void DiscreteProblem::create_matrix()
{
// remove any previous matrix
free_matrix_indices();
free_matrix_values();
// calculate the total number of DOFs
ndofs = 0;
for (int i = 0; i < neq; i++)
ndofs += spaces[i]->get_num_dofs();
if (!quiet) verbose("Ndofs: %d", ndofs);
if (!ndofs) return;
// get row and column indices of nonzero matrix elements
Page** pages = new Page*[ndofs];
memset(pages, 0, sizeof(Page*) * ndofs);
if (!quiet) { verbose("Calculating matrix sparse structure..."); begin_time(); }
precalculate_sparse_structure(pages);
// initialize the arrays Ap and Ai
Ap = (int*) malloc(sizeof(int) * (ndofs+1));
int aisize = get_num_indices(pages, ndofs);
Ai = (int*) malloc(sizeof(int) * aisize);
if (Ai == NULL) error("Out of memory. Could not allocate the array Ai.");
// sort the indices and remove duplicities, insert into Ai
int i, pos = 0, num;
for (i = 0; i < ndofs; i++)
{
Ap[i] = pos;
pos += sort_and_store_indices(pages[i], Ai + pos, Ai + aisize);
}
Ap[i] = pos;
if (!quiet) verbose(" Nonzeros: %d\n Total matrix size: %0.1lf MB\n (time: %g sec)",
pos, (double) get_matrix_size() / (1024*1024), end_time());
delete [] pages;
// shrink Ai to the actual size
int* oldAi = Ai;
Ai = (int*) realloc(Ai, sizeof(int) * pos);
if (oldAi != Ai) warn("Realloc moved Ai when shrinking."); // this should not happen
// UMFPACK: perform symbolic analysis of the matrix
if (!quiet) { verbose("Performing UMFPACK symbolic analysis..."); begin_time(); }
int status = umfpack_symbolic(ndofs, ndofs, Ap, Ai, NULL, &Symbolic, NULL, NULL);
if (status != UMFPACK_OK) umfpack_status(status);
if (!quiet) verbose(" (time: %g sec)", end_time());
equi = (double*) malloc(sizeof(double) * ndofs);
if (equi == NULL) error("Out of memory. Error allocating the equilibration vector.");
for (int i = 0; i < ndofs; i++)
equi[i] = 1.0;
is_equi = false;
}
int main(int argc, char* argv[])
{
// Load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// Initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// Create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// Enumerate basis functions
space.assign_dofs();
// Initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, bilinear_form, bilinear_form_ord, SYM);
wf.add_liform(0, linear_form, linear_form_ord);
wf.add_liform_surf(0, linear_form_surf, linear_form_surf_ord, 2);
// Visualize solution and mesh
ScalarView sview("Coarse solution", 0, 100, 798, 700);
OrderView oview("Polynomial orders", 800, 100, 798, 700);
// Matrix solver
UmfpackSolver solver;
// Time measurement
double cpu = 0;
begin_time();
// Solve the problem
Solution sln;
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln);
// Time measurement
cpu += end_time();
// View the solution and mesh
sview.show(&sln);
oview.show(&space);
// Print timing information
verbose("Total running time: %g sec", cpu);
// wait for all views to be closed
View::wait("Waiting for all views to be closed.");
return 0;
}
/** Nonadaptive solver.*/
void solveNonadaptive(Mesh &mesh, NonlinSystem &nls,
Solution &Cp, Solution &Ci, Solution &phip, Solution &phii) {
begin_time();
//VectorView vview("electric field [V/m]", 0, 0, 600, 600);
ScalarView Cview("Concentration [mol/m3]", 0, 0, 800, 800);
ScalarView phiview("Voltage [V]", 650, 0, 600, 600);
#ifdef CONT_OUTPUT
phiview.show(&phii);
Cview.show(&Ci);
Cview.wait_for_keypress();
#endif
Solution Csln, phisln;
for (int n = 1; n <= NSTEP; n++) {
#ifdef VERBOSE
info("\n---- Time step %d ----", n);
#endif
int it = 1;
double res_l2_norm;
do {
#ifdef VERBOSE
info("\n -------- Time step %d, Newton iter %d --------\n", n, it);
#endif
it++;
nls.assemble();
nls.solve(2, &Csln, &phisln);
res_l2_norm = nls.get_residuum_l2_norm();
#ifdef VERBOSE
info("Residuum L2 norm: %g\n", res_l2_norm);
#endif
Ci.copy(&Csln);
phii.copy(&phisln);
} while (res_l2_norm > NEWTON_TOL);
#ifdef CONT_OUTPUT
phiview.show(&phii);
Cview.show(&Ci);
#endif
phip.copy(&phii);
Cp.copy(&Ci);
}
verbose("\nTotal run time: %g sec", end_time());
Cview.show(&Ci);
phiview.show(&phii);
//MeshView mview("small.mesh", 100, 30, 800, 800);
//mview.show(&mesh);
