int main(int argc, char* argv[])
{
// load the mesh file
Mesh mesh;
mesh.load("sample.mesh");
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create the x displacement space
H1Space xdisp(&mesh, &shapeset);
xdisp.set_bc_types(bc_types);
xdisp.set_bc_values(bc_values);
xdisp.set_uniform_order(P_INIT);
int ndofs = xdisp.assign_dofs(0);
// create the y displacement space
H1Space ydisp(&mesh, &shapeset);
ydisp.set_bc_types(bc_types);
ydisp.set_bc_values(bc_values);
ydisp.set_uniform_order(P_INIT);
ndofs += ydisp.assign_dofs(ndofs);
// initialize the weak formulation
WeakForm wf(2);
wf.add_biform(0, 0, callback(bilinear_form_0_0), SYM); // Note that only one symmetric part is
wf.add_biform(0, 1, callback(bilinear_form_0_1), SYM); // added in the case of symmetric bilinear
wf.add_biform(1, 1, callback(bilinear_form_1_1), SYM); // forms.
wf.add_liform_surf(0, callback(linear_form_surf_0), 3);
wf.add_liform_surf(1, callback(linear_form_surf_1), 3);
// initialize the linear system and solver
UmfpackSolver umfpack;
LinSystem sys(&wf, &umfpack);
sys.set_spaces(2, &xdisp, &ydisp);
sys.set_pss(1, &pss);
// assemble the stiffness matrix and solve the system
Solution xsln, ysln;
sys.assemble();
sys.solve(2, &xsln, &ysln);
// visualize the solution
ScalarView view("Von Mises stress [Pa]", 50, 50, 1200, 600);
VonMisesFilter stress(&xsln, &ysln, lambda, mu);
view.show(&stress, EPS_HIGH, FN_VAL_0, &xsln, &ysln, 1.5e5);
// wait for keyboard or mouse input
View::wait("Waiting for keyboard or mouse input.");
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("sample.mesh", &mesh);
// Perform uniform mesh refinement.
mesh.refine_all_elements();
// Create x- and y- displacement space using the default H1 shapeset.
H1Space xdisp(&mesh, bc_types, essential_bc_values, P_INIT);
H1Space ydisp(&mesh, bc_types, essential_bc_values, P_INIT);
// Initialize the weak formulation.
WeakForm wf(2);
wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), H2D_SYM); // Note that only one symmetric part is
wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), H2D_SYM); // added in the case of symmetric bilinear
wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), H2D_SYM); // forms.
wf.add_vector_form_surf(0, callback(linear_form_surf_0), GAMMA_3_BDY);
wf.add_vector_form_surf(1, callback(linear_form_surf_1), GAMMA_3_BDY);
// Initialize the linear system.
LinSystem ls(&wf, Tuple<Space*>(&xdisp, &ydisp));
// Assemble and solve the matrix problem.
Solution xsln, ysln;
ls.assemble();
ls.solve(Tuple<Solution*>(&xsln, &ysln));
// Visualize the solution.
ScalarView view("Von Mises stress [Pa]", 0, 0, 800, 400);
VonMisesFilter stress(&xsln, &ysln, lambda, mu);
view.show_mesh(false);
view.show(&stress, H2D_EPS_HIGH, H2D_FN_VAL_0, &xsln, &ysln, 1.5e5);
// Wait for the view to be closed.
View::wait();
return 0;
}
int main(int argc, char **args)
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh mesh;
ExodusIIReader mloader;
mloader.load("brick_with_hole_hex.e", &mesh);
// Perform initial mesh refinement.
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Create H1 space with default shapeset for x-displacement component.
H1Space xdisp(&mesh, bc_types_x, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Create H1 space with default shapeset for y-displacement component.
H1Space ydisp(&mesh, bc_types_y, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Create H1 space with default shapeset for z-displacement component.
H1Space zdisp(&mesh, bc_types_z, essential_bc_values, Ord3(P_INIT_X, P_INIT_Y, P_INIT_Z));
// Initialize weak formulation.
