// performs a check, whether two given blocks are similar
double get_block_distance (block_t* ref_block, block_t* cmp_block, int const sigma, double const th_2d) {
int const bs = ref_block->block_size;
double ref_mat[bs][bs];
double cmp_mat[bs][bs];
double sub_mat[bs][bs];
double distance = 0.0;
// subtract 128 for DCT transformation
shift_values (bs, ref_block, ref_mat);
shift_values (bs, cmp_block, cmp_mat);
// perform DCT on reference block by two matrix multiplications
dct_2d (bs, ref_mat);
// perform DCT on compare block by two matrix multiplications
dct_2d (bs, cmp_mat);
// perform thresholding on reference block
hard_threshold_2d (bs, ref_mat, th_2d, sigma);
// perform thresholding on compare block
hard_threshold_2d (bs, cmp_mat, th_2d, sigma);
// subtract compare block from reference block
subtract_blocks (bs, ref_mat, cmp_mat, sub_mat);
// perform L2 norm on the difference of the two matrices
distance = l2_norm(bs, sub_mat) / (double)bs;
return distance;
}
void Utility::l2_normalize(std::vector<float>& v){
float norm = l2_norm(v);
if(norm == 0.f){
std::cerr << "0 norm" << std::endl;
exit(1);
}
std::for_each(v.begin(), v.end(), [&](float& v){v /= norm;});
}
bool CVertexRingElement::_updateRotationMatrixSolidOrShell(const int isshell, const Vector3d* vertexpos)
{
const double ERRTOL = 1e-4;
double3x3 A;
int rank, dim=3;
m_quat0 = m_quat; //save last quat, also use it as the initial guess
m_R0 = m_R;
//asemble the matrix
const int strideP = sizeof(CVertexRingNode);
const int strideQ = sizeof(Vector3d);
const int strideW = sizeof(CVertexRingNode);
const double *P = &m_pVertexRingNode[0].m_lpos0.x;
const double *Q = &vertexpos[0].x;
const double *Weight = &m_pVertexRingNode[0].m_weight;
_computeLeastSquareMatrix(m_nv, P, strideP, Q, strideQ, Weight, strideW, A);
//test the sign of delta
const double delta = A.Det();
if (delta>=0){
//polar_decomp(dim, ERRTOL, A.x, m_R.x, rank);
//return true;
double Sxx=A.x[0], Sxy=A.x[1], Sxz=A.x[2];
double Syx=A.x[3], Syy=A.x[4], Syz=A.x[5];
double Szx=A.x[6], Szy=A.x[7], Szz=A.x[8];
Matrix2d m;
m.x[0][0]=Sxx + Syy + Szz, m.x[0][1]=Syz - Szy, m.x[0][2]=Szx - Sxz, m.x[0][3]=Sxy - Syx;
m.x[1][0]=m.x[0][1], m.x[1][1]=Sxx - Syy - Szz, m.x[1][2]=Sxy + Syx, m.x[1][3]=Szx + Sxz;
m.x[2][0]=m.x[0][2], m.x[2][1]=m.x[1][2]; m.x[2][2]= - Sxx + Syy - Szz, m.x[2][3]= Syz + Szy;
m.x[3][0]=m.x[0][3], m.x[3][1]=m.x[1][3], m.x[3][2]=m.x[2][3], m.x[3][3]= - Sxx - Syy + Szz;
const double ERRTOL = 1e-8;
double eigenvalue;
Vector4d quat, guess(m_quat.w, m_quat.x, m_quat.y, m_quat.z);
const bool r = RayleighQuotientIteration(m, guess, ERRTOL, quat, eigenvalue);
m_quat.x=quat[1], m_quat.y=quat[2], m_quat.z=quat[3], m_quat.w=quat[0];
Quaternion *pquat = (Quaternion*)&m_quat.x;
typedef double M33[3][3];
pquat->getRotationMatrix(*((M33*)&m_R.x));
return r;
}
//if solid, use lazzy approach to do nothing, since we don't know the axis to flip
if (!isshell){
return false;
}
//compute relfection of the shell vertices using vertex normal
bool r = true;
const double MATRIXDIST = 1.0;
Vector3d norm = m_normal;
_computeReflectedLeastSquareMatrix(m_nv, P, strideP, Q, strideQ, Weight, strideW, norm, A);
polar_decomp(dim, ERRTOL, A.x, m_R.x, rank);
const double l2dist = l2_norm(m_R, m_R0);
if (l2dist>=MATRIXDIST) r=false;
return r;
}
void
recognize_glyph_one (contours gl, int& level, string& best, double& best_rec) {
array<tree> disc1;
array<double> cont1;
invariants (gl, 1, disc1, cont1);
array<tree> disc2;
array<double> cont2;
invariants (gl, 2, disc2, cont2);
best= "";
best_rec= -100.0;
for (int i=0; i<N(learned_names); i++)
if (N(learned_glyphs[i]) == N(gl) && disc1 == learned_disc1[i]) {
string name= learned_names[i];
array<double> cont= learned_cont1[i];
double dist= l2_norm (cont - cont1) / sqrt (N(cont1));
double rec = 1.0 - dist;
if (rec > best_rec) { best_rec= rec; best= name; }
//cout << name << ": " << 100.0 * rec << "%\n";
}
if (best != "") {
//cout << "disc= " << disc1 << "\n";
//cout << "cont= " << cont1 << "\n";
level= 1;
return;
}
for (int i=0; i<N(learned_names); i++)
if (N(learned_glyphs[i]) == N(gl) && disc2 == learned_disc2[i]) {