View::wait();
}
void DiscreteProblem::assemble_matrix_and_rhs(bool rhsonly)
{
int i, j, k, l, m, n;
bool bnd[4], nat[neq];
EdgePos ep[4];
if (!ndofs) return;
warned_order = false;
if (!rhsonly)
{
alloc_matrix_values();
if (!quiet) { verbose("Assembling stiffness matrix..."); begin_time(); }
}
else
{
memset(RHS, 0, sizeof(scalar) * ndofs);
if (!quiet) { verbose("Assembling RHS..."); begin_time(); }
}
// create slave pss's for test functions, init quadrature points
PrecalcShapeset* spss[neq];
PrecalcShapeset *fu, *fv;
for (i = 0; i < neq; i++)
{
spss[i] = new PrecalcShapeset(pss[i]);
pss [i]->set_quad_2d(&g_quad_2d_std);
spss[i]->set_quad_2d(&g_quad_2d_std);
}
// initialize buffer
buffer = NULL;
mat_size = 0;
get_matrix_buffer(9);
// initialize assembly lists, refmap
AsmList al[neq], *am, *an;
RefMap* refmap = new RefMap[neq];
for (i = 0; i < neq; i++)
refmap[i].set_quad_2d(&g_quad_2d_std);
for (i = 0; i < num_extern; i++)
extern_fns[i]->set_quad_2d(&g_quad_2d_std);
// init multi-mesh traversal
int nm = neq + num_extern;
Mesh* meshes[nm];
Transformable* fn[nm];
for (i = 0; i < neq; i++)
meshes[i] = spaces[i]->get_mesh();
memcpy(fn, pss, neq * sizeof(Transformable*));
for (i = 0; i < num_extern; i++) {
meshes[neq+i] = extern_fns[i]->get_mesh();
fn[neq+i] = extern_fns[i];
}
// todo: kdyz maji nektere slozky stejnou sit, at sdili i refmapy
// - ale to bysme potrebovali slave RefMap
// loop through all elements
Element** e;
Traverse trav;
trav.begin(nm, meshes, fn);
while ((e = trav.get_next_state(bnd, ep)) != NULL)
{
// set maximum integration order for use in integrals, see limit_order()
update_limit_table(e[0]->get_mode());
// obtain assembly lists for the element at all spaces, set appropriate mode for each pss
for (i = 0; i < neq; i++)
{
spaces[i]->get_element_assembly_list(e[i], al + i);
// todo: neziskavat znova, pokud se element nezmenil
if (is_equi)
for (j = 0; j < al[i].cnt; j++)
if (al[i].dof[j] >= 0)
al[i].coef[j] /= equi[al[i].dof[j]];
spss[i]->set_active_element(e[i]);
spss[i]->set_master_transform();
refmap[i].set_active_element(e[i]);
refmap[i].force_transform(pss[i]->get_transform(), pss[i]->get_ctm());
}
// go through all equation-blocks of the element stiffness matrix, assemble volume integrals
for (m = 0, am = al; m < neq; m++, am++)
{
fv = spss[m];
if (!rhsonly)
{
for (n = 0, an = al; n < neq; n++, an++)
{
fu = pss[n];
BiForm* bf = biform[m] + n;
if (!bf->sym && !bf->unsym) continue;
if (bf->unsym == BF_SYM || bf->unsym == BF_ANTISYM) continue;
bool tra = (biform[n][m].unsym == BF_SYM || biform[n][m].unsym == BF_ANTISYM);
// assemble the (m,n)-block of the stiffness matrix
scalar sy, un, **mat = get_matrix_buffer(std::max(am->cnt, an->cnt));
for (i = 0; i < am->cnt; i++)
{
if (!tra && (k = am->dof[i]) < 0) continue;
fv->set_active_shape(am->idx[i]);
// unsymmetric block
if (!bf->sym)
{
for (j = 0; j < an->cnt; j++)
{
fu->set_active_shape(an->idx[j]);
un = bf->unsym(fu, fv, refmap+n, refmap+m) * an->coef[j] * am->coef[i];
if (an->dof[j] < 0) Dir[k] -= un; else mat[i][j] = un;
}
}
// symmetric block
else
{
for (j = 0; j < an->cnt; j++)
{
scalar coef = an->coef[j] * am->coef[i];
if (an->dof[j] < 0)
{
fu->set_active_shape(an->idx[j]);
un = bf->unsym ? bf->unsym(fu, fv, refmap+n, refmap+m) * coef : 0.0;
sy = bf->sym(fu, fv, refmap+n, refmap+m) * coef;
Dir[k] -= (un + sy);
}
if (j >= i)
{
fu->set_active_shape(an->idx[j]);
un = bf->unsym ? bf->unsym(fu, fv, refmap+n, refmap+m) * coef : 0.0;
mat[j][i] = sy = bf->sym (fu, fv, refmap+n, refmap+m) * coef;
mat[i][j] = (un + sy);
}
else if (bf->unsym)
{
fu->set_active_shape(an->idx[j]);
mat[i][j] += bf->unsym(fu, fv, refmap+n, refmap+m) * coef;
}
}
}
}
// insert the local stiffness matrix into the global one
insert_matrix(mat, am->dof, an->dof, am->cnt, an->cnt);
// insert also the off-diagonal (anti-)symmetric block, if required
if (tra)
{
if (biform[n][m].unsym == BF_ANTISYM) chsgn(mat, am->cnt, an->cnt);
transpose(mat, am->cnt, an->cnt);
insert_matrix(mat, an->dof, am->dof, an->cnt, am->cnt);
// we also need to take care of the RHS...
