int main()
{
// Time measurement.
TimePeriod cpu_time;
cpu_time.tick();
// Create coarse mesh, set Dirichlet BC, enumerate basis functions.
Space* space = new Space(A, B, NELEM, DIR_BC_LEFT, DIR_BC_RIGHT, P_INIT, NEQ);
// Enumerate basis functions, info for user.
int ndof = Space::get_num_dofs(space);
info("ndof: %d", ndof);
// Initialize the weak formulation.
WeakForm wf;
wf.add_matrix_form(jacobian);
wf.add_vector_form(residual);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem *dp_coarse = new DiscreteProblem(&wf, space, is_linear);
if(JFNK == 0)
{
// Newton's loop on coarse mesh.
// Fill vector coeff_vec using dof and coeffs arrays in elements.
double *coeff_vec_coarse = new double[Space::get_num_dofs(space)];
get_coeff_vector(space, coeff_vec_coarse);
// Set up the solver, matrix, and rhs according to the solver selection.
SparseMatrix* matrix_coarse = create_matrix(matrix_solver);
Vector* rhs_coarse = create_vector(matrix_solver);
Solver* solver_coarse = create_linear_solver(matrix_solver, matrix_coarse, rhs_coarse);
int it = 1;
while (1)
{
// Obtain the number of degrees of freedom.
int ndof_coarse = Space::get_num_dofs(space);
// Assemble the Jacobian matrix and residual vector.
dp_coarse->assemble(coeff_vec_coarse, matrix_coarse, rhs_coarse);
// Calculate the l2-norm of residual vector.
double res_l2_norm = get_l2_norm(rhs_coarse);
// Info for user.
info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(space), res_l2_norm);
// If l2 norm of the residual vector is within tolerance, then quit.
// NOTE: at least one full iteration forced
// here because sometimes the initial
// residual on fine mesh is too small.
if(res_l2_norm < NEWTON_TOL_COARSE && it > 1) break;
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
for(int i = 0; i < ndof_coarse; i++) rhs_coarse->set(i, -rhs_coarse->get(i));
// Solve the linear system.
if(!solver_coarse->solve())
error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof_coarse; i++) coeff_vec_coarse[i] += solver_coarse->get_solution()[i];
// If the maximum number of iteration has been reached, then quit.
if (it >= NEWTON_MAX_ITER) error ("Newton method did not converge.");
// Copy coefficients from vector y to elements.
set_coeff_vector(coeff_vec_coarse, space);
it++;
}
// Cleanup.
delete matrix_coarse;
delete rhs_coarse;
delete solver_coarse;
delete [] coeff_vec_coarse;
}
else
jfnk_cg(dp_coarse, space, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_COARSE, NEWTON_MAX_ITER, matrix_solver);
// Cleanup.
delete dp_coarse;
// DOF and CPU convergence graphs.
SimpleGraph graph_dof_est, graph_cpu_est;
SimpleGraph graph_dof_exact, graph_cpu_exact;
// Adaptivity loop:
int as = 1;
double ftr_errors[MAX_ELEM_NUM]; // This array decides what
// elements will be refined.
bool done = false;
do
{
info("---- Adaptivity step %d:", as);
// Construct globally refined reference mesh and setup reference space.
Space* ref_space = construct_refined_space(space);
// Initialize the FE problem.
bool is_linear = false;
DiscreteProblem* dp = new DiscreteProblem(&wf, ref_space, is_linear);
if(JFNK == 0)
{
// 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);
// Newton's loop on the fine mesh.
info("Solving on fine mesh:");
// Fill vector coeff_vec using dof and coeffs arrays in elements.
double *coeff_vec = new double[Space::get_num_dofs(ref_space)];
get_coeff_vector(ref_space, coeff_vec);
int it = 1;
while (1)
{
// Obtain the number of degrees of freedom.
int ndof = Space::get_num_dofs(ref_space);
// Assemble the Jacobian matrix and residual vector.
dp->assemble(coeff_vec, matrix, rhs);
// Calculate the l2-norm of residual vector.
double res_l2_norm = get_l2_norm(rhs);
// Info for user.
info("---- Newton iter %d, ndof %d, res. l2 norm %g", it, Space::get_num_dofs(ref_space), res_l2_norm);
// If l2 norm of the residual vector is within tolerance, then quit.