string name= learned_names[i];
array<double> cont= learned_cont2[i];
double dist= l2_norm (cont - cont2) / sqrt (N(cont2));
double rec = 1.0 - dist;
if (rec > best_rec) { best_rec= rec; best= name; }
//cout << name << ": " << 100.0 * rec << "%\n";
}
level= 2;
}
int main(int argc, char **args) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &args, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
if (argc < 2) error("Not enough parameters");
H1ShapesetLobattoHex shapeset;
printf("* Loading mesh '%s'\n", args[1]);
Mesh mesh;
Mesh3DReader mesh_loader;
if (!mesh_loader.load(args[1], &mesh)) error("Loading mesh file '%s'\n", args[1]);
printf("* Setup space #1\n");
H1Space space1(&mesh, &shapeset);
space1.set_bc_types(bc_types);
order3_t o1(2, 2, 2);
printf(" - Setting uniform order to (%d, %d, %d)\n", o1.x, o1.y, o1.z);
space1.set_uniform_order(o1);
printf("* Setup space #2\n");
H1Space space2(&mesh, &shapeset);
space2.set_bc_types(bc_types);
order3_t o2(4, 4, 4);
printf(" - Setting uniform order to (%d, %d, %d)\n", o2.x, o2.y, o2.z);
space2.set_uniform_order(o2);
int ndofs = 0;
ndofs += space1.assign_dofs();
ndofs += space2.assign_dofs(ndofs);
printf(" - Number of DOFs: %d\n", ndofs);
printf("* Calculating a solution\n");
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoMatrix mat;
PardisoVector rhs;
PardisoLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
WeakForm wf(2);
wf.add_matrix_form(0, 0, bilinear_form_1<double, scalar>, bilinear_form_1<ord_t, ord_t>, SYM);
wf.add_vector_form(0, linear_form_1<double, scalar>, linear_form_1<ord_t, ord_t>);
wf.add_matrix_form(1, 1, bilinear_form_2<double, scalar>, bilinear_form_2<ord_t, ord_t>, SYM);
wf.add_vector_form(1, linear_form_2<double, scalar>, linear_form_2<ord_t, ord_t>);
LinearProblem lp(&wf, Tuple<Space *>(&space1, &space2));
// assemble stiffness matrix
Timer assemble_timer("Assembling stiffness matrix");
assemble_timer.start();
lp.assemble(&mat, &rhs);
assemble_timer.stop();
// solve the stiffness matrix
Timer solve_timer("Solving stiffness matrix");
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
// output the measured values
printf("%s: %s (%lf secs)\n", assemble_timer.get_name(), assemble_timer.get_human_time(), assemble_timer.get_seconds());
printf("%s: %s (%lf secs)\n", solve_timer.get_name(), solve_timer.get_human_time(), solve_timer.get_seconds());
if (solved) {
// solution 1
Solution sln1(&mesh);
sln1.set_coeff_vector(&space1, solver.get_solution());
ExactSolution esln1(&mesh, exact_sln_fn_1);
// norm
double h1_sln_norm1 = h1_norm(&sln1);
double h1_err_norm1 = h1_error(&sln1, &esln1);
printf(" - H1 solution norm: % le\n", h1_sln_norm1);
printf(" - H1 error norm: % le\n", h1_err_norm1);
double l2_sln_norm1 = l2_norm(&sln1);
double l2_err_norm1 = l2_error(&sln1, &esln1);
printf(" - L2 solution norm: % le\n", l2_sln_norm1);
printf(" - L2 error norm: % le\n", l2_err_norm1);
if (h1_err_norm1 > EPS || l2_err_norm1 > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
// solution 2
Solution sln2(&mesh);
sln2.set_coeff_vector(&space2, solver.get_solution());
ExactSolution esln2(&mesh, exact_sln_fn_2);
// norm
double h1_sln_norm2 = h1_norm(&sln2);
double h1_err_norm2 = h1_error(&sln2, &esln2);
printf(" - H1 solution norm: % le\n", h1_sln_norm2);
printf(" - H1 error norm: % le\n", h1_err_norm2);
double l2_sln_norm2 = l2_norm(&sln2);
double l2_err_norm2 = l2_error(&sln2, &esln2);
printf(" - L2 solution norm: % le\n", l2_sln_norm2);
printf(" - L2 error norm: % le\n", l2_err_norm2);
if (h1_err_norm2 > EPS || l2_err_norm2 > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
#ifdef OUTPUT_DIR
// output
const char *of_name = OUTPUT_DIR "/solution.pos";
FILE *ofile = fopen(of_name, "w");
if (ofile != NULL) {
GmshOutputEngine output(ofile);
output.out(&sln1, "Uh_1");
output.out(&esln1, "U1");
output.out(&sln2, "Uh_2");
output.out(&esln2, "U2");
fclose(ofile);
}
else {
warning("Can not open '%s' for writing.", of_name);
}
#endif
}
#ifdef WITH_PETSC
mat.free();
rhs.free();
PetscFinalize();
#endif
TRACE_END;
return res;
}