for (j = 0; j < am->cnt; j++)
if (am->dof[j] < 0)
for (i = 0; i < an->cnt; i++)
if (an->dof[i] >= 0)
Dir[an->dof[i]] -= mat[i][j];
}
}
}
// assemble rhs (linear form)
if (!liform[m].lf) continue;
for (i = 0; i < am->cnt; i++)
{
if (am->dof[i] < 0) continue;
fv->set_active_shape(am->idx[i]);
RHS[am->dof[i]] += liform[m].lf(fv, refmap+m) * am->coef[i];
}
}
// assemble surface integrals now: loop through boundary edges of the element
if (rhsonly) continue; // fixme
for (int edge = 0; edge < e[0]->nvert; edge++)
{
if (!bnd[edge]) continue;
// obtain the list of shape functions which are nonzero on this edge
for (i = 0; i < neq; i++)
if ((nat[i] = (spaces[i]->bc_type_callback(ep[edge].marker) == BC_NATURAL)))
spaces[i]->get_edge_assembly_list(e[i], edge, al + i);
// loop through the equation-blocks
for (m = 0, am = al; m < neq; m++, am++)
{
if (!nat[m]) continue;
fv = spss[m];
ep[edge].base = trav.get_base();
ep[edge].space_v = spaces[m];
for (n = 0, an = al; n < neq; n++, an++)
{
if (!nat[n]) continue;
BiForm* bf = biform[m] + n;
if (!bf->surf) continue;
fu = pss[n];
ep[edge].space_u = spaces[n];
// assemble the surface part of the bilinear form
scalar bi, **mat = get_matrix_buffer(std::max(am->cnt, an->cnt));
for (i = 0; i < am->cnt; i++)
{
if ((k = am->dof[i]) < 0) continue;
fv->set_active_shape(am->idx[i]);
for (j = 0; j < an->cnt; j++)
{
fu->set_active_shape(an->idx[j]);
bi = bf->surf(fu, fv, refmap+n, refmap+m, ep+edge) * an->coef[j] * am->coef[i];
if (an->dof[j] >= 0) mat[i][j] = bi; else Dir[k] -= bi;
}
}
insert_matrix(mat, am->dof, an->dof, am->cnt, an->cnt);
}
// assemble the surface part of the linear form
if (!liform[m].surf) continue;
for (i = 0; i < am->cnt; i++)
{
if (am->dof[i] < 0) continue;
fv->set_active_shape(am->idx[i]);
RHS[am->dof[i]] += liform[m].surf(fv, refmap+m, ep+edge) * am->coef[i];
}
}
}
}
trav.finish();
for (i = 0; i < ndofs; i++)
RHS[i] += Dir[i];
if (!quiet) verbose(" (time: %g sec)", end_time());
for (i = 0; i < neq; i++) delete spss[i];
delete [] buffer;
delete [] refmap;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("square_quad.mesh", &mesh);
// initial mesh refinement
for (int i=0; i < INIT_REF_NUM; i++) mesh.refine_all_elements();
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
wf.add_liform(0, linear_form, linear_form_ord);
// visualize solution and mesh
ScalarView sview("Coarse solution", 0, 100, 798, 700);
OrderView oview("Polynomial orders", 800, 100, 798, 700);
// matrix solver
UmfpackSolver solver;
// prepare selector
RefinementSelectors::H1UniformHP selector(ISO_ONLY, ADAPT_TYPE, 1.0, H2DRS_DEFAULT_ORDER, &shapeset);
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculate error wrt. exact solution
ExactSolution exact(&mesh, fndd);
double error = h1_error(&sln_coarse, &exact) * 100;
info("\nExact solution error: %g%%", error);
// view the solution
sview.show(&sln_coarse);
oview.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
H1AdaptHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// add entries to DOF convergence graphs
graph_dof_exact.add_values(space.get_num_dofs(), error);
graph_dof_exact.save("conv_dof_exact.dat");
graph_dof_est.add_values(space.get_num_dofs(), err_est);
graph_dof_est.save("conv_dof_est.dat");
// add entries to CPU convergence graphs
graph_cpu_exact.add_values(cpu, error);
graph_cpu_exact.save("conv_cpu_exact.dat");
graph_cpu_est.add_values(cpu, err_est);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, &selector, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
//sview.wait_for_keypress();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
sview.set_title("Final solution");
sview.show(&sln_fine);
// wait for keyboard or mouse input
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("square_quad.mesh", &mesh);
if(P_INIT == 1) P_INIT++; // this is because there are no degrees of freedom
// on the coarse mesh lshape.mesh if P_INIT == 1
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
wf.add_liform(0, callback(linear_form));
// visualize solution and mesh
//ScalarView sview("Coarse solution", 0, 0, 500, 400);
//OrderView oview("Polynomial orders", 505, 0, 500, 400);
// matrix solver
UmfpackSolver solver;
// prepare selector
RefinementSelectors::H1NonUniformHP selector(ISO_ONLY, ADAPT_TYPE, 1.0, H2DRS_DEFAULT_ORDER, &shapeset);
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculate error wrt. exact solution
ExactSolution exact(&mesh, fndd);
double error = h1_error(&sln_coarse, &exact) * 100;
info("\nExact solution error: %g%%", error);
// view the solution
//sview.show(&sln_coarse);
//oview.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
H1AdaptHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// add entries to DOF convergence graphs
graph_dof_exact.add_values(space.get_num_dofs(), error);
graph_dof_exact.save("conv_dof_exact.dat");
graph_dof_est.add_values(space.get_num_dofs(), err_est);
graph_dof_est.save("conv_dof_est.dat");
// add entries to CPU convergence graphs
graph_cpu_exact.add_values(cpu, error);
graph_cpu_exact.save("conv_cpu_exact.dat");
graph_cpu_est.add_values(cpu, err_est);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
done = hp.adapt(THRESHOLD, STRATEGY, &selector, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
// wait for keyboard or mouse input
//sview.wait_for_keypress("Click into the mesh window and press any key to proceed.");
}
while (done == false);
verbose("Total running time: %g sec", cpu);
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
int n_dof_allowed = 49;
printf("n_dof_actual = %d\n", ndofs);
printf("n_dof_allowed = %d\n", n_dof_allowed); // ndofs was 49 at the time this test was created
if (ndofs <= n_dof_allowed) {
printf("Success!\n");
return ERROR_SUCCESS;
}
else {
printf("Failure!\n");