WeakForm wf(3);
wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), HERMES_SYM);
wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), HERMES_SYM);
wf.add_matrix_form(0, 2, callback(bilinear_form_0_2), HERMES_SYM);
wf.add_vector_form_surf(0, callback(surf_linear_form_x), bdy_force);
wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), HERMES_SYM);
wf.add_matrix_form(1, 2, callback(bilinear_form_1_2), HERMES_SYM);
wf.add_vector_form_surf(1, callback(surf_linear_form_y), bdy_force);
wf.add_matrix_form(2, 2, callback(bilinear_form_2_2), HERMES_SYM);
wf.add_vector_form_surf(2, callback(surf_linear_form_z), bdy_force);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::Tuple<Space *>(&xdisp, &ydisp, &zdisp), is_linear);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Initialize the preconditioner in the case of SOLVER_AZTECOO.
if (matrix_solver == SOLVER_AZTECOO)
{
((AztecOOSolver*) solver)->set_solver(iterative_method);
((AztecOOSolver*) solver)->set_precond(preconditioner);
// Using default iteration parameters (see solver/aztecoo.h).
}
// Assemble stiffness matrix and load vector.
info("Assembling the linear problem (ndof: %d).", Space::get_num_dofs(Hermes::Tuple<Space *>(&xdisp, &ydisp, &zdisp)));
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution xsln(xdisp.get_mesh());
Solution ysln(ydisp.get_mesh());
Solution zsln(zdisp.get_mesh());
if(solver->solve()) Solution::vector_to_solutions(solver->get_solution(),
Hermes::Tuple<Space *>(&xdisp, &ydisp, &zdisp), Hermes::Tuple<Solution *>(&xsln, &ysln, &zsln));
else error ("Matrix solver failed.\n");
// Output all components of the solution.
if (solution_output) out_fn_vtk(&xsln, &ysln, &zsln, "sln");
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solutions saved. Total running time: %g s.", cpu_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
return 0;
}
int main(int argc, char* argv[])
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Load the mesh.
Mesh xmesh, ymesh, tmesh;
MeshReaderH2D 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.
// Initialize boundary conditions.
BCTypes bc_types_x_y;
bc_types_x_y.add_bc_dirichlet(BDY_BOTTOM);
bc_types_x_y.add_bc_neumann(Hermes::vector<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::vector<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<double> xdisp(&xmesh, &bc_types_x_y, &bc_values_x_y, P_INIT_DISP);
H1Space<double> ydisp(MULTI ? &ymesh : &xmesh, &bc_types_x_y, &bc_values_x_y, P_INIT_DISP);
H1Space<double> 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<double> 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::vector<Space<double> *>* ref_spaces = Space<double>::construct_refined_spaces(Hermes::vector<Space<double> *>(&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<double>* matrix = create_matrix<double>(matrix_solver_type);
Vector<double>* rhs = create_vector<double>(matrix_solver_type);
LinearSolver<double>* solver = create_linear_solver<double>(matrix_solver_type, 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::vector<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::vector<Space<double> *>(&xdisp, &ydisp, &temp), Hermes::vector<Solution *>(&ref_xdisp_sln, &ref_ydisp_sln, &ref_temp_sln),
Hermes::vector<Solution *>(&xdisp_sln, &ydisp_sln, &temp_sln), matrix_solver_type);
// 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::vector<Space<double> *>(&xdisp, &ydisp, &temp));
adaptivity->set_error_form(0, 0, bilinear_form_0_0<double, double>, bilinear_form_0_0<Ord, Ord>);
adaptivity->set_error_form(0, 1, bilinear_form_0_1<double, double>, bilinear_form_0_1<Ord, Ord>);
adaptivity->set_error_form(0, 2, bilinear_form_0_2<double, double>, bilinear_form_0_2<Ord, Ord>);
adaptivity->set_error_form(1, 0, bilinear_form_1_0<double, double>, bilinear_form_1_0<Ord, Ord>);
adaptivity->set_error_form(1, 1, bilinear_form_1_1<double, double>, bilinear_form_1_1<Ord, Ord>);
adaptivity->set_error_form(1, 2, bilinear_form_1_2<double, double>, bilinear_form_1_2<Ord, Ord>);
adaptivity->set_error_form(2, 2, bilinear_form_2_2<double, double>, bilinear_form_2_2<Ord, Ord>);
// 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 *>(&xdisp_sln, &ydisp_sln, &temp_sln),
Hermes::vector<Solution *>(&ref_xdisp_sln, &ref_ydisp_sln, &ref_temp_sln), &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<double>::get_num_dofs(), Space<double>::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<double>::get_num_dofs(), Space<double>::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<double>::get_num_dofs(), Space<double>::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<double>::get_num_dofs(Hermes::vector<Space<double> *>(&xdisp, &ydisp, &temp)), Space<double>::get_num_dofs(*ref_spaces), err_est_rel_total);
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space<double>::get_num_dofs(Hermes::vector<Space<double> *>(&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::vector<RefinementSelectors::Selector *>(&selector, &selector, &selector),
THRESHOLD, STRATEGY, MESH_REGULARITY);
}
if (Space<double>::get_num_dofs(Hermes::vector<Space<double> *>(&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[])
{
// Load the mesh file.