int main(int argc, char **args) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &args, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
TRACE_START("trace.txt");
DEBUG_OUTPUT_ON;
SET_VERBOSE_LEVEL(0);
if (argc < 5) error("Not enough parameters");
sscanf(args[2], "%d", &m);
sscanf(args[3], "%d", &n);
sscanf(args[4], "%d", &o);
printf("* Loading mesh '%s'\n", args[1]);
Mesh mesh;
Mesh3DReader mloader;
if (!mloader.load(args[1], &mesh)) error("Loading mesh file '%s'\n", args[1]);
H1ShapesetLobattoHex shapeset;
printf("* Setting the space up\n");
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
int mx = maxn(4, m, n, o, 4);
order3_t order(mx, mx, mx);
// order3_t order(1, 1, 1);
// order3_t order(m, n, o);
printf(" - Setting uniform order to (%d, %d, %d)\n", mx, mx, mx);
space.set_uniform_order(order);
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
printf("* Calculating a solution\n");
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoMatrix mat;
PardisoVector rhs;
PardisoLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<ord_t, ord_t>, SYM);
wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>);
wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<ord_t, ord_t>);
LinearProblem lp(&wf, &space);
// assemble stiffness matrix
printf(" - assembling...\n"); fflush(stdout);
Timer assemble_timer;
assemble_timer.start();
lp.assemble(&mat, &rhs);
assemble_timer.stop();
printf("%s (%lf secs)\n", assemble_timer.get_human_time(), assemble_timer.get_seconds());
// solve the stiffness matrix
printf(" - solving... "); fflush(stdout);
Timer solve_timer;
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
printf("%s (%lf secs)\n", solve_timer.get_human_time(), solve_timer.get_seconds());
// mat.dump(stdout, "a");
// rhs.dump(stdout, "b");
if (solved) {
Solution sln(&mesh);
sln.set_coeff_vector(&space, solver.get_solution());
// printf("* Solution:\n");
// double *s = solver.get_solution();
// for (int i = 1; i <= ndofs; i++) {
// printf(" x[% 3d] = % lf\n", i, s[i]);
// }
ExactSolution ex_sln(&mesh, exact_solution);
// norm
double h1_sln_norm = h1_norm(&sln);
double h1_err_norm = h1_error(&sln, &ex_sln);
printf(" - H1 solution norm: % le\n", h1_sln_norm);
printf(" - H1 error norm: % le\n", h1_err_norm);
double l2_sln_norm = l2_norm(&sln);
double l2_err_norm = l2_error(&sln, &ex_sln);
printf(" - L2 solution norm: % le\n", l2_sln_norm);
printf(" - L2 error norm: % le\n", l2_err_norm);
if (h1_err_norm > EPS || l2_err_norm > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
#if 0 //def OUTPUT_DIR
printf("* Output\n");
// output
const char *of_name = OUTPUT_DIR "/solution.pos";
FILE *ofile = fopen(of_name, "w");
if (ofile != NULL) {
ExactSolution ex_sln(&mesh, exact_solution);
DiffFilter eh(&sln, &ex_sln);
// DiffFilter eh_dx(&mesh, &sln, &ex_sln, FN_DX, FN_DX);
// DiffFilter eh_dy(&mesh, &sln, &ex_sln, FN_DY, FN_DY);
// DiffFilter eh_dz(&mesh, &sln, &ex_sln, FN_DZ, FN_DZ);
GmshOutputEngine output(ofile);
output.out(&sln, "Uh");
// output.out(&sln, "Uh dx", FN_DX_0);
// output.out(&sln, "Uh dy", FN_DY_0);
// output.out(&sln, "Uh dz", FN_DZ_0);
output.out(&eh, "Eh");
// output.out(&eh_dx, "Eh dx");
// output.out(&eh_dy, "Eh dy");
// output.out(&eh_dz, "Eh dz");
output.out(&ex_sln, "U");
// output.out(&ex_sln, "U dx", FN_DX_0);
// output.out(&ex_sln, "U dy", FN_DY_0);
// output.out(&ex_sln, "U dz", FN_DZ_0);
fclose(ofile);
}
else {
warning("Can not open '%s' for writing.", of_name);
}
#endif
}
else
res = ERR_FAILURE;
#ifdef WITH_PETSC
mat.free();
rhs.free();
PetscFinalize();
#endif
TRACE_END;
return res;
}
int main(int argc, char **args)
{
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &args, (char *) PETSC_NULL, PETSC_NULL);
#endif
if (argc < 2) error("Not enough parameters.");
printf("* Loading mesh '%s'\n", args[1]);
Mesh mesh1;
H3DReader mesh_loader;
if (!mesh_loader.load(args[1], &mesh1)) error("Loading mesh file '%s'\n", args[1]);
#if defined RHS2
Ord3 order(P_INIT_X, P_INIT_Y, P_INIT_Z);
printf(" - Setting uniform order to (%d, %d, %d)\n", order.x, order.y, order.z);
// Create an H1 space with default shapeset.