return ERROR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
if (ALIGN_MESH) mloader.load("oven_load_circle.mesh", &mesh);
else mloader.load("oven_load_square.mesh", &mesh);
//mesh.refine_all_elements();
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace space(&mesh, &shapeset);
space.set_bc_types(e_bc_types);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form));
wf.add_liform_surf(0, callback(linear_form_surf));
// visualize solution and mesh
VectorView eview("Electric field",0,0,800, 590);
OrderView ord("Order", 800, 0, 700, 590);
/*
// view the basis functions
VectorBaseView bview;
vbview.show(&space);
vbview.wait_for_keypress();
*/
// matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_cpu_est;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// coarse problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// show real part of the solution
AbsFilter abs(&sln_coarse);
eview.set_min_max_range(0, 4e3);
eview.show(&abs);
ord.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem ref(&sys);
ref.assemble();
ref.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
hp.set_biform(0, 0, callback(hcurl_form_kappa));
double err_est_adapt = hp.calc_error(&sln_coarse, &sln_fine) * 100;
double err_est_hcurl = hcurl_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate (adapt): %g%%", err_est_adapt);
info("Error estimate (hcurl): %g%%", err_est_hcurl);
// add entries to DOF convergence graphs
graph_dof_est.add_values(space.get_num_dofs(), err_est_hcurl);
graph_dof_est.save("conv_dof_est.dat");
// add entries to CPU convergence graphs
graph_cpu_est.add_values(cpu, err_est_hcurl);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est_adapt too large, adapt the mesh
if (err_est_adapt < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait("Waiting for all views to be closed.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("screen-quad.mesh", &mesh);
// mloader.load("screen-tri.mesh", &mesh);
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
// visualize solution and mesh
ScalarView Xview_r("Electric field X - real", 0, 0, 450, 420);
ScalarView Yview_r("Electric field Y - real", 460, 0, 450, 420);
ScalarView Xview_i("Electric field X - imag", 920, 0, 450, 420);
ScalarView Yview_i("Electric field Y - imag", 1380, 0, 450, 420);
OrderView ord("Polynomial Orders", 0, 460, 450, 420);
/*
// view the basis functions
VectorBaseView bview;
vbview.show(&space);
vbview.wait_for_keypress();
*/
// matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculating error wrt. exact solution
Solution ex;
ex.set_exact(&mesh, exact);
double err_exact = 100 * hcurl_error(&sln_coarse, &ex);
info("Exact solution error: %g%%", err_exact);
// visualization
RealFilter real(&sln_coarse);
ImagFilter imag(&sln_coarse);
Xview_r.set_min_max_range(-3.0, 1.0);
//Xview_r.show_scale(false);
Xview_r.show(&real, EPS_NORMAL, FN_VAL_0);
Yview_r.set_min_max_range(-4.0, 4.0);
//Yview_r.show_scale(false);
Yview_r.show(&real, EPS_NORMAL, FN_VAL_1);
Xview_i.set_min_max_range(-1.0, 4.0);
//Xview_i.show_scale(false);
Xview_i.show(&imag, EPS_NORMAL, FN_VAL_0);
Yview_i.set_min_max_range(-4.0, 4.0);
//Yview_i.show_scale(false);
Yview_i.show(&imag, EPS_NORMAL, FN_VAL_1);
ord.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem ref(&sys);
ref.assemble();
ref.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
double err_est_adapt = hp.calc_error(&sln_coarse, &sln_fine) * 100;
double err_est_hcurl = hcurl_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate (adapt): %g%%", err_est_adapt);
info("Error estimate (hcurl): %g%%", err_est_hcurl);
// add entries to DOF convergence graphs
graph_dof_exact.add_values(space.get_num_dofs(), err_exact);
graph_dof_exact.save("conv_dof_exact.dat");
graph_dof_est.add_values(space.get_num_dofs(), err_est_hcurl);
graph_dof_est.save("conv_dof_est.dat");
// add entries to CPU convergence graphs
graph_cpu_exact.add_values(cpu, err_exact);
graph_cpu_exact.save("conv_cpu_exact.dat");
graph_cpu_est.add_values(cpu, err_est_hcurl);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est_adapt too large, adapt the mesh
if (err_est_adapt < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait("Waiting for all views to be closed.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("lshape3q.mesh", &mesh);
// mloader.load("lshape3t.mesh", &mesh);
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
wf.add_biform_surf(0, 0, callback(bilinear_form_surf));
wf.add_liform_surf(0, linear_form_surf, linear_form_surf_ord);
// visualize solution and mesh
OrderView ordview("Polynomial Orders", 600, 0, 600, 500);
VectorView vecview("Real part of Electric Field - VectorView", 0, 0, 600, 500);
/*
// view the basis functions
VectorBaseView bview;
vbview.show(&space);
vbview.wait_for_keypress();
*/
// matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculating error wrt. exact solution
ExactSolution ex(&mesh, exact);
double err_exact = 100 * hcurl_error(&sln_coarse, &ex);
info("Exact solution error: %g%%", err_exact);
// show real part of the solution and mesh
ordview.show(&space);
RealFilter real(&sln_coarse);
vecview.set_min_max_range(0, 1);
vecview.show(&real, EPS_HIGH);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&sys);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
double err_est_adapt = hp.calc_error(&sln_coarse, &sln_fine) * 100;
double err_est_hcurl = hcurl_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate (adapt): %g%%", err_est_adapt);
info("Error estimate (hcurl): %g%%", err_est_hcurl);
// add entries to DOF convergence graphs
graph_dof_exact.add_values(space.get_num_dofs(), err_exact);
graph_dof_exact.save("conv_dof_exact.dat");
graph_dof_est.add_values(space.get_num_dofs(), err_est_hcurl);
graph_dof_est.save("conv_dof_est.dat");
// add entries to CPU convergence graphs