// NOTE: at least one full iteration forced
// here because sometimes the initial
// residual on fine mesh is too small.
if(res_l2_norm < NEWTON_TOL_REF && it > 1) break;
// Multiply the residual vector with -1 since the matrix
// equation reads J(Y^n) \deltaY^{n+1} = -F(Y^n).
for(int i = 0; i < ndof; i++) rhs->set(i, -rhs->get(i));
// Solve the linear system.
if(!solver->solve())
error ("Matrix solver failed.\n");
// Add \deltaY^{n+1} to Y^n.
for (int i = 0; i < ndof; i++) coeff_vec[i] += solver->get_solution()[i];
// If the maximum number of iteration has been reached, then quit.
if (it >= NEWTON_MAX_ITER) error ("Newton method did not converge.");
// Copy coefficients from vector y to elements.
set_coeff_vector(coeff_vec, ref_space);
it++;
}
// Cleanup.
delete matrix;
delete rhs;
delete solver;
delete [] coeff_vec;
}
else
jfnk_cg(dp, ref_space, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_COARSE, NEWTON_MAX_ITER, matrix_solver);
// Cleanup.
delete dp;
// Starting with second adaptivity step, obtain new coarse
// mesh solution via projecting the fine mesh solution.
if(as > 1)
{
info("Projecting the fine mesh solution onto the coarse mesh.");
// Project the fine mesh solution (defined on space_ref) onto the coarse mesh (defined on space).
OGProjection::project_global(space, ref_space, matrix_solver);
}
double max_qoi_err_est = 0;
for (int i=0; i < space->get_n_active_elem(); i++)
{
if (GOAL_ORIENTED == 1)
{
// Use quantity of interest.
double qoi_est = quantity_of_interest(space, X_QOI);
double qoi_ref_est = quantity_of_interest(ref_space, X_QOI);
ftr_errors[i] = fabs(qoi_ref_est - qoi_est);
}
else
{
// Use global norm
double err_est_array[MAX_ELEM_NUM];
ftr_errors[i] = calc_err_est(NORM, space, ref_space, err_est_array);
}
// Info for user.
info("Elem [%d]: absolute error (est) = %g%%", i, ftr_errors[i]);
// Time measurement.
cpu_time.tick();
// Calculating maximum of QOI FTR error for plotting purposes
if (GOAL_ORIENTED == 1)
{
if (ftr_errors[i] > max_qoi_err_est)
max_qoi_err_est = ftr_errors[i];
}
else
{
double qoi_est = quantity_of_interest(space, X_QOI);
double qoi_ref_est = quantity_of_interest(ref_space, X_QOI);
double err_est = fabs(qoi_ref_est - qoi_est);
if (err_est > max_qoi_err_est)
max_qoi_err_est = err_est;
}
}
// Add entries to convergence graphs.
if (EXACT_SOL_PROVIDED)
{
double qoi_est = quantity_of_interest(space, X_QOI);
double u[MAX_EQN_NUM], dudx[MAX_EQN_NUM];
exact_sol(X_QOI, u, dudx);
double err_qoi_exact = fabs(u[0] - qoi_est);
// Info for user.
info("Relative error (exact) = %g %%", err_qoi_exact);
// Add entry to DOF and CPU convergence graphs.
graph_dof_exact.add_values(Space::get_num_dofs(space), err_qoi_exact);
graph_cpu_exact.add_values(cpu_time.accumulated(), err_qoi_exact);
}
// Add entry to DOF and CPU convergence graphs.
graph_dof_est.add_values(Space::get_num_dofs(space), max_qoi_err_est);
graph_cpu_est.add_values(cpu_time.accumulated(), max_qoi_err_est);
// Decide whether the max. FTR error in the quantity of interest
// is sufficiently small.
if(max_qoi_err_est < TOL_ERR_QOI) break;
// Returns updated coarse and fine meshes, with the last
// coarse and fine mesh solutions on them, respectively.