printf("* Setting the space up\n");
H1Space space(&mesh1, bc_types, essential_bc_values, order);
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
printf("* Calculating a solution\n");
// duplicate the mesh
Mesh mesh2;
mesh2.copy(mesh1);
// do some changes
mesh2.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
mesh2.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Solution fsln(&mesh2);
fsln.set_const(-6.0);
#else
// duplicate the mesh
Mesh mesh2;
mesh2.copy(mesh1);
Mesh mesh3;
mesh3.copy(mesh1);
// change meshes
mesh1.refine_all_elements(H3D_REFT_HEX_X);
mesh2.refine_all_elements(H3D_REFT_HEX_Y);
mesh3.refine_all_elements(H3D_REFT_HEX_Z);
printf("* Setup spaces\n");
Ord3 o1(2, 2, 2);
printf(" - Setting uniform order to (%d, %d, %d)\n", o1.x, o1.y, o1.z);
H1Space space1(&mesh1, bc_types_1, essential_bc_values_1, o1);
Ord3 o2(2, 2, 2);
printf(" - Setting uniform order to (%d, %d, %d)\n", o2.x, o2.y, o2.z);
H1Space space2(&mesh2, bc_types_2, essential_bc_values_2, o2);
Ord3 o3(1, 1, 1);
printf(" - Setting uniform order to (%d, %d, %d)\n", o3.x, o3.y, o3.z);
H1Space space3(&mesh3, bc_types_3, essential_bc_values_3, o3);
int ndofs = 0;
ndofs += space1.assign_dofs();
ndofs += space2.assign_dofs(ndofs);
ndofs += space3.assign_dofs(ndofs);
printf(" - Number of DOFs: %d\n", ndofs);
#endif
#if defined WITH_UMFPACK
MatrixSolverType matrix_solver = SOLVER_UMFPACK;
#elif defined WITH_PETSC
MatrixSolverType matrix_solver = SOLVER_PETSC;
#elif defined WITH_MUMPS
MatrixSolverType matrix_solver = SOLVER_MUMPS;
#endif
#ifdef RHS2
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, HERMES_SYM);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>, HERMES_ANY_INT, &fsln);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, &space, is_linear);
#elif defined SYS3
WeakForm wf(3);
wf.add_matrix_form(0, 0, biform_1_1<double, scalar>, biform_1_1<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form(0, 1, biform_1_2<double, scalar>, biform_1_2<Ord, Ord>, HERMES_NONSYM);
wf.add_vector_form(0, liform_1<double, scalar>, liform_1<Ord, Ord>);
wf.add_matrix_form(1, 1, biform_2_2<double, scalar>, biform_2_2<Ord, Ord>, HERMES_SYM);
wf.add_matrix_form(1, 2, biform_2_3<double, scalar>, biform_2_3<Ord, Ord>, HERMES_NONSYM);
wf.add_vector_form(1, liform_2<double, scalar>, liform_2<Ord, Ord>);
wf.add_matrix_form(2, 2, biform_3_3<double, scalar>, biform_3_3<Ord, Ord>, HERMES_SYM);
// Initialize discrete problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::vector<Space *>(&space1, &space2, &space3), is_linear);
#endif
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// 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.
dp.assemble(matrix, rhs);
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
bool solved = solver->solve();
// Time measurement.
cpu_time.tick();
// Print timing information.
info("Solution and mesh with polynomial orders saved. Total running time: %g s", cpu_time.accumulated());
// Time measurement.
TimePeriod sln_time;
sln_time.tick();
if (solved) {
#ifdef RHS2
// Solve the linear system. If successful, obtain the solution.
info("Solving the linear problem.");
Solution sln(&mesh1);
Solution::vector_to_solution(solver->get_solution(), &space, &sln);
// Set exact solution.
ExactSolution ex_sln(&mesh1, exact_solution);
// Norm.
double h1_sln_norm = h1_norm(&sln);
double h1_err_norm = h1_error(&sln, &ex_sln);
printf(" - H1 solution norm: % le\n", h1_sln_norm);
printf(" - H1 error norm: % le\n", h1_err_norm);
double l2_sln_norm = l2_norm(&sln);
double l2_err_norm = l2_error(&sln, &ex_sln);
printf(" - L2 solution norm: % le\n", l2_sln_norm);
printf(" - L2 error norm: % le\n", l2_err_norm);
if (h1_err_norm > EPS || l2_err_norm > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
#elif defined SYS3
// Solution 1.