graph_cpu_exact.add_values(cpu, err_exact);
graph_cpu_exact.save("conv_cpu_exact.dat");
graph_cpu_est.add_values(cpu, err_est_hcurl);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est_adapt too large, adapt the mesh
if (err_est_adapt < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
vecview.set_title("Final solution");
vecview.show(&sln_fine);
// wait for keyboard or mouse input
View::wait("Waiting for all views to be closed.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
mesh.load("square_quad.mesh");
if(P_INIT == 1) mesh.refine_all_elements(); // this is because there are no degrees of freedom
// on the coarse mesh lshape.mesh if P_INIT == 1
// initialize the shapeset and the cache
H1ShapesetOrtho shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, bilinear_form, SYM);
wf.add_liform(0, linear_form);
// visualize solution and mesh
ScalarView sview("Coarse solution", 0, 100, 798, 700);
OrderView oview("Polynomial orders", 800, 100, 798, 700);
// matrix solver
UmfpackSolver solver;
// convergence graph wrt. the number of degrees of freedom
GnuplotGraph graph;
graph.set_log_y();
graph.set_captions("Error Convergence for the Inner Layer Problem", "Degrees of Freedom", "Error [%]");
graph.add_row("exact error", "k", "-", "o");
graph.add_row("error estimate", "k", "--");
// convergence graph wrt. CPU time
GnuplotGraph graph_cpu;
graph_cpu.set_captions("Error Convergence for the Inner Layer Problem", "CPU Time", "Error Estimate [%]");
graph_cpu.add_row("exact error", "k", "-", "o");
graph_cpu.add_row("error estimate", "k", "--");
graph_cpu.set_log_y();
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculate error wrt. exact solution
ExactSolution exact(&mesh, fndd);
double error = h1_error(&sln_coarse, &exact) * 100;
info("\nExact solution error: %g%%", error);
// view the solution and mesh
sview.show(&sln_coarse);
oview.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
H1OrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// add entry to DOF convergence graph
graph.add_values(0, space.get_num_dofs(), error);
graph.add_values(1, space.get_num_dofs(), err_est);
graph.save("conv_dof.gp");
// add entry to CPU convergence graph
graph_cpu.add_values(0, cpu, error);
graph_cpu.add_values(1, cpu, err_est);
graph_cpu.save("conv_cpu.gp");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
sview.set_title("Final solution");
sview.show(&sln_fine);
// wait for keyboard or mouse input
printf("Waiting for keyboard or mouse input.\n");
View::wait();
return 0;
}
void Linearizer::process_solution(MeshFunction* sln, int item, double eps, double max_abs,
MeshFunction* xdisp, MeshFunction* ydisp, double dmult)
{
lock_data();
begin_time();
// initialization
this->sln = sln;
this->item = item;
this->eps = eps;
this->xdisp = xdisp;
this->ydisp = ydisp;
this->dmult = dmult;
nv = nt = ne = 0;
del_slot = -1;
if (!item) error("'item' cannot be zero.");
get_gv_a_b(item, ia, ib);
if (ib >= 6) error("Invalid 'item'.");
disp = (xdisp != NULL || ydisp != NULL);
if (disp && (xdisp == NULL || ydisp == NULL))
error("Both displacement components must be supplied.");
// estimate the required number of vertices and triangles
Mesh* mesh = sln->get_mesh();
int nn = mesh->get_num_elements();
int ev = std::max(32 * nn, 10000); // todo: check this
int et = std::max(64 * nn, 20000);
int ee = std::max(24 * nn, 7500);
// check that displacement meshes are the same
if (disp)
{
unsigned seq1 = mesh->get_seq();
unsigned seq2 = xdisp->get_mesh()->get_seq();
unsigned seq3 = ydisp->get_mesh()->get_seq();
if (seq1 != seq2 || seq1 != seq3)
error("Displacements must be defined on the same mesh as the solution.");
}
// reuse or allocate vertex, triangle and edge arrays
lin_init_array(verts, double3, cv, ev);
lin_init_array(tris, int3, ct, et);
lin_init_array(edges, int3, ce, ee);
info = (int4*) malloc(sizeof(int4) * cv);
// initialize the hash table
int size = 0x2000;
while (size*2 < cv) size *= 2;
hash_table = (int*) malloc(sizeof(int) * size);
memset(hash_table, 0xff, sizeof(int) * size);
mask = size-1;
// select the linearization quadrature
Quad2D *old_quad, *old_quad_x, *old_quad_y;
old_quad = sln->get_quad_2d();
sln->set_quad_2d(&quad_lin);
if (disp) { old_quad_x = xdisp->get_quad_2d();
old_quad_y = ydisp->get_quad_2d();
xdisp->set_quad_2d(&quad_lin);
ydisp->set_quad_2d(&quad_lin); }
// create all top-level vertices (corresponding to vertex nodes), with
// all parent-son relations preserved; this is necessary for regularization to
// work on irregular meshes
nn = mesh->get_max_node_id();
int* id2id = new int[nn];
memset(id2id, 0xff, sizeof(int) * nn);
bool finished;
do
{
finished = true;
Node* node;
for_all_vertex_nodes(node, mesh)
{
if (id2id[node->id] < 0 && node->ref != TOP_LEVEL_REF)
if (node->p1 < 0)
id2id[node->id] = get_vertex(node->id, node->id, node->x, node->y, 0);
else if (id2id[node->p1] >= 0 && id2id[node->p2] >= 0)
id2id[node->id] = get_vertex(id2id[node->p1], id2id[node->p2], node->x, node->y, 0);
else
finished = false;
}
}
while (!finished);
auto_max = (max_abs < 0.0);
max = auto_max ? 0.0 : max_abs;
// obtain the solution in vertices, estimate the maximum solution value
Element* e;
for_all_active_elements(e, mesh)
{
sln->set_active_element(e);
sln->set_quad_order(0, item);
scalar* val = sln->get_values(ia, ib);
if (val == NULL) error("item not defined in the solution.");
scalar *dx, *dy;
if (disp)
{
xdisp->set_active_element(e);
ydisp->set_active_element(e);
xdisp->set_quad_order(0, FN_VAL);
ydisp->set_quad_order(0, FN_VAL);
dx = xdisp->get_fn_values();
dy = ydisp->get_fn_values();
}
for (unsigned int i = 0; i < e->nvert; i++)
{
double f = getval(i);
if (auto_max && finite(f) && fabs(f) > max) max = fabs(f);
int id = id2id[e->vn[i]->id];
verts[id][2] = f;
if (disp)
{
