// l2 product
double l2_product(RealFunction *fu, RealFunction *fv) {
_F_
Quad3D *quad = get_quadrature(MODE);
// integrate with maximum order
order3_t o = fu->get_fn_order() + fv->get_fn_order() + order3_t(2, 2, 2);
o.limit();
int np = quad->get_num_points(o);
QuadPt3D *pt = quad->get_points(o);
fu->precalculate(np, pt, FN_DEFAULT);
fv->precalculate(np, pt, FN_DEFAULT);
scalar *u0, *u1, *u2;
u0 = fu->get_fn_values(0);
u1 = fu->get_fn_values(1);
u2 = fu->get_fn_values(2);
scalar *v0, *v1, *v2;
v0 = fv->get_fn_values(0);
v1 = fv->get_fn_values(1);
v2 = fv->get_fn_values(2);
// integrating over reference brick -> jacobian is 1.0 (we do not have to bother with refmap)
double result = 0.0;
for (int i = 0; i < np; i++)
result += pt[i].w * (REAL(sqr(u0[i] - v0[i]) + sqr(u1[i] - v1[i]) + sqr(u2[i] - v2[i])));
return result;
}
bool test_lin_indep(Shapeset *shapeset) {
_F_
printf("I. linear independency\n");
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
ShapeFunction pss_u(shapeset), pss_v(shapeset);
int n = Hex::NUM_EDGES * shapeset->get_num_edge_fns(H3D_MAX_ELEMENT_ORDER)
+ Hex::NUM_FACES * shapeset->get_num_face_fns(order2_t(H3D_MAX_ELEMENT_ORDER, H3D_MAX_ELEMENT_ORDER))
+ shapeset->get_num_bubble_fns(order3_t(H3D_MAX_ELEMENT_ORDER, H3D_MAX_ELEMENT_ORDER, H3D_MAX_ELEMENT_ORDER));
printf("number of functions = %d\n", n);
int *fn_idx = new int[n];
int m = 0;
// edge fns
for (int i = 0; i < Hex::NUM_EDGES; i++) {
int order = H3D_MAX_ELEMENT_ORDER;
int *edge_idx = shapeset->get_edge_indices(i, 0, order);
for (int j = 0; j < shapeset->get_num_edge_fns(order); j++, m++)
fn_idx[m] = edge_idx[j];
}
// face fns
for (int i = 0; i < Hex::NUM_FACES; i++) {
order2_t order(H3D_MAX_ELEMENT_ORDER, H3D_MAX_ELEMENT_ORDER);
int *face_idx = shapeset->get_face_indices(i, 0, order);
for (int j = 0; j < shapeset->get_num_face_fns(order); j++, m++)
fn_idx[m] = face_idx[j];
}
// bubble
order3_t order(H3D_MAX_ELEMENT_ORDER, H3D_MAX_ELEMENT_ORDER, H3D_MAX_ELEMENT_ORDER);
int *bubble_idx = shapeset->get_bubble_indices(order);
for (int j = 0; j < shapeset->get_num_bubble_fns(order); j++, m++)
fn_idx[m] = bubble_idx[j];
// precalc structure
mat.prealloc(n);
for (int i = 0; i < n; i++)
for (int j = 0; j < n; j++)
mat.pre_add_ij(i, j);
mat.alloc();
rhs.alloc(n);
printf("assembling matrix ");
for (int i = 0; i < n; i++) {
pss_u.set_active_shape(fn_idx[i]);
printf(".");
fflush(stdout); // prevent caching of output (to see that it did not freeze)
for (int j = 0; j < n; j++) {
pss_v.set_active_shape(fn_idx[j]);
double value = l2_product(&pss_u, &pss_v);
mat.add(i, j, value);
}
}
printf("\n");
for (int i = 0; i < n; i++)
rhs.add(i, 0.0);
printf("solving matrix\n");
// solve the system
if (solver.solve()) {
double *sln = solver.get_solution();
bool indep = true;
for (int i = 1; i < n + 1; i++) {
if (sln[i] >= EPS) {
indep = false;
break;
}
}
if (indep)
printf("ok\n");
else
printf("Shape functions are not linearly independent\n");
}
else {
printf("Shape functions are not linearly independent\n");
}
delete[] fn_idx;
return true;
}
/***********************************************************************************
* main program *
************************************************************************************/
int main(int argc, char **args)
{
#ifdef WITH_PETSC
PetscInitialize(NULL, NULL, PETSC_NULL, PETSC_NULL);
PetscPushErrorHandler(PetscIgnoreErrorHandler, PETSC_NULL); // Disable PETSc error handler.
#endif
// Load the inital mesh.
Mesh mesh;
Mesh3DReader mesh_loader;
mesh_loader.load("hexahedron.mesh3d", &mesh);
// Initial uniform mesh refinements.
printf("Performing %d initial mesh refinements.\n", INIT_REF_NUM);
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Word_t (nelem) = mesh.get_num_elements();
printf("New number of elements is %d.\n", nelem);
//Initialize the shapeset and the cache.
H1ShapesetLobattoHex shapeset;
//Matrix solver.
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
// Graphs of DOF convergence.
GnuplotGraph graph;
graph.set_captions("", "Degrees of Freedom", "Error [%]");
graph.set_log_y();
graph.add_row("Total error", "k", "-", "O");
// Create H1 space to setup the problem.
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
space.set_uniform_order(order3_t(P_INIT, P_INIT, P_INIT));
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(biform<double, double>, biform<ord_t, ord_t>, SYM, ANY);
wf.add_vector_form(liform<double, double>, liform<ord_t, ord_t>, ANY);
// Initialize the coarse mesh problem.