Mesh mesh;
H2DReader mloader;
mloader.load("sample.mesh", &mesh);
// Create the x- and y-displacement spaces.
H1Space xdisp(&mesh, bc_types, essential_bc_values, P_INIT);
H1Space ydisp(&mesh, bc_types, essential_bc_values, P_INIT);
// Initialize the weak formulation.
WeakForm wf(2);
wf.add_matrix_form(0, 0, callback(bilinear_form_0_0), H2D_SYM); // Note that only one symmetric part is
wf.add_matrix_form(0, 1, callback(bilinear_form_0_1), H2D_SYM); // added in the case of symmetric bilinear
wf.add_matrix_form(1, 1, callback(bilinear_form_1_1), H2D_SYM); // forms.
wf.add_vector_form_surf(0, callback(linear_form_surf_0), GAMMA_3_BDY);
wf.add_vector_form_surf(1, callback(linear_form_surf_1), GAMMA_3_BDY);
// Initialize the linear system.
LinSystem sys(&wf, Tuple<Space*>(&xdisp, &ydisp));
// Testing n_dof and correctness of solution vector
// for p_init = 1, 2, ..., 10
int success = 1;
Solution xsln, ysln;
for (int p_init = 1; p_init <= 10; p_init++) {
printf("********* p_init = %d *********\n", p_init);
xdisp.set_uniform_order(p_init);
ydisp.set_uniform_order(p_init);
// Assemble and solve the matrix problem.
sys.assemble();
sys.solve(Tuple<Solution*>(&xsln, &ysln));
scalar *sol_vector;
int n_dof;
sys.get_solution_vector(sol_vector, n_dof);
printf("n_dof = %d\n", n_dof);
double sum = 0;
for (int i=0; i < n_dof; i++) sum += sol_vector[i];
printf("coefficient sum = %g\n", sum);
// Actual test. The values of 'sum' depend on the
// current shapeset. If you change the shapeset,
// you need to correct these numbers.
if (p_init == 1 && fabs(sum - 3.50185e-06) > 1e-3) success = 0;
if (p_init == 2 && fabs(sum - 4.34916e-06) > 1e-3) success = 0;
if (p_init == 3 && fabs(sum - 4.60553e-06) > 1e-3) success = 0;
if (p_init == 4 && fabs(sum - 4.65616e-06) > 1e-3) success = 0;
if (p_init == 5 && fabs(sum - 4.62893e-06) > 1e-3) success = 0;
if (p_init == 6 && fabs(sum - 4.64336e-06) > 1e-3) success = 0;
if (p_init == 7 && fabs(sum - 4.63724e-06) > 1e-3) success = 0;
if (p_init == 8 && fabs(sum - 4.64491e-06) > 1e-3) success = 0;
if (p_init == 9 && fabs(sum - 4.64582e-06) > 1e-3) success = 0;
if (p_init == 10 && fabs(sum - 4.65028e-06) > 1e-3) success = 0;
}
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
if (success == 1) {
printf("Success!\n");
return ERROR_SUCCESS;
}
else {
printf("Failure!\n");
return ERROR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh xmesh, ymesh;
H2DReader mloader;
mloader.load("bracket.mesh", &xmesh);
// create initial mesh for the vertical displacement component,
// identical to the mesh for the horizontal displacement
// (bracket.mesh becomes a master mesh)
ymesh.copy(&xmesh);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset xpss(&shapeset);
PrecalcShapeset ypss(&shapeset);
// create the x displacement space
H1Space xdisp(&xmesh, &shapeset);
xdisp.set_bc_types(bc_types);
xdisp.set_bc_values(bc_values);
xdisp.set_uniform_order(P_INIT);
// create the y displacement space
H1Space ydisp(MULTI ? &ymesh : &xmesh, &shapeset);
ydisp.set_bc_types(bc_types);
ydisp.set_bc_values(bc_values);
ydisp.set_uniform_order(P_INIT);
// enumerate basis functions
int ndofs = xdisp.assign_dofs();
ndofs += ydisp.assign_dofs(ndofs);
// initialize the weak formulation
WeakForm wf(2);
