double ang_between(double x1[3], double x2[3]) {
double mydot = dot3(x1, x2);
double mag1 = mag3(x1);
double mag2 = mag3(x2);
double cos_ang = mydot/mag1/mag2;
if (cos_ang > 1)
cos_ang = 1;
if (cos_ang < -1)
cos_ang = -1;
return acos(cos_ang);
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Create an H1 space.
H1Space* phi_space = new H1Space(&mesh, bc_types, essential_bc_values, P_INIT);
H1Space* psi_space = new H1Space(&mesh, bc_types, essential_bc_values, P_INIT);
int ndof = get_num_dofs(Tuple<Space *>(phi_space, psi_space));
info("ndof = %d.", ndof);
// Initialize previous time level solutions.
Solution phi_prev_time, psi_prev_time;
phi_prev_time.set_exact(&mesh, init_cond_phi);
psi_prev_time.set_exact(&mesh, init_cond_psi);
// Initialize the weak formulation.
WeakForm wf(2);
wf.add_matrix_form(0, 0, callback(biform_euler_0_0));
wf.add_matrix_form(0, 1, callback(biform_euler_0_1));
wf.add_matrix_form(1, 0, callback(biform_euler_1_0));
wf.add_matrix_form(1, 1, callback(biform_euler_1_1));
wf.add_vector_form(0, callback(liform_euler_0), H2D_ANY, &phi_prev_time);
wf.add_vector_form(1, callback(liform_euler_1), H2D_ANY, &psi_prev_time);
// Time stepping loop:
int nstep = T_FINAL;
for(int ts = 1; ts <= nstep; ts++)
{
info("Time step %d:", ts);
// Newton's method.
info("Solving linear system.");
Solution phi, psi;
bool is_complex = true;
if (!solve_linear(Tuple<Space *>(phi_space, psi_space), &wf, matrix_solver,
Tuple<Solution *>(&phi, &psi), NULL, is_complex))
error("Linear solve failed.");
// Update previous time level solution.
phi_prev_time.copy(&phi);
psi_prev_time.copy(&psi);
}
AbsFilter mag2(&psi_prev_time);
AbsFilter mag3(&phi_prev_time);
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
int success = 1;
double eps = 1e-5;
double val = std::abs(mag2.get_pt_value(0.0, 0.0));
info("Coordinate ( 0, 0) psi value = %lf", std::abs(mag2.get_pt_value(0.0, 0.0)));
if (fabs(val - (0.000008)) > eps) {
printf("Coordinate ( 0, 0) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(-0.5, -0.5));
info("Coordinate (-0.5,-0.5) psi value = %lf", std::abs(mag2.get_pt_value(-0.5, -0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate (-0.5,-0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(0.5, -0.5));
info("Coordinate ( 0.5,-0.5) psi value = %lf", std::abs(mag2.get_pt_value(0.5, -0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate ( 0.5,-0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(0.5, 0.5));
info("Coordinate ( 0.5, 0.5) psi value = %lf", std::abs(mag2.get_pt_value(0.5, 0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate ( 0.5, 0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(-0.5, 0.5));
info("Coordinate (-0.5, 0.5) psi value = %lf", std::abs(mag2.get_pt_value(-0.5, 0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate (-0.5, 0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(0.0, 0.0));
info("Coordinate ( 0, 0) phi value = %lf", std::abs(mag3.get_pt_value(0.0, 0.0)));
if (fabs(val - (0.000003)) > eps) {
printf("Coordinate ( 0, 0) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(-0.5, -0.5));
info("Coordinate (-0.5,-0.5) phi value = %lf", std::abs(mag3.get_pt_value(-0.5, -0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate (-0.5,-0.5) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(0.5, -0.5));
info("Coordinate ( 0.5,-0.5) phi value = %lf", std::abs(mag3.get_pt_value(0.5, -0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate ( 0.5,-0.5) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(0.5, 0.5));
info("Coordinate ( 0.5, 0.5) phi value = %lf", std::abs(mag3.get_pt_value(0.5, 0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate ( 0.5, 0.5) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(-0.5, 0.5));
info("Coordinate (-0.5, 0.5) phi value = %lf", std::abs(mag3.get_pt_value(-0.5, 0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate (-0.5, 0.5) phi value = %lf\n", val);
success = 0;
}
if (success == 1) {
printf("Success!\n");
return ERROR_SUCCESS;
}
else {
printf("Failure!\n");
return ERROR_FAILURE;
}
}
void normalize(double y[3], double x[3]) {
double mymag = mag3(x);
for (unsigned int i = 0; i < 3; i++)
y[i] = y[i]/mymag;
}
int main(int argc, char* argv[])
{
// Load the mesh.
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
// Initial mesh refinements.
for(int i = 0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Enter boundary markers.
BCTypes bc_types;
bc_types.add_bc_dirichlet(Hermes::Tuple<int>(BDY_BOTTOM, BDY_RIGHT, BDY_TOP, BDY_LEFT));
// Enter Dirichlet boundary values.