verts[id][0] = e->vn[i]->x + dmult*realpart(dx[i]);
verts[id][1] = e->vn[i]->y + dmult*realpart(dy[i]);
}
}
}
int main(int argc, char* argv[])
{
// load the mesh file
Mesh mesh;
H2DReader mloader;
mloader.load("square.mesh", &mesh);
// initial mesh refinements
for(int i = 0; i < INIT_GLOB_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(1,INIT_BDY_REF_NUM);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create an H1 space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
space.assign_dofs();
// previous solution for the Newton's iteration
Solution u_prev;
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(jac), UNSYM, ANY, 1, &u_prev);
wf.add_liform(0, callback(res), ANY, 1, &u_prev);
// initialize the nonlinear system and solver
UmfpackSolver umfpack;
NonlinSystem nls(&wf, &umfpack);
nls.set_spaces(1, &space);
nls.set_pss(1, &pss);
// DOF and CPU convergence graphs
SimpleGraph graph_dof, graph_cpu;
// project the function init_cond() on the mesh
// to obtain initial guess u_prev for the Newton's method
nls.set_ic(init_cond, &mesh, &u_prev, PROJ_TYPE);
// visualise the initial ocndition
ScalarView view("Initial condition", 0, 0, 700, 600);
view.show(&u_prev);
OrderView oview("Initial mesh", 720, 0, 700, 600);
oview.show(&space);
//printf("Click into the image window and press any key to proceed.\n");
//view.wait_for_keypress();
// adaptivity loop
double cpu = 0.0, err_est;
int a_step = 1;
bool done = false;
do {
a_step++;
// Newton's loop on the coarse mesh
int it = 1;
double res_l2_norm;
Solution sln_coarse;
do
{
info("\n---- Adapt step %d, Newton iter %d (coarse mesh) ---------------------------------\n", a_step, it++);
printf("ndof = %d\n", space.get_num_dofs());
// time measurement
begin_time();
// assemble the Jacobian matrix and residual vector,
// solve the system
nls.assemble();
nls.solve(1, &sln_coarse);
// calculate the l2-norm of residual vector
res_l2_norm = nls.get_residuum_l2_norm();
info("Residuum L2 norm: %g\n", res_l2_norm);
// time measurement
cpu += end_time();
// visualise the solution
char title[100];
sprintf(title, "Temperature (coarse mesh), Newton iteration %d", it-1);
view.set_title(title);
view.show(&sln_coarse);
sprintf(title, "Coarse mesh, Newton iteration %d", it-1);
oview.set_title(title);
oview.show(&space);
//printf("Click into the image window and press any key to proceed.\n");
//view.wait_for_keypress();
// save the new solution as "previous" for the
// next Newton's iteration
u_prev.copy(&sln_coarse);
}
while (res_l2_norm > NEWTON_TOL);
// Setting initial guess for the Newton's method on the fine mesh
Solution sln_fine, u_prev_fine;
RefNonlinSystem rs(&nls);
rs.prepare();
rs.set_ic(&u_prev, &u_prev);
// Newton's loop on the fine mesh
it = 1;
do {
info("\n---- Adapt step %d, Newton iter %d (fine mesh) ---------------------------------\n", a_step, it++);
// time measurement
begin_time();
// assemble the Jacobian matrix and residual vector,
// solve the system
rs.assemble();
rs.solve(1, &sln_fine);
// calculate the l2-norm of residual vector
res_l2_norm = rs.get_residuum_l2_norm();
info("Residuum L2 norm: %g\n", res_l2_norm);
// time measurement
cpu += end_time();
// visualise the solution
char title[100];
sprintf(title, "Temperature (fine mesh), Newton iteration %d", it-1);
view.set_title(title);
view.show(&sln_fine);
sprintf(title, "Fine mesh, Newton iteration %d", it-1);
oview.set_title(title);
oview.show(rs.get_ref_space(0));
//printf("Click into the image window and press any key to proceed.\n");
//view.wait_for_keypress();
u_prev.copy(&sln_fine);
} while (res_l2_norm > NEWTON_TOL_REF);
// time measurement
begin_time();
// calculate element errors and total error estimate
H1OrthoHP hp(1, &space);
err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%%", err_est);
// add entry to DOF convergence graph
graph_dof.add_values(space.get_num_dofs(), err_est);
graph_dof.save("conv_dof.dat");
// add entry to CPU convergence graph
graph_cpu.add_values(cpu, err_est);
graph_cpu.save("conv_cpu.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
int ndof = space.assign_dofs();
if (ndof >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
if (ALIGN_MESH) mesh.load("oven_load_circle.mesh");
else mesh.load("oven_load_square.mesh");
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace space(&mesh, &shapeset);
space.set_bc_types(e_bc_types);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, bilinear_form);
wf.add_liform_surf(0, linear_form_surf);
// visualize solution and mesh
VectorView eview("Electric field",0,0,800, 590);
OrderView ord("Order", 800, 0, 700, 590);
// matrix solver
UmfpackSolver solver;
// convergence graph wrt. the number of degrees of freedom
GnuplotGraph graph;
graph.set_captions("Error Convergence for the Waveguide Problem", "Degrees of Freedom", "Error Estimate [%]");
graph.add_row("error estimate", "-", "o");
graph.set_log_y();
// convergence graph wrt. CPU time
GnuplotGraph graph_cpu;
graph_cpu.set_captions("Error Convergence for the Waveguide Problem", "CPU Time", "Error Estimate [%]");
graph_cpu.add_row("error estimate", "-", "o");
graph_cpu.set_log_y();
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// coarse problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// show real part of the solution
AbsFilter abs(&sln_coarse);
eview.set_min_max_range(0, 4e3);
eview.show(&abs);
ord.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem ref(&sys);
ref.assemble();
ref.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
hp.set_kappa(sqr(kappa));
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Hcurl error estimate: %g%%", hcurl_error(&sln_coarse, &sln_fine) * 100);
info("Adapt error estimate: %g%%", err_est);
// add entry to DOF convergence graph
graph.add_values(0, space.get_num_dofs(), err_est);