// The coefficient vectors and numbers of degrees of freedom
// on both meshes are also updated.
adapt(NORM, ADAPT_TYPE, THRESHOLD, ftr_errors, space, ref_space);
as++;
// Plot meshes, results, and errors.
adapt_plotting(space, ref_space, NORM, EXACT_SOL_PROVIDED, exact_sol);
// Cleanup.
delete ref_space;
}
while (done == false);
info("Total running time: %g s", cpu_time.accumulated());
// Save convergence graphs.
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.save("conv_cpu_est.dat");
graph_dof_exact.save("conv_dof_exact.dat");
graph_cpu_exact.save("conv_cpu_exact.dat");
// Test variable.
bool success = true;
info("ndof = %d.", Space::get_num_dofs(space));
if (Space::get_num_dofs(space) > 150) success = false;
if (success)
{
info("Success!");
return ERROR_SUCCESS;
}
else
{
info("Failure!");
return ERROR_FAILURE;
}
}
int main() {
// Create coarse mesh, set Dirichlet BC, enumerate
// basis functions
Mesh *mesh = new Mesh(A, B, N_elem, P_init, N_eq);
mesh->set_bc_left_dirichlet(0, Val_dir_left);
mesh->set_bc_right_dirichlet(0, Val_dir_right);
mesh->assign_dofs();
// Create discrete problem on coarse mesh
DiscreteProblem *dp = new DiscreteProblem();
dp->add_matrix_form(0, 0, jacobian);
dp->add_vector_form(0, residual);
// Convergence graph wrt. the number of degrees of freedom
// (goal-oriented adaptivity)
GnuplotGraph graph_ftr;
graph_ftr.set_log_y();
graph_ftr.set_captions("Convergence History", "Degrees of Freedom", "QOI error");
graph_ftr.add_row("QOI error - FTR (exact)", "k", "-", "o");
graph_ftr.add_row("QOI error - FTR (est)", "k", "--");
// Main adaptivity loop
int adapt_iterations = 1;
double ftr_errors[MAX_ELEM_NUM]; // This array decides what
// elements will be refined.
ElemPtr2 ref_ftr_pairs[MAX_ELEM_NUM]; // To store element pairs from the
// FTR solution. Decides how
// elements will be hp-refined.
for (int i=0; i < MAX_ELEM_NUM; i++) {
ref_ftr_pairs[i][0] = new Element();
ref_ftr_pairs[i][1] = new Element();
}
while(1) {
printf("============ Adaptivity step %d ============\n", adapt_iterations);
printf("N_dof = %d\n", mesh->get_n_dof());
// Newton's loop on coarse mesh
int success;
if(JFNK == 0) {
newton(dp, mesh, NULL, NEWTON_TOL_COARSE, NEWTON_MAXITER);
}
else {
jfnk_cg(dp, mesh, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_COARSE, NEWTON_MAXITER);
}
// For every element perform its fast trial refinement (FTR),
// calculate the norm of the difference between the FTR
// solution and the coarse mesh solution, and store the
// error in the ftr_errors[] array.
int n_elem = mesh->get_n_active_elem();
double max_qoi_err_est = 0;
for (int i=0; i < n_elem; i++) {
printf("=== Starting FTR of Elem [%d]\n", i);
// Replicate coarse mesh including solution.