wf.add_biform(0, 0, callback(bilinear_form_0_0), SYM); // note that only one symmetric part is
wf.add_biform(0, 1, callback(bilinear_form_0_1), SYM); // added in the case of symmetric bilinear
wf.add_biform(1, 1, callback(bilinear_form_1_1), SYM); // forms
wf.add_liform_surf(1, callback(linear_form_surf_1), marker_top);
// visualization of solution and meshes
OrderView xoview("X polynomial orders", 0, 0, 500, 500);
OrderView yoview("Y polynomial orders", 510, 0, 500, 500);
ScalarView sview("Von Mises stress [Pa]", 1020, 0, 500, 500);
// matrix solver
UmfpackSolver umfpack;
// DOF and CPU convergence graphs
SimpleGraph graph_dof, graph_cpu;
// adaptivity loop
int it = 1;
bool done = false;
double cpu = 0.0;
Solution x_sln_coarse, y_sln_coarse;
Solution x_sln_fine, y_sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
//calculating the number of degrees of freedom
ndofs = xdisp.assign_dofs();
ndofs += ydisp.assign_dofs(ndofs);
printf("xdof=%d, ydof=%d\n", xdisp.get_num_dofs(), ydisp.get_num_dofs());
// solve the coarse mesh problem
LinSystem ls(&wf, &umfpack);
ls.set_spaces(2, &xdisp, &ydisp);
ls.set_pss(2, &xpss, &ypss);
ls.assemble();
ls.solve(2, &x_sln_coarse, &y_sln_coarse);
// time measurement
cpu += end_time();
// view the solution -- this can be slow; for illustration only
VonMisesFilter stress_coarse(&x_sln_coarse, &y_sln_coarse, mu, lambda);
sview.set_min_max_range(0, 3e4);
sview.show(&stress_coarse);
xoview.show(&xdisp);
yoview.show(&ydisp);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(2, &x_sln_fine, &y_sln_fine);
// calculate element errors and total error estimate
H1OrthoHP hp(2, &xdisp, &ydisp);
hp.set_biform(0, 0, bilinear_form_0_0<scalar, scalar>, bilinear_form_0_0<Ord, Ord>);
hp.set_biform(0, 1, bilinear_form_0_1<scalar, scalar>, bilinear_form_0_1<Ord, Ord>);
hp.set_biform(1, 0, bilinear_form_1_0<scalar, scalar>, bilinear_form_1_0<Ord, Ord>);
hp.set_biform(1, 1, bilinear_form_1_1<scalar, scalar>, bilinear_form_1_1<Ord, Ord>);
double err_est = hp.calc_error_2(&x_sln_coarse, &y_sln_coarse, &x_sln_fine, &y_sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// time measurement
cpu += end_time();
// add entry to DOF convergence graph
graph_dof.add_values(xdisp.get_num_dofs() + ydisp.get_num_dofs(), err_est);
graph_dof.save("conv_dof.dat");
// add entry to CPU convergence graph
graph_cpu.add_values(cpu, err_est);
graph_cpu.save("conv_cpu.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY, CONV_EXP, MAX_ORDER, SAME_ORDERS);
ndofs = xdisp.assign_dofs();
ndofs += ydisp.assign_dofs(ndofs);
if (ndofs >= NDOF_STOP) done = true;
}
}
while (!done);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
VonMisesFilter stress_fine(&x_sln_fine, &y_sln_fine, mu, lambda);
sview.set_title("Final solution");
sview.set_min_max_range(0, 3e4);
sview.show(&stress_fine);
// wait for all views to be closed
View::wait();
return 0;
}
/***********************************************************************************
* main program *
***********************************************************************************/
int main(int argc, char **argv) {
#ifdef WITH_PETSC
PetscInitialize(&argc, &argv, (char *) PETSC_NULL, PETSC_NULL);
PetscPushErrorHandler(PetscIgnoreErrorHandler, PETSC_NULL); // Disable PETSc error handler.