graph.save("conv_dof.gp");
// add entry to CPU convergence graph
graph_cpu.add_values(0, cpu, err_est);
graph_cpu.save("conv_cpu.gp");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
printf("Waiting for keyboard or mouse input.\n");
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// Load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("domain.mesh", &mesh);
mesh.refine_all_elements();
// Initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// Create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// Enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, bilinear_form, bilinear_form_ord, SYM);
wf.add_liform(0, linear_form, linear_form_ord);
wf.add_liform_surf(0, linear_form_surf, linear_form_surf_ord, 2);
// Visualize solution and mesh
ScalarView sview("Coarse solution", 0, 100, 798, 700);
OrderView oview("Polynomial orders", 800, 100, 798, 700);
// Matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof, graph_cpu;
// Adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// Time measurement
begin_time();
// Solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// Time measurement
cpu += end_time();
// View the solution and mesh
sview.show(&sln_coarse);
oview.show(&space);
// Time measurement
begin_time();
// Solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(1, &sln_fine);
// Calculate error estimate wrt. fine mesh solution
H1OrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// add entry to DOF convergence graph
graph_dof.add_values(space.get_num_dofs(), err_est);
graph_dof.save("conv_dof.dat");
// add entry to CPU convergence graph
graph_cpu.add_values(cpu, err_est);
graph_cpu.save("conv_cpu.dat");
// If err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// Time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// Show the fine solution - this is the final result
sview.set_title("Final solution");
sview.show(&sln_fine);
// Wait for keyboard or mouse input
View::wait("Waiting for all views to be closed.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh xmesh, ymesh;
H2DReader mloader;
mloader.load("bracket.mesh", &xmesh);
// create initial mesh for the vertical displacement component,
// identical to the mesh for the horizontal displacement
// (bracket.mesh becomes a master mesh)
ymesh.copy(&xmesh);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset xpss(&shapeset);
PrecalcShapeset ypss(&shapeset);
// create the x displacement space
H1Space xdisp(&xmesh, &shapeset);
xdisp.set_bc_types(bc_types);
xdisp.set_bc_values(bc_values);
xdisp.set_uniform_order(P_INIT);
// create the y displacement space
H1Space ydisp(MULTI ? &ymesh : &xmesh, &shapeset);
ydisp.set_bc_types(bc_types);
ydisp.set_bc_values(bc_values);
ydisp.set_uniform_order(P_INIT);
// enumerate basis functions
int ndofs = xdisp.assign_dofs();
ndofs += ydisp.assign_dofs(ndofs);
// initialize the weak formulation
WeakForm wf(2);
wf.add_biform(0, 0, callback(bilinear_form_0_0), SYM); // note that only one symmetric part is
wf.add_biform(0, 1, callback(bilinear_form_0_1), SYM); // added in the case of symmetric bilinear
wf.add_biform(1, 1, callback(bilinear_form_1_1), SYM); // forms
wf.add_liform_surf(1, callback(linear_form_surf_1), marker_top);
// visualization of solution and meshes
OrderView xoview("X polynomial orders", 0, 0, 500, 500);
OrderView yoview("Y polynomial orders", 510, 0, 500, 500);
ScalarView sview("Von Mises stress [Pa]", 1020, 0, 500, 500);
// matrix solver
UmfpackSolver umfpack;
// DOF and CPU convergence graphs
SimpleGraph graph_dof, graph_cpu;
// adaptivity loop
int it = 1;
bool done = false;
double cpu = 0.0;
Solution x_sln_coarse, y_sln_coarse;
Solution x_sln_fine, y_sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
//calculating the number of degrees of freedom
ndofs = xdisp.assign_dofs();
ndofs += ydisp.assign_dofs(ndofs);
printf("xdof=%d, ydof=%d\n", xdisp.get_num_dofs(), ydisp.get_num_dofs());
// solve the coarse mesh problem
LinSystem ls(&wf, &umfpack);
ls.set_spaces(2, &xdisp, &ydisp);
ls.set_pss(2, &xpss, &ypss);
ls.assemble();
ls.solve(2, &x_sln_coarse, &y_sln_coarse);
// time measurement
cpu += end_time();
// view the solution -- this can be slow; for illustration only
VonMisesFilter stress_coarse(&x_sln_coarse, &y_sln_coarse, mu, lambda);
sview.set_min_max_range(0, 3e4);
sview.show(&stress_coarse);
xoview.show(&xdisp);
yoview.show(&ydisp);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(2, &x_sln_fine, &y_sln_fine);
// calculate element errors and total error estimate
H1OrthoHP hp(2, &xdisp, &ydisp);
hp.set_biform(0, 0, bilinear_form_0_0<scalar, scalar>, bilinear_form_0_0<Ord, Ord>);
hp.set_biform(0, 1, bilinear_form_0_1<scalar, scalar>, bilinear_form_0_1<Ord, Ord>);
hp.set_biform(1, 0, bilinear_form_1_0<scalar, scalar>, bilinear_form_1_0<Ord, Ord>);
hp.set_biform(1, 1, bilinear_form_1_1<scalar, scalar>, bilinear_form_1_1<Ord, Ord>);
double err_est = hp.calc_error_2(&x_sln_coarse, &y_sln_coarse, &x_sln_fine, &y_sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// time measurement
cpu += end_time();
// add entry to DOF convergence graph
graph_dof.add_values(xdisp.get_num_dofs() + ydisp.get_num_dofs(), err_est);
graph_dof.save("conv_dof.dat");
// add entry to CPU convergence graph
graph_cpu.add_values(cpu, err_est);
graph_cpu.save("conv_cpu.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY, CONV_EXP, MAX_ORDER, SAME_ORDERS);
ndofs = xdisp.assign_dofs();
ndofs += ydisp.assign_dofs(ndofs);
if (ndofs >= NDOF_STOP) done = true;
}
}
while (!done);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
VonMisesFilter stress_fine(&x_sln_fine, &y_sln_fine, mu, lambda);
sview.set_title("Final solution");
sview.set_min_max_range(0, 3e4);
sview.show(&stress_fine);
// wait for all views to be closed
