int main()
{
std_setup();
int N = 12;
double X0 = 10;
int n1 = 256;
int n2 = n1;
rgrid2D grid( n1, -X0, X0, n2, -X0, X0 );
rgrid2D * AN = new rgrid2D [N+1];
for (int k=0; k<=N; k++ )
AN[k] = grid;
rgrid2D * NU = new rgrid2D [N+1];
for (int k=0; k<=N; k++ )
NU[k] = grid;
// laplacian_2d_fd Del2;
// Del2.init( grid.n1, grid.n2, grid.b1-grid.a1, grid.b2-grid.a2, 24, 24 );
double gamma = 0.4;
int m = 12;
laplacian_2d_hdaf Del2;
Del2.init( grid.n1, grid.n2, grid.b1-grid.a1, grid.b2-grid.a2, m, m, gamma, gamma );
for (int k=0; k<=N; k++ )
AN[k] = gauss(k);
NU[0] = AN[0];
for (int k=1; k<=N; k++ )
Del2.execute( NU[k-1].array, NU[k].array );
double * x = ml_alloc<double> (N);
double * y = ml_alloc<double> (N);
for (int k=1; k<=N; k++ )
{
y[k-1] = log10(l2_error( AN[k].array, NU[k].array, n1, n2 ));
x[k-1] = k;
if (k >1 ) cout << k << "\t" << y[k-1] << "\t" << y[k-1]-y[k-2] << endl;
else cout << k << "\t" << y[k-1] << endl;
sprintf(fname, "/workspace/output/temp/numeric_%02d.png", k );
plotGrid2D_1( NU[k], fname,cmap);
sprintf(fname, "/workspace/output/temp/analytic_%02d.png", k );
plotGrid2D_1( AN[k], fname,cmap);
}
double slope, wefqewf;
ml_slope( x, y, N, slope, wefqewf );
cout << slope << endl;
}
int main(int argc, char **argv)
{
int res = ERR_SUCCESS;
set_verbose(false);
if (argc < 2) error("Not enough parameters");
printf("* Loading mesh '%s'\n", argv[1]);
Mesh mesh;
Mesh3DReader mesh_loader;
if (!mesh_loader.load(argv[1], &mesh)) error("loading mesh file '%s'\n", argv[1]);
H1ShapesetLobattoHex shapeset;
#if defined NONLIN1
order3_t order(1, 1, 1);
#else
order3_t order(2, 2, 2);
#endif
printf("* Setting the space up\n");
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_essential_bc_values(essential_bc_values);
printf(" - Setting uniform order to (%d, %d, %d)\n", order.x, order.y, order.z);
space.set_uniform_order(order);
int ndofs = space.assign_dofs();
printf(" - Number of DOFs: %d\n", ndofs);
#if defined NONLIN2
// do L2 projection of zero function
WeakForm proj_wf;
proj_wf.add_matrix_form(biproj_form<double, scalar>, biproj_form<ord_t, ord_t>, SYM);
proj_wf.add_vector_form(liproj_form<double, scalar>, liproj_form<ord_t, ord_t>);
LinearProblem lp(&proj_wf, &space);
#ifdef WITH_UMFPACK
UMFPackMatrix m;
UMFPackVector v;
UMFPackLinearSolver sl(&m, &v);
#elif defined WITH_MUMPS
MumpsMatrix m;
MumpsVector v;
MumpsSolver sl(&m, &v);
#endif
lp.assemble(&m, &v);
sl.solve();
double *ps = sl.get_solution();
#endif
printf("* Calculating a solution\n");
WeakForm wf(1);
wf.add_matrix_form(0, 0, jacobi_form<double, scalar>, jacobi_form<ord_t, ord_t>, UNSYM);
wf.add_vector_form(0, resid_form<double, scalar>, resid_form<ord_t, ord_t>);
DiscreteProblem dp(&wf, &space);
NoxSolver solver(&dp);
#if defined NONLIN2
solver.set_init_sln(ps);
#endif
solver.set_conv_iters(10);
printf(" - solving..."); fflush(stdout);
Timer solve_timer;
solve_timer.start();
bool solved = solver.solve();
solve_timer.stop();
if (solved) {
printf(" done in %s (%lf secs), iters = %d\n", solve_timer.get_human_time(),
solve_timer.get_seconds(), solver.get_num_iters());
double *s = solver.get_solution();
Solution sln(&mesh);
sln.set_coeff_vector(&space, s);
Solution ex_sln(&mesh);
#ifdef NONLIN1
ex_sln.set_const(100.0);
#else
ex_sln.set_exact(exact_solution);
#endif
double h1_err = h1_error(&sln, &ex_sln);
printf(" - H1 error norm: % le\n", h1_err);
double l2_err = l2_error(&sln, &ex_sln);
printf(" - L2 error norm: % le\n", l2_err);
if (h1_err > EPS || l2_err > EPS) {
// calculated solution is not enough precise
res = ERR_FAILURE;
}
#ifdef OUTPUT_DIR
printf("* Output\n");
// output
const char *of_name = OUTPUT_DIR "/solution.vtk";
FILE *ofile = fopen(of_name, "w");
if (ofile != NULL) {
VtkOutputEngine output(ofile);
output.out(&sln, "Uh", FN_VAL_0);
fclose(ofile);
}
else {
warning("Cann not open '%s' for writing.", of_name);
}
#endif
}
else
res = ERR_FAILURE;
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);
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()
{
std_setup();
mp::mp_init(100);
int n = pow(2,12);
double a = 0.0;
double b = ml_2pi;
int m = 4;
double gamma = 0.75;
vector<double > frequency;
vector<double > error;
vector<double > measured_response;
vector<double > response;
vector<double > expected_error;
for (int k=1; k<=n/2; k += max(n/100,1) )
{
double K = (ml_2pi/(b-a))*k;
double * signal = ml_alloc<double > (n);
for (int i=0; i<n; i++)
{
double x = ((b-a)*i)/n+a;
signal[i] = cos( x*K );
}
complex<double > * fft_ker=0;
hdaf_filter_kernel ( fft_ker, b-a, n, m, (ml_2pi/(b-a))*(gamma*n/2) );
double * signal_filtered=0;
complex<double > * workspace=0;
fft( signal, workspace, n );
for (int i=0; i<n/2+1; i++)
workspace[i] *= fft_ker[i];
ifft( workspace, signal_filtered, n );
//---------------
cout << K << "\t" << l2_error( signal, signal_filtered, n ) << endl;
hdaf_delta_hat delta( m, sqrt(2*m+1)/( (ml_2pi/(b-a))*(gamma*n/2) ) );
frequency.push_back( K );
measured_response.push_back( rms(signal_filtered,n)/rms(signal,n ) );
response.push_back ( delta(K) );
expected_error.push_back ( log10( fabs(delta(K)-1.0)+1E-18 ) );
error.push_back( log10(fabs(l2_error( signal, signal_filtered, n )) +1E-18) );
ml_free(fft_ker);
ml_free(signal);
}
sprintf( fname, "/workspace/output/temp/frequency" );
output ( frequency, fname );
sprintf( fname, "/workspace/output/temp/measured_response" );
output ( measured_response, fname );
sprintf( fname, "/workspace/output/temp/error" );
output ( error, fname );
sprintf( fname, "/workspace/output/temp/expected_error" );
output ( expected_error, fname );
sprintf( fname, "/workspace/output/temp/response" );
output ( response, fname );
std_exit();
}
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;
}
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;
}