#endif
// Load the initial mesh.
Mesh mesh;
Mesh3DReader mloader;
mloader.load("l-beam.mesh3d", &mesh);
// Initial uniform mesh refinements.
printf("Performing %d initial mesh refinements.\n", INIT_REF_NUM);
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Word_t (nelem) = mesh.get_num_elements();
printf("New number of elements is %d.\n", (int) nelem);
// Initialize the shapeset and the cache.
H1ShapesetLobattoHex shapeset;
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoMatrix mat;
PardisoVector rhs;
PardisoLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
// Create H1 spaces x-displacement component.
H1Space xdisp(&mesh, &shapeset);
xdisp.set_bc_types(bc_types_x);
xdisp.set_uniform_order(order3_t(P_INIT, P_INIT, P_INIT));
// Create H1 spaces y-displacement component.
H1Space ydisp(&mesh, &shapeset);
ydisp.set_bc_types(bc_types_y);
ydisp.set_uniform_order(order3_t(P_INIT, P_INIT, P_INIT));
// Create H1 spaces z-displacement component.
H1Space zdisp(&mesh, &shapeset);
zdisp.set_bc_types(bc_types_z);
zdisp.set_uniform_order(order3_t(P_INIT, P_INIT, P_INIT));
// Assign DOF.
int ndofs = 0;
ndofs += xdisp.assign_dofs(ndofs);
ndofs += ydisp.assign_dofs(ndofs);
ndofs += zdisp.assign_dofs(ndofs);
printf(" - Number of DOFs: %d\n", ndofs);
// Initialized the Weak formulation.
WeakForm wf(3);
wf.add_matrix_form(0, 0, bilinear_form_0_0<double, scalar>, bilinear_form_0_0<ord_t, ord_t>, SYM);
wf.add_matrix_form(0, 1, bilinear_form_0_1<double, scalar>, bilinear_form_0_1<ord_t, ord_t>, SYM);
wf.add_matrix_form(0, 2, bilinear_form_0_2<double, scalar>, bilinear_form_0_2<ord_t, ord_t>, SYM);
wf.add_vector_form_surf(0, surf_linear_form_0<double, scalar>, surf_linear_form_0<ord_t, ord_t>);
wf.add_matrix_form(1, 1, bilinear_form_1_1<double, scalar>, bilinear_form_1_1<ord_t, ord_t>, SYM);
wf.add_matrix_form(1, 2, bilinear_form_1_2<double, scalar>, bilinear_form_1_2<ord_t, ord_t>, SYM);
wf.add_vector_form_surf(1, surf_linear_form_1<double, scalar>, surf_linear_form_1<ord_t, ord_t>);
wf.add_matrix_form(2, 2, bilinear_form_2_2<double, scalar>, bilinear_form_2_2<ord_t, ord_t>, SYM);
wf.add_vector_form_surf(2, surf_linear_form_2<double, scalar>, surf_linear_form_2<ord_t, ord_t>, 5);
// Initialize the mesh problem.