Mesh *mesh_ref_local = mesh->replicate();
// Perform FTR of element 'i'
mesh_ref_local->reference_refinement(i, 1);
printf("Elem [%d]: fine mesh created (%d DOF).\n",
i, mesh_ref_local->assign_dofs());
// Newton's loop on the FTR mesh
if(JFNK == 0) {
newton(dp, mesh_ref_local, NULL, NEWTON_TOL_COARSE, NEWTON_MAXITER);
}
else {
jfnk_cg(dp, mesh_ref_local, MATRIX_SOLVER_TOL, MATRIX_SOLVER_MAXITER,
JFNK_EPSILON, NEWTON_TOL_REF, NEWTON_MAXITER);
}
// Print FTR solution (enumerated)
Linearizer *lxx = new Linearizer(mesh_ref_local);
char out_filename[255];
sprintf(out_filename, "solution_ref_%d.gp", i);
lxx->plot_solution(out_filename);
delete lxx;
// Calculate FTR errors for refinement purposes
if (GOAL_ORIENTED == 1) {
// Use quantity of interest.
double qoi_est = quantity_of_interest(mesh, X_QOI);
double qoi_ref_est = quantity_of_interest(mesh_ref_local, X_QOI);
ftr_errors[i] = fabs(qoi_ref_est - qoi_est);
}
else {
// Use global norm
double err_est_array[MAX_ELEM_NUM];
ftr_errors[i] = calc_error_estimate(NORM, mesh, mesh_ref_local,
err_est_array);
}
// Calculating maximum of QOI FTR error for plotting purposes
if (GOAL_ORIENTED == 1) {
if (ftr_errors[i] > max_qoi_err_est)
max_qoi_err_est = ftr_errors[i];
}
else {
double qoi_est = quantity_of_interest(mesh, X_QOI);
double qoi_ref_est = quantity_of_interest(mesh_ref_local, X_QOI);
double err_est = fabs(qoi_ref_est - qoi_est);
if (err_est > max_qoi_err_est)
max_qoi_err_est = err_est;
}
// Copy the reference element pair for element 'i'
// into the ref_ftr_pairs[i][] array
Iterator *I = new Iterator(mesh);
Iterator *I_ref = new Iterator(mesh_ref_local);
Element *e, *e_ref;
while (1) {
e = I->next_active_element();
e_ref = I_ref->next_active_element();
if (e->id == i) {
e_ref->copy_into(ref_ftr_pairs[e->id][0]);
// coarse element 'e' was split in space
if (e->level != e_ref->level) {
e_ref = I_ref->next_active_element();
e_ref->copy_into(ref_ftr_pairs[e->id][1]);
}
break;
}
}
delete I;
delete I_ref;
delete mesh_ref_local;
}
// Add entries to convergence graphs
if (EXACT_SOL_PROVIDED) {
double qoi_est = quantity_of_interest(mesh, X_QOI);
double u[MAX_EQN_NUM], dudx[MAX_EQN_NUM];
exact_sol(X_QOI, u, dudx);
double err_qoi_exact = fabs(u[0] - qoi_est);
// plotting error in quantity of interest wrt. exact value
graph_ftr.add_values(0, mesh->get_n_dof(), err_qoi_exact);
}
graph_ftr.add_values(1, mesh->get_n_dof(), max_qoi_err_est);
// Decide whether the max. FTR error in the quantity of interest
// is sufficiently small
if(max_qoi_err_est < TOL_ERR_QOI) break;
// debug
if (adapt_iterations == 3) break;
// Returns updated coarse mesh with the last solution on it.
adapt(NORM, ADAPT_TYPE, THRESHOLD, ftr_errors,
mesh, ref_ftr_pairs);
adapt_iterations++;
}
// Plot meshes, results, and errors
adapt_plotting(mesh, ref_ftr_pairs,
NORM, EXACT_SOL_PROVIDED, exact_sol);
// Save convergence graph
graph_ftr.save("conv_dof.gp");
printf("Done.\n");
return 1;
}