BCValues bc_values;
bc_values.add_zero(Hermes::Tuple<int>(BDY_BOTTOM, BDY_RIGHT, BDY_TOP, BDY_LEFT));
// Create an H1 space.
H1Space* phi_space = new H1Space(&mesh, &bc_types, &bc_values, P_INIT);
H1Space* psi_space = new H1Space(&mesh, &bc_types, &bc_values, P_INIT);
int ndof = Space::get_num_dofs(Hermes::Tuple<Space *>(phi_space, psi_space));
info("ndof = %d.", ndof);
// Initialize previous time level solutions.
Solution phi_prev_time, psi_prev_time;
phi_prev_time.set_exact(&mesh, init_cond_phi);
psi_prev_time.set_exact(&mesh, init_cond_psi);
// Initialize the weak formulation.
WeakForm wf(2);
wf.add_matrix_form(0, 0, callback(biform_euler_0_0));
wf.add_matrix_form(0, 1, callback(biform_euler_0_1));
wf.add_matrix_form(1, 0, callback(biform_euler_1_0));
wf.add_matrix_form(1, 1, callback(biform_euler_1_1));
wf.add_vector_form(0, callback(liform_euler_0), HERMES_ANY, &phi_prev_time);
wf.add_vector_form(1, callback(liform_euler_1), HERMES_ANY, &psi_prev_time);
// Time stepping loop:
int nstep = T_FINAL;
for(int ts = 1; ts <= nstep; ts++)
{
info("Time step %d:", ts);
info("Solving linear system.");
// Initialize the FE problem.
bool is_linear = true;
DiscreteProblem dp(&wf, Hermes::Tuple<Space *>(phi_space, psi_space), is_linear);
SparseMatrix* matrix = create_matrix(matrix_solver);
Vector* rhs = create_vector(matrix_solver);
Solver* solver = create_linear_solver(matrix_solver, matrix, rhs);
// Assemble the stiffness matrix and right-hand side vector.
info("Assembling the stiffness matrix and right-hand side vector.");
dp.assemble(matrix, rhs);
// Solve the linear system and if successful, obtain the solution.
info("Solving the matrix problem.");
if(solver->solve())
Solution::vector_to_solutions(solver->get_solution(), Hermes::Tuple<Space *>(phi_space, psi_space), Hermes::Tuple<Solution *>(&phi_prev_time, &psi_prev_time));
else
error ("Matrix solver failed.\n");
}
AbsFilter mag2(&psi_prev_time);
AbsFilter mag3(&phi_prev_time);
int success = 1;
double eps = 1e-5;
double val = std::abs(mag2.get_pt_value(0.0, 0.0));
info("Coordinate ( 0, 0) psi value = %lf", std::abs(mag2.get_pt_value(0.0, 0.0)));
if (fabs(val - (0.000008)) > eps) {
printf("Coordinate ( 0, 0) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(-0.5, -0.5));
info("Coordinate (-0.5,-0.5) psi value = %lf", std::abs(mag2.get_pt_value(-0.5, -0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate (-0.5,-0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(0.5, -0.5));
info("Coordinate ( 0.5,-0.5) psi value = %lf", std::abs(mag2.get_pt_value(0.5, -0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate ( 0.5,-0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(0.5, 0.5));
info("Coordinate ( 0.5, 0.5) psi value = %lf", std::abs(mag2.get_pt_value(0.5, 0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate ( 0.5, 0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag2.get_pt_value(-0.5, 0.5));
info("Coordinate (-0.5, 0.5) psi value = %lf", std::abs(mag2.get_pt_value(-0.5, 0.5)));
if (fabs(val - (0.000004)) > eps) {
printf("Coordinate (-0.5, 0.5) psi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(0.0, 0.0));
info("Coordinate ( 0, 0) phi value = %lf", std::abs(mag3.get_pt_value(0.0, 0.0)));
if (fabs(val - (0.000003)) > eps) {
printf("Coordinate ( 0, 0) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(-0.5, -0.5));
info("Coordinate (-0.5,-0.5) phi value = %lf", std::abs(mag3.get_pt_value(-0.5, -0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate (-0.5,-0.5) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(0.5, -0.5));
info("Coordinate ( 0.5,-0.5) phi value = %lf", std::abs(mag3.get_pt_value(0.5, -0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate ( 0.5,-0.5) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(0.5, 0.5));
info("Coordinate ( 0.5, 0.5) phi value = %lf", std::abs(mag3.get_pt_value(0.5, 0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate ( 0.5, 0.5) phi value = %lf\n", val);
success = 0;
}
val = std::abs(mag3.get_pt_value(-0.5, 0.5));
info("Coordinate (-0.5, 0.5) phi value = %lf", std::abs(mag3.get_pt_value(-0.5, 0.5)));
if (fabs(val - (0.000001)) > eps) {
printf("Coordinate (-0.5, 0.5) phi value = %lf\n", val);
success = 0;
}
if (success == 1) {
printf("Success!\n");
return ERR_SUCCESS;
}
else {
printf("Failure!\n");
return ERR_FAILURE;
}
}