LinearProblem lp(&wf);
lp.set_spaces(Tuple<Space *>(&xdisp, &ydisp, &zdisp));
// Assemble stiffness matrix
printf(" - Assembling... "); fflush(stdout);
Timer tmr_assemble;
tmr_assemble.start();
bool assembled = lp.assemble(&mat, &rhs);
tmr_assemble.stop();
if (assembled)
printf("done in %s (%lf secs)\n", tmr_assemble.get_human_time(), tmr_assemble.get_seconds());
else
error("failed!");
// Solve the stiffness matrix.
printf(" - Solving... "); fflush(stdout);
Timer tmr_solve;
tmr_solve.start();
bool solved = solver.solve();
tmr_solve.stop();
if (solved)
printf("done in %s (%lf secs)\n", tmr_solve.get_human_time(), tmr_solve.get_seconds());
else {
printf("failed\n");
}
// Construct a solution.
double *s = solver.get_solution();
Solution xsln(&mesh), ysln(&mesh), zsln(&mesh);
xsln.set_fe_solution(&xdisp, s);
ysln.set_fe_solution(&ydisp, s);
zsln.set_fe_solution(&zdisp, s);
// Output the solutions.
printf(" - Output... "); fflush(stdout);
out_fn(&xsln, &ysln, &zsln, "disp");
printf("done\n");
#ifdef WITH_PETSC
mat.free();
rhs.free();
PetscFinalize();
#endif
return 1;
}
int main(int argc, char* argv[])
{
// load the mesh file
Mesh mesh;
H2DReader mloader;
mloader.load("sample.mesh", &mesh);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create the x displacement space
H1Space xdisp(&mesh, &shapeset);
xdisp.set_bc_types(bc_types);
xdisp.set_bc_values(bc_values);
// create the y displacement space
H1Space ydisp(&mesh, &shapeset);
ydisp.set_bc_types(bc_types);
ydisp.set_bc_values(bc_values);
// initialize the weak formulation
WeakForm wf(2);
wf.add_biform(0, 0, callback(bilinear_form_0_0), SYM); // Note that only one symmetric part is
wf.add_biform(0, 1, callback(bilinear_form_0_1), SYM); // added in the case of symmetric bilinear
wf.add_biform(1, 1, callback(bilinear_form_1_1), SYM); // forms.
wf.add_liform_surf(0, callback(linear_form_surf_0), 3);
wf.add_liform_surf(1, callback(linear_form_surf_1), 3);
// initialize the linear system and solver
UmfpackSolver umfpack;
LinSystem sys(&wf, &umfpack);
sys.set_spaces(2, &xdisp, &ydisp);
sys.set_pss(1, &pss);
// testing n_dof and correctness of solution vector
// for p_init = 1, 2, ..., 10
int success = 1;
for (int p_init = 1; p_init <= 10; p_init++) {
printf("********* p_init = %d *********\n", p_init);
xdisp.set_uniform_order(p_init);
int ndofs = xdisp.assign_dofs(0);
ydisp.set_uniform_order(p_init);
ndofs += ydisp.assign_dofs(ndofs);
// assemble the stiffness matrix and solve the system
Solution xsln, ysln;
sys.assemble();
sys.solve(2, &xsln, &ysln);
scalar *sol_vector;
int n_dof;
sys.get_solution_vector(sol_vector, n_dof);
printf("n_dof = %d\n", n_dof);
double sum = 0;
for (int i=0; i < n_dof; i++) sum += sol_vector[i];
printf("coefficient sum = %g\n", sum);
// Actual test. The values of 'sum' depend on the
// current shapeset. If you change the shapeset,
// you need to correct these numbers.
if (p_init == 1 && fabs(sum - 3.50185e-06) > 1e-3) success = 0;
if (p_init == 2 && fabs(sum - 4.34916e-06) > 1e-3) success = 0;
if (p_init == 3 && fabs(sum - 4.60553e-06) > 1e-3) success = 0;
if (p_init == 4 && fabs(sum - 4.65616e-06) > 1e-3) success = 0;
if (p_init == 5 && fabs(sum - 4.62893e-06) > 1e-3) success = 0;
if (p_init == 6 && fabs(sum - 4.64336e-06) > 1e-3) success = 0;
if (p_init == 7 && fabs(sum - 4.63724e-06) > 1e-3) success = 0;
if (p_init == 8 && fabs(sum - 4.64491e-06) > 1e-3) success = 0;
if (p_init == 9 && fabs(sum - 4.64582e-06) > 1e-3) success = 0;
if (p_init == 10 && fabs(sum - 4.65028e-06) > 1e-3) success = 0;
}
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
if (success == 1) {
printf("Success!\n");
return ERROR_SUCCESS;
}
else {
printf("Failure!\n");
return ERROR_FAILURE;
}
}