Solution sln1(&mesh1);
Solution sln2(&mesh2);
Solution sln3(&mesh3);
Solution::vector_to_solution(solver->get_solution(), &space1, &sln1);
Solution::vector_to_solution(solver->get_solution(), &space2, &sln2);
Solution::vector_to_solution(solver->get_solution(), &space3, &sln3);
ExactSolution esln1(&mesh1, exact_sln_fn_1);
ExactSolution esln2(&mesh2, exact_sln_fn_2);
ExactSolution esln3(&mesh3, exact_sln_fn_3);
// Norm.
double h1_err_norm1 = h1_error(&sln1, &esln1);
double h1_err_norm2 = h1_error(&sln2, &esln2);
double h1_err_norm3 = h1_error(&sln3, &esln3);
double l2_err_norm1 = l2_error(&sln1, &esln1);
double l2_err_norm2 = l2_error(&sln2, &esln2);
double l2_err_norm3 = l2_error(&sln3, &esln3);
printf(" - H1 error norm: % le\n", h1_err_norm1);
printf(" - L2 error norm: % le\n", l2_err_norm1);
if (h1_err_norm1 > EPS || l2_err_norm1 > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
printf(" - H1 error norm: % le\n", h1_err_norm2);
printf(" - L2 error norm: % le\n", l2_err_norm2);
if (h1_err_norm2 > EPS || l2_err_norm2 > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
printf(" - H1 error norm: % le\n", h1_err_norm3);
printf(" - L2 error norm: % le\n", l2_err_norm3);
if (h1_err_norm3 > EPS || l2_err_norm3 > EPS) {
// Calculated solution is not enough precise.
res = ERR_FAILURE;
}
#endif
#ifdef RHS2
out_fn_vtk(&sln, "solution");
#elif defined SYS3
out_fn_vtk(&sln1, "sln1");
out_fn_vtk(&sln2, "sln2");
out_fn_vtk(&sln3, "sln3");
#endif
}
else
res = ERR_FAILURE;
// Print timing information.
info("Solution and mesh with polynomial orders saved. Total running time: %g s", sln_time.accumulated());
// Clean up.
delete matrix;
delete rhs;
delete solver;
return res;
}
int main(int argc, char **argv) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &argv, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
if (argc < 5) error("Not enough parameters.");
H1ShapesetLobattoHex shapeset;
printf("* Loading mesh '%s'\n", argv[1]);
Mesh mesh;
Mesh3DReader mloader;
if (!mloader.load(argv[1], &mesh)) error("Loading mesh file '%s'\n", argv[1]);
printf("* Setting the space up\n");
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
int o[3] = { 0, 0, 0 };
sscanf(argv[2], "%d", o + 0);
sscanf(argv[3], "%d", o + 1);
sscanf(argv[4], "%d", o + 2);
order3_t order(o[0], o[1], o[2]);
printf(" - Setting uniform order to (%d, %d, %d)\n", order.x, order.y, order.z);
space.set_uniform_order(order);
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<ord_t, ord_t>, SYM, ANY);
wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>, ANY);
LinearProblem lp(&wf);
lp.set_space(&space);
bool done = false;
int iter = 0;
do {
Timer assemble_timer("Assembling stiffness matrix");
Timer solve_timer("Solving stiffness matrix");
printf("\n=== Iter #%d ================================================================\n", iter);
printf("\nSolution\n");
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoMatrix mat;
PardisoVector rhs;
PardisoLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
// assemble stiffness matrix
printf(" - Assembling... "); fflush(stdout);
assemble_timer.reset();
assemble_timer.start();
lp.assemble(&mat, &rhs);
assemble_timer.stop();
printf("done in %s (%lf secs)\n", assemble_timer.get_human_time(), assemble_timer.get_seconds());
// solve the stiffness matrix
printf(" - Solving... "); fflush(stdout);
solve_timer.reset();
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
if (solved)
printf("done in %s (%lf secs)\n", solve_timer.get_human_time(), solve_timer.get_seconds());
else {
res = ERR_FAILURE;
printf("failed\n");
break;
}
printf("Reference solution\n");
#if defined WITH_UMFPACK
UMFPackLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_PETSC
PetscLinearSolver rsolver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsSolver rsolver(&mat, &rhs);
#endif
Mesh rmesh;
rmesh.copy(mesh);
rmesh.refine_all_elements(H3D_H3D_H3D_REFT_HEX_XYZ);
