_num_dofs((*ref_spaces)[0]), err_est_rel[0]*100); info("ndof_coarse[ydisp]: %d, ndof_fine[ydisp]: %d, err_est_rel[ydisp]: %g%%", ydisp.Space::get_num_dofs(), Space::get_num_dofs((*ref_spaces)[1]), err_est_rel[1]*100); info("ndof_coarse[temp]: %d, ndof_fine[temp]: %d, err_est_rel[temp]: %g%%", temp.Space::get_num_dofs(), Space::get_num_dofs((*ref_spaces)[2]), err_est_rel[2]*100); info("ndof_coarse_total: %d, ndof_fine_total: %d, err_est_rel_total: %g%%", Space::get_num_dofs(Hermes::Tuple<Space *>(&xdisp, &ydisp, &temp)), Space::get_num_dofs(*ref_spaces), err_est_rel_total); // Add entry to DOF and CPU convergence graphs. graph_dof_est.add_values(Space::get_num_dofs(Hermes::Tuple<Space *>(&xdisp, &ydisp, &temp)), err_est_rel_total); graph_dof_est.save("conv_dof_est.dat"); graph_cpu_est.add_values(cpu_time.accumulated(), err_est_rel_total); graph_cpu_est.save("conv_cpu_est.dat"); // If err_est too large, adapt the mesh. if (err_est_rel_total < ERR_STOP) done = true; else { info("Adapting coarse mesh."); done = adaptivity->adapt(Hermes::Tuple<RefinementSelectors::Selector *>(&selector, &selector, &selector), THRESHOLD, STRATEGY, MESH_REGULARITY); } if (Space::get_num_dofs(Hermes::Tuple<Space *>(&xdisp, &ydisp, &temp)) >= NDOF_STOP) done = true; // Clean up. delete solver; delete matrix; delete rhs; delete adaptivity; if(done == false) for(unsigned int i = 0; i < ref_spaces->size(); i++) delete (*ref_spaces)[i]->get_mesh(); delete ref_spaces; delete dp; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); // Show the reference solution - the final result. s_view_0.set_title("Fine mesh Solution[xdisp]"); s_view_0.show(&ref_xdisp_sln); s_view_1.set_title("Fine mesh Solution[ydisp]"); s_view_1.show(&ref_ydisp_sln); s_view_1.set_title("Fine mesh Solution[temp]"); s_view_1.show(&ref_temp_sln); // Wait for all views to be closed. View::wait(); return 0; };
int main(int argc, char* argv[]) { // Time measurement. TimePeriod cpu_time; cpu_time.tick(); // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("domain2.mesh", &mesh); // Perform initial mesh refinements. 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::vector<int>(BDY_RIGHT, BDY_TOP, BDY_LEFT)); bc_types.add_bc_neumann(BDY_BUTTOM); // Create an H1 space with default shapeset. H1Space space(&mesh, &bc_types, essential_bc_values, P_INIT); // Initialize the weak formulation. WeakForm wf; wf.add_matrix_form(callback(bilinear_form_iron), HERMES_SYM, 3); wf.add_matrix_form(callback(bilinear_form_wire), HERMES_SYM, 2); wf.add_matrix_form(callback(bilinear_form_air), HERMES_SYM, 1); wf.add_vector_form(callback(linear_form_wire), 2); // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Initialize refinement selector. H1ProjBasedSelector selector(CAND_LIST, CONV_EXP, H2DRS_DEFAULT_ORDER); // DOF and CPU convergence graphs initialization. SimpleGraph graph_dof, graph_cpu; // 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); if (matrix_solver == SOLVER_AZTECOO) { ((AztecOOSolver*) solver)->set_solver(iterative_method); ((AztecOOSolver*) solver)->set_precond(preconditioner); // Using default iteration parameters (see solver/aztecoo.h). } 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."); Adapt* adaptivity = new Adapt(&space); double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 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); } 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; // Increase counter. as++; } while (done == false); verbose("Total running time: %g s", cpu_time.accumulated()); int ndof = Space::get_num_dofs(&space); #define ERROR_SUCCESS 0 #define ERROR_FAILURE -1 printf("ndof allowed = %d\n", 650); printf("ndof actual = %d\n", ndof); if (ndof < 650) { // ndofs was 625 atthe time this test was created printf("Success!\n"); return ERROR_SUCCESS; } else { printf("Failure!\n"); return ERROR_FAILURE; } }
int main(int argc, char* argv[]) { // Load the mesh. Mesh mesh; H2DReader mloader; mloader.load("square_quad.mesh", &mesh); // quadrilaterals // mloader.load("square_tri.mesh", &mesh); // triangles // Perform initial mesh refinement. for (int i=0; i<INIT_REF_NUM; i++) mesh.refine_all_elements(); mesh.refine_towards_boundary(BDY_LAYER, INIT_REF_NUM_BDY); // Enter boundary markers. BCTypes bc_types; bc_types.add_bc_dirichlet(Hermes::Tuple<int>(BDY_LAYER, BDY_REST)); // Enter Dirichlet boundary values. BCValues bc_values; bc_values.add_function(BDY_LAYER, essential_bc_values); bc_values.add_const(BDY_REST, 1.0); // 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)); if (STABILIZATION_ON == true) { wf.add_matrix_form(callback(bilinear_form_stabilization)); } if (SHOCK_CAPTURING_ON == true) { wf.add_matrix_form(callback(bilinear_form_shock_capturing)); } // Initialize coarse and reference mesh solution. Solution sln, ref_sln; // Initialize refinement selector. H1ProjBasedSelector 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); // 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); int n_dof_allowed = 570; printf("n_dof_actual = %d\n", ndof); printf("n_dof_allowed = %d\n", n_dof_allowed);// ndofs was 558 at the time this test was created if (ndof <= n_dof_allowed) { printf("Success!\n"); return ERR_SUCCESS; } else { printf("Failure!\n"); return ERR_FAILURE; } }
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); info("N_dof = %d.", Space::get_num_dofs(space)); // Initialize the weak formulation. WeakForm wf(4); wf.add_matrix_form(0, 0, jacobian_1_1); wf.add_matrix_form(0, 1, jacobian_1_2); wf.add_matrix_form(1, 0, jacobian_2_1); wf.add_matrix_form(1, 1, jacobian_2_2); wf.add_matrix_form(1, 2, jacobian_2_3); wf.add_matrix_form(2, 1, jacobian_3_2); wf.add_matrix_form(2, 2, jacobian_3_3); wf.add_matrix_form(2, 3, jacobian_3_4); wf.add_matrix_form(3, 2, jacobian_4_3); wf.add_matrix_form(3, 3, jacobian_4_4); wf.add_vector_form(0, residual_1); wf.add_vector_form(1, residual_2); wf.add_vector_form(2, residual_3); wf.add_vector_form(3, residual_4); // 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(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); // 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); // Time measurement. cpu_time.tick(); // Calculate element errors and total error estimate. info("Calculating error estimate."); Adapt* adaptivity = new Adapt(&space); double err_est_rel = adaptivity->calc_err_est(&sln, &ref_sln) * 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 = 1230; printf("n_dof_actual = %d\n", ndof); // was 1218 at the time this test was last revisited 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; } }