LinProblem lp(&wf);
lp.set_space(&space);
// Adaptivity loop.
int as = 0;
bool done = false;
do {
printf("\n---- Adaptivity step %d:\n", as);
printf("\nSolving on coarse mesh:\n");
// Procedures for coarse mesh problem.
// Assign DOF.
int ndof = space.assign_dofs();
printf(" - Number of DOF: %d\n", ndof);
// Assemble stiffness matrix and rhs.
printf(" - Assembling... ");
fflush(stdout);
if (lp.assemble(&mat, &rhs))
printf("done in %lf secs.\n", lp.get_time());
else
error("failed!");
// Solve the system.
printf(" - Solving... ");
fflush(stdout);
bool solved = solver.solve();
if (solved)
printf("done in %lf secs.\n", solver.get_time());
else
{
printf("Failed.\n");
break;
}
// Construct a solution.
Solution sln(&mesh);
sln.set_fe_solution(&space, solver.get_solution());
// Output the orders and the solution.
if (do_output)
{
out_orders(&space, "order", as);
out_fn(&sln, "sln", as);
}
// Solving fine mesh problem.
printf("Solving on fine mesh:\n");
// Matrix solver.
#if defined WITH_UMFPACK
UMFPackLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_PETSC
PetscLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsSolver rsolver(&mat, &rhs);
#endif
// Construct the refined mesh for reference(refined) solution.
Mesh rmesh;
rmesh.copy(mesh);
rmesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
// Setup space for the reference (globally refined) solution.
Space *rspace = space.dup(&rmesh);
rspace->copy_orders(space, 1);
// Initialize the mesh problem for reference solution.
LinProblem rlp(&wf);
rlp.set_space(rspace);
// Assign DOF.
int rndof = rspace->assign_dofs();
printf(" - Number of DOF: %d\n", rndof);
// Assemble stiffness matric and rhs.
printf(" - Assembling... ");
fflush(stdout);
if (rlp.assemble(&mat, &rhs))
printf("done in %lf secs.\n", rlp.get_time());
else
error("failed!");
// Solve the system.
printf(" - Solving... ");
fflush(stdout);
bool rsolved = rsolver.solve();
if (rsolved)
printf("done in %lf secs.\n", rsolver.get_time());
else
{
printf("failed.\n");
break;
}
// Construct the reference(refined) solution.
Solution rsln(&rmesh);
rsln.set_fe_solution(rspace, rsolver.get_solution());
// Compare coarse and fine mesh.
// Calculate the error estimate wrt. refined mesh solution.
double err = h1_error(&sln, &rsln);
printf(" - H1 error: % lf\n", err * 100);
// Save it to the graph.
graph.add_value(0, ndof, err * 100);
if (do_output)
graph.save("conv.gp");
// Calculate error estimates for adaptivity.
printf("Adaptivity\n");
printf(" - calculating error: ");
fflush(stdout);
H1Adapt hp(&space);
double err_est = hp.calc_error(&sln, &rsln) * 100;
printf("% lf %%\n", err_est);
// If error is too large, adapt the mesh.
if (err_est < ERR_STOP)
{
printf("\nDone\n");
break;
}
printf(" - adapting... ");
fflush(stdout);
hp.adapt(THRESHOLD);
printf("done in %lf secs (refined %d element(s)).\n", hp.get_adapt_time(), hp.get_num_refined_elements());
if (rndof >= NDOF_STOP)
{
printf("\nDone.\n");
break;
}
// Clean up.
delete rspace;
// Next adaptivity step.
as++;
mat.free();
rhs.free();
} while (!done);
#ifdef WITH_PETSC
PetscFinalize();
#endif
return 1;
}
/***********************************************************************************
* 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 **args)
{
set_verbose(false);
if (argc < 3) error("Not enough parameters");
char *type = args[1];
Mesh mesh;
Mesh3DReader mesh_loader;
if (!mesh_loader.load(args[2], &mesh)) error("Loading mesh file '%s'\n", args[2]);
if (strcmp(type, "sln") == 0) {
// Testing on Exact solution which always gives the same value (values from Solution may differ by epsilon)
ExactSolution ex_sln(&mesh, exact_solution);
output.out(&ex_sln, "U");
}
else if (strcmp(type, "vec-sln") == 0) {
// Testing on Exact solution which always gives the same value (values from Solution may differ by epsilon)
ExactSolution ex_sln(&mesh, exact_vec_solution);
output.out(&ex_sln, "U");
}
else if (strcmp(type, "3sln") == 0) {
// Testing on Exact solution which always gives the same value (values from Solution may differ by epsilon)
ExactSolution ex_sln0(&mesh, exact_solution0);
ExactSolution ex_sln1(&mesh, exact_solution1);
ExactSolution ex_sln2(&mesh, exact_solution2);
output.out(&ex_sln0, &ex_sln1, &ex_sln2, "U");
}
else if (strcmp(type, "ord") == 0) {
H1ShapesetLobattoHex shapeset;
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
order3_t order;
if (mesh.elements[1]->get_mode() == MODE_HEXAHEDRON)
order = order3_t(2, 3, 4);
else if (mesh.elements[1]->get_mode() == MODE_TETRAHEDRON)
order = order3_t(3);
else
error(H3D_ERR_NOT_IMPLEMENTED);
space.set_uniform_order(order);
output.out_orders(&space, "orders");
}
else if (strcmp(type, "bc") == 0) {
output.out_bc(&mesh);
}
else if (strcmp(type, "mat") == 0) {
StiffMatrix mat;
test_mat(&mesh, mat);
output.out(&mat);
}
else if (strcmp(type, "mm") == 0) {
test_mm(&mesh);
}
return 0;
}