Space *rspace = space.dup(&rmesh);
rspace->copy_orders(space, 1);
LinearProblem rlp(&wf);
rlp.set_space(rspace);
int rndofs = rspace->assign_dofs();
printf(" - Number of DOFs: %d\n", rndofs);
printf(" - Assembling... "); fflush(stdout);
assemble_timer.reset();
assemble_timer.start();
rlp.assemble(&mat, &rhs);
assemble_timer.stop();
printf("done in %s (%lf secs)\n", assemble_timer.get_human_time(), assemble_timer.get_seconds());
printf(" - Solving... "); fflush(stdout);
solve_timer.reset();
solve_timer.start();
bool rsolved = rsolver.solve();
solve_timer.stop();
if (rsolved)
printf("done in %s (%lf secs)\n", solve_timer.get_human_time(), solve_timer.get_seconds());
else {
res = ERR_FAILURE;
printf("failed\n");
break;
}
Solution sln(&mesh);
sln.set_coeff_vector(&space, solver.get_solution());
Solution rsln(&rmesh);
rsln.set_coeff_vector(rspace, rsolver.get_solution());
printf("Adaptivity:\n");
H1Adapt hp(&space);
double tol = hp.calc_error(&sln, &rsln) * 100;
printf(" - tolerance: "); fflush(stdout);
printf("% lf\n", tol);
if (tol < TOLERANCE) {
printf("\nDone\n");
ExactSolution ex_sln(&mesh, exact_solution);
// norm
double h1_sln_norm = h1_norm(&sln);
double h1_err_norm = h1_error(&sln, &ex_sln);
printf(" - H1 solution norm: % le\n", h1_sln_norm);
printf(" - H1 error norm: % le\n", h1_err_norm);
double l2_sln_norm = l2_norm(&sln);
double l2_err_norm = l2_error(&sln, &ex_sln);
printf(" - L2 solution norm: % le\n", l2_sln_norm);
printf(" - L2 error norm: % le\n", l2_err_norm);
if (h1_err_norm > EPS || l2_err_norm > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
break;
}
Timer t("");
printf(" - adapting... "); fflush(stdout);
t.start();
hp.adapt(THRESHOLD);
t.stop();
printf("done in %lf secs (refined %d element(s))\n", t.get_seconds(), hp.get_num_refined_elements());
iter++;
} while (!done);
#ifdef WITH_PETSC
PetscFinalize();
#endif
return res;
}
int main(int argc, char **args) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(NULL, NULL, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
TRACE_START("trace.txt");
DEBUG_OUTPUT_ON;
SET_VERBOSE_LEVEL(0);
try {
for (int i = 0; i < 48; i++) {
for (int j = 0; j < 48; j++) {
// int i = 5; {
// int j = 0; {
printf("Config: %d, %d ", i, j);
Mesh mesh;
for (Word_t k = 0; k < countof(vtcs); k++)
mesh.add_vertex(vtcs[k].x, vtcs[k].y, vtcs[k].z);
Word_t h1[] = {
hexs[0][i][0] + 1, hexs[0][i][1] + 1, hexs[0][i][2] + 1, hexs[0][i][3] + 1,
hexs[0][i][4] + 1, hexs[0][i][5] + 1, hexs[0][i][6] + 1, hexs[0][i][7] + 1 };
mesh.add_hex(h1);
Word_t h2[] = {
hexs[1][j][0] + 1, hexs[1][j][1] + 1, hexs[1][j][2] + 1, hexs[1][j][3] + 1,
hexs[1][j][4] + 1, hexs[1][j][5] + 1, hexs[1][j][6] + 1, hexs[1][j][7] + 1 };
mesh.add_hex(h2);
// bc
for (Word_t k = 0; k < countof(bnd); k++) {
Word_t facet_idxs[Quad::NUM_VERTICES] = { bnd[k][0] + 1, bnd[k][1] + 1, bnd[k][2] + 1, bnd[k][3] + 1 };
mesh.add_quad_boundary(facet_idxs, bnd[k][4]);
}
mesh.ugh();
// mesh.dump();
// Element *hx[] = { mesh.elements[1], mesh.elements[2] };
// printf("[%d, %d]\n", hx[0]->get_face_orientation(1), hx[1]->get_face_orientation(2));
// Word_t fidx[4];
// hx[1]->get_face_vertices(2, fidx);
// printf("FI: %d, %d, %d, %d\n", fidx[0], fidx[1], fidx[2], fidx[3]);
printf("\n");
#ifdef OUTPUT_DIR
BEGIN_BLOCK
// output the mesh
const char *of_name = OUTPUT_DIR "/ref.msh";
FILE *ofile = fopen(of_name, "w");
if (ofile != NULL) {
GmshOutputEngine output(ofile);
output.out(&mesh);
fclose(ofile);
}
else {
warning("Can not open '%s' for writing.", of_name);
}
END_BLOCK
#endif
H1ShapesetLobattoHex shapeset;
// printf("* Setting the space up\n");
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
#ifdef XM_YN_ZO
order3_t ord(4, 4, 4);
#elif defined XM_YN_ZO_2
order3_t ord(4, 4, 4);
#elif defined X2_Y2_Z2
order3_t ord(2, 2, 2);
#endif
// printf(" - Setting uniform order to (%d, %d, %d)\n", dir_x, dir_y, dir_z);
space.set_uniform_order(ord);
space.assign_dofs();
// printf("* Calculating a solution\n");
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoLinearSolver solver;
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
WeakForm wf;
#ifdef DIRICHLET
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<ord_t, ord_t>, SYM);
wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>);
#elif defined NEWTON
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<ord_t, ord_t>, SYM);
wf.add_matrix_form_surf(bilinear_form_surf<double, scalar>, bilinear_form_surf<ord_t, ord_t>);
wf.add_vector_form(linear_form<double, scalar>, linear_form<ord_t, ord_t>);
wf.add_vector_form_surf(linear_form_surf<double, scalar>, linear_form_surf<ord_t, ord_t>);
#endif
LinProblem lp(&wf);
lp.set_space(&space);
// assemble stiffness matrix
lp.assemble(&mat, &rhs);
// solve the stiffness matrix
bool solved = solver.solve();
if (!solved) throw ERR_FAILURE;
// {
// char file_name[1024];
// sprintf(file_name, "%s/matrix-%d-%d", OUTPUT_DIR, i, j);
// FILE *file = fopen(file_name, "w");
// if (file != NULL) {
// solver.dump_matrix(file, "A");
// solver.dump_rhs(file, "b");
//
// fclose(file);
// }
// }
Solution sln(&mesh);
sln.set_fe_solution(&space, solver.get_solution());
ExactSolution exsln(&mesh, exact_solution);
// norm
double h1_sln_norm = h1_norm(&sln);
double h1_err_norm = h1_error(&sln, &exsln);
printf(" - H1 solution norm: % le\n", h1_sln_norm);
printf(" - H1 error norm: % le\n", h1_err_norm);
double l2_sln_norm = l2_norm(&sln);
double l2_err_norm = l2_error(&sln, &exsln);
printf(" - L2 solution norm: % le\n", l2_sln_norm);
printf(" - L2 error norm: % le\n", l2_err_norm);
assert(h1_sln_norm > 0 && h1_err_norm > 0);
assert(l2_sln_norm > 0 && l2_err_norm > 0);
// // out fn
// char fname[4096];
// sprintf(fname, "%s/cfg-%d-%d.pos", OUTPUT_DIR, i, j);
// FILE *fnf = fopen(fname, "w");
// assert(fnf != NULL);
// GmshOutputEngine out(fnf);
// char var[64];
// sprintf(var, "%d_%d", i, j);
// out.out(&sln, var);
// fclose(fnf);
//
// char mfname[4096];
// sprintf(mfname, "%s/mesh-%d-%d.ref", OUTPUT_DIR, i, j);
// FILE *mfnf = fopen(mfname, "w");
// assert(mfnf != NULL);
// GmshOutputEngine outm(mfnf);
// outm.out(&mesh);
// fclose(mfnf);
if (h1_err_norm > EPS || l2_err_norm > EPS) {
// calculated solution is not enough precise
printf("Solution is not precise enough.\n");
throw ERR_FAILURE;
}
printf("Passed\n");
}
}
}
catch (int e) {
res = e;
printf("Failed\n");
}
#ifdef WITH_PETSC
PetscFinalize();
#endif
TRACE_END;
return res;
}
void fem(size_t n, double errors[2], double (*fn_f)(double, double),
double (*fn_g)(unsigned char, double, double),
double (*fn_u)(double, double))
{
mesh m;
crs_matrix mat;
double * u, * rhs;
double local_stiffness[3][3];
double local_load[3];
size_t elem;
/* 1. Allocate and generate mesh */
get_mesh(&m, n);
#ifdef PRINT_DEBUG
print_mesh(&m);
#endif
/* 2. Allocate the linear system */
init_matrix(&mat, &m);
u = (double *) malloc(sizeof(double) * m.n_vertices);
if (u == NULL) err_exit("Allocation of solution vector failed!");
memset(u, 0, sizeof(double) * m.n_vertices);
rhs = (double *) malloc(sizeof(double) * m.n_vertices);
if (rhs == NULL)
err_exit("Allocation of right hand side failed!");
memset(rhs, 0, sizeof(double) * m.n_vertices);
/* 3. Assemble the matrix */
for (elem = 0; elem < m.n_triangles; ++elem)
{
/* Compute local stiffness and load */
get_local_stiffness(local_stiffness, &m, elem);
get_local_load(local_load, &m, elem, fn_f);
#ifdef PRINT_DEBUG
print_local_stiffness(local_stiffness);
print_local_load(local_load);
#endif
/* insert into global matrix and rhs */
assemble_local2global_stiffness(local_stiffness, &mat, &m, elem);
assemble_local2global_load(local_load, rhs, &m, elem);
}
#ifdef PRINT_DEBUG
printf("Matrix after assembly:\n");
print_matrix(&mat);
printf("rhs after assembly:\n");
for(size_t i = 0; i < m.n_vertices; ++i) {
printf("%5.2f\n", rhs[i]);
}
printf("\n");
#endif
/* 4. Apply boundary conditions */
apply_dbc(&mat, rhs, &m, fn_g);
#ifdef PRINT_DEBUG
printf("Matrix after application of BCs:\n");
print_matrix(&mat);
printf("rhs after application of BCs:\n");
for(size_t i = 0; i < m.n_vertices; ++i) {
printf("%5.2f\n", rhs[i]);
}
printf("\n");
#endif
/* 5. Solve the linear system */
solve(&mat, u, rhs);
/* 6. Evaluate error */
errors[0] = l2_norm(u, &m, fn_u);
errors[1] = inf_norm(u, &m, fn_u);
/* free allocated resources */
free(u);
free(rhs);
rhs = NULL;
free_matrix(&mat);
free_mesh(&m);
}
int main(int argc, char **argv) {
int res = ERR_SUCCESS;
#ifdef WITH_PETSC
PetscInitialize(&argc, &argv, (char *) PETSC_NULL, PETSC_NULL);
#endif
set_verbose(false);
if (argc < 3) error("Not enough parameters");
printf("* Loading mesh '%s'\n", argv[1]);
Mesh mesh;
H3DReader mesh_loader;
if (!mesh_loader.load(argv[1], &mesh)) error("Loading mesh file '%s'\n", argv[1]);
int o;
sscanf(argv[2], "%d", &o);
printf(" - Setting uniform order to %d\n", o);
printf("* Setting the space up\n");
H1Space space(&mesh, bc_types, essential_bc_values, o);
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
printf("* Calculating a solution\n");
#if defined WITH_UMFPACK
UMFPackMatrix mat;
UMFPackVector rhs;
UMFPackLinearSolver solver(&mat, &rhs);
#elif defined WITH_PARDISO
PardisoMatrix mat;
PardisoVector rhs;
PardisoLinearSolver solver(&mat, &rhs);
#elif defined WITH_PETSC
PetscMatrix mat;
PetscVector rhs;
PetscLinearSolver solver(&mat, &rhs);
#elif defined WITH_MUMPS
MumpsMatrix mat;
MumpsVector rhs;
MumpsSolver solver(&mat, &rhs);
#endif
WeakForm wf;
wf.add_matrix_form(bilinear_form<double, scalar>, bilinear_form<Ord, Ord>, SYM);
wf.add_vector_form(linear_form<double, scalar>, linear_form<Ord, Ord>);
DiscreteProblem dp(&wf, &space, true);
// assemble stiffness matrix
Timer assemble_timer("Assembling stiffness matrix");
assemble_timer.start();
dp.assemble(&mat, &rhs);
assemble_timer.stop();
// solve the stiffness matrix
Timer solve_timer("Solving stiffness matrix");
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
// output the measured values
printf("%s: %s (%lf secs)\n", assemble_timer.get_name(), assemble_timer.get_human_time(), assemble_timer.get_seconds());
printf("%s: %s (%lf secs)\n", solve_timer.get_name(), solve_timer.get_human_time(), solve_timer.get_seconds());
if (solved) {
Solution sln(&mesh);
sln.set_coeff_vector(&space, solver.get_solution());
ExactSolution ex_sln(&mesh, exact_solution);
// norm
double h1_sln_norm = h1_norm(&sln);
double h1_err_norm = h1_error(&sln, &ex_sln);
printf(" - H1 solution norm: % le\n", h1_sln_norm);
printf(" - H1 error norm: % le\n", h1_err_norm);
double l2_sln_norm = l2_norm(&sln);
double l2_err_norm = l2_error(&sln, &ex_sln);
printf(" - L2 solution norm: % le\n", l2_sln_norm);
printf(" - L2 error norm: % le\n", l2_err_norm);
if (h1_err_norm > EPS || l2_err_norm > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
#if 0 //def OUTPUT_DIR
// output
const char *of_name = OUTPUT_DIR "/solution.pos";
FILE *ofile = fopen(of_name, "w");
if (ofile != NULL) {
ExactSolution ex_sln(&mesh, exact_solution);
DiffFilter eh(&sln, &ex_sln);
// DiffFilter eh_dx(&mesh, &sln, &ex_sln, FN_DX, FN_DX);
// DiffFilter eh_dy(&mesh, &sln, &ex_sln, FN_DY, FN_DY);
// DiffFilter eh_dz(&mesh, &sln, &ex_sln, FN_DZ, FN_DZ);
GmshOutputEngine output(ofile);
output.out(&sln, "Uh");
// output.out(&sln, "Uh dx", FN_DX_0);
// output.out(&sln, "Uh dy", FN_DY_0);
// output.out(&sln, "Uh dz", FN_DZ_0);
output.out(&eh, "Eh");
// output.out(&eh_dx, "Eh dx");
// output.out(&eh_dy, "Eh dy");
// output.out(&eh_dz, "Eh dz");
output.out(&ex_sln, "U");
// output.out(&ex_sln, "U dx", FN_DX_0);
// output.out(&ex_sln, "U dy", FN_DY_0);
// output.out(&ex_sln, "U dz", FN_DZ_0);
fclose(ofile);
}
else {
warning("Can not open '%s' for writing.", of_name);
}
#endif
}
#ifdef WITH_PETSC
mat.free();
rhs.free();
PetscFinalize();
#endif
TRACE_END;
return res;
}