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("motor.mesh", &mesh);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(biform1), SYM, 1);
wf.add_biform(0, 0, callback(biform2), SYM, 2);
// visualize solution, gradient, and mesh
ScalarView sview("Coarse solution", 0, 0, 600, 1000);
VectorView gview("Gradient", 610, 0, 600, 1000);
OrderView oview("Polynomial orders", 1220, 0, 600, 1000);
//gview.set_min_max_range(0.0, 400.0);
// matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof, graph_cpu;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// view the solution -- this can be slow; for illustration only
sview.show(&sln_coarse);
gview.show(&sln_coarse, &sln_coarse, EPS_NORMAL, FN_DX_0, FN_DY_0);
oview.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate element errors and total error estimate
H1OrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%%", err_est);
// time measurement
cpu += end_time();
// add entry to DOF convergence graph
graph_dof.add_values(space.get_num_dofs(), err_est);
graph_dof.save("conv_dof.dat");
// add entry to CPU convergence graph
graph_cpu.add_values(cpu, err_est);
graph_cpu.save("conv_cpu.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
sview.set_title("Final solution");
sview.show(&sln_fine);
gview.show(&sln_fine, &sln_fine, EPS_HIGH, FN_DX_0, FN_DY_0);
// wait for all views to be closed
View::wait();
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("square_quad.mesh", &mesh);
// mloader.load("square_tri.mesh", &mesh);
for (int i=0; i<INIT_REF_NUM; i++) mesh.refine_all_elements();
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
wf.add_liform(0, callback(linear_form));
// matrix solver
UmfpackSolver solver;
// prepare selector
RefinementSelectors::H1NonUniformHP selector(ISO_ONLY, ADAPT_TYPE, CONV_EXP, H2DRS_DEFAULT_ORDER, &shapeset);
// convergence graph wrt. the number of degrees of freedom
GnuplotGraph graph;
graph.set_log_y();
graph.set_captions("Error Convergence for the Inner Layer Problem", "Degrees of Freedom", "Error [%]");
graph.add_row("exact error", "k", "-", "o");
graph.add_row("error estimate", "k", "--");
// convergence graph wrt. CPU time
GnuplotGraph graph_cpu;
graph_cpu.set_captions("Error Convergence for the Inner Layer Problem", "CPU Time", "Error Estimate [%]");
graph_cpu.add_row("exact error", "k", "-", "o");
graph_cpu.add_row("error estimate", "k", "--");
graph_cpu.set_log_y();
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculate error wrt. exact solution
ExactSolution exact(&mesh, fndd);
double error = h1_error(&sln_coarse, &exact) * 100;
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&ls);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
H1AdaptHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Exact solution error: %g%%", error);
info("Estimate of error: %g%%", err_est);
// add entry to DOF convergence graph
graph.add_values(0, space.get_num_dofs(), error);
graph.add_values(1, space.get_num_dofs(), err_est);
graph.save("conv_dof.gp");
// add entry to CPU convergence graph
graph_cpu.add_values(0, cpu, error);
graph_cpu.add_values(1, cpu, err_est);
graph_cpu.save("conv_cpu.gp");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, &selector, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
int n_dof_allowed = 4000;
printf("n_dof_actual = %d\n", ndofs);
printf("n_dof_allowed = %d\n", n_dof_allowed);
if (ndofs <= n_dof_allowed) {
printf("Success!\n");
return ERROR_SUCCESS;
}
else {
printf("Failure!\n");
return ERROR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
mesh.load("screen-quad.mesh");
// mesh.load("screen-tri.mesh");
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
// visualize solution and mesh
ScalarView Xview_r("Electric field X - real", 0, 0, 320, 320);
ScalarView Yview_r("Electric field Y - real", 325, 0, 320, 320);
ScalarView Xview_i("Electric field X - imag", 650, 0, 320, 320);
ScalarView Yview_i("Electric field Y - imag", 975, 0, 320, 320);
OrderView ord("Polynomial Orders", 325, 400, 600, 600);
// matrix solver
UmfpackSolver solver;
// convergence graph wrt. the number of degrees of freedom
GnuplotGraph graph;
graph.set_captions("Error Convergence for the Screen Problem in H(curl)", "Degrees of Freedom", "Error [%]");
graph.add_row("exact error", "k", "-", "o");
graph.add_row("error estimate", "k", "--");
graph.set_log_y();
// convergence graph wrt. CPU time
GnuplotGraph graph_cpu;
graph_cpu.set_captions("Error Convergence for the Screen Problem in H(curl)", "CPU Time", "Error [%]");
graph_cpu.add_row("exact error", "k", "-", "o");
graph_cpu.add_row("error estimate", "k", "--");
graph_cpu.set_log_y();
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculating error wrt. exact solution
Solution ex;
ex.set_exact(&mesh, exact);
double error = 100 * hcurl_error(&sln_coarse, &ex);
info("Exact solution error: %g%%", error);
// visualization
RealFilter real(&sln_coarse);
ImagFilter imag(&sln_coarse);
Xview_r.set_min_max_range(-3.0, 1.0);
Xview_r.show_scale(false);
Xview_r.show(&real, EPS_NORMAL, FN_VAL_0);
Yview_r.set_min_max_range(-4.0, 4.0);
Yview_r.show_scale(false);
Yview_r.show(&real, EPS_NORMAL, FN_VAL_1);
Xview_i.set_min_max_range(-1.0, 4.0);
Xview_i.show_scale(false);
Xview_i.show(&imag, EPS_NORMAL, FN_VAL_0);
Yview_i.set_min_max_range(-4.0, 4.0);
Yview_i.show_scale(false);
Yview_i.show(&imag, EPS_NORMAL, FN_VAL_1);
ord.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem ref(&sys);
ref.assemble();
ref.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%%", err_est);
// add entry to DOF convergence graph
graph.add_values(0, space.get_num_dofs(), error);
graph.add_values(1, space.get_num_dofs(), err_est);
graph.save("conv_dof.gp");
// add entry to CPU convergence graph
graph_cpu.add_values(0, cpu, error);
graph_cpu.add_values(1, cpu, err_est);
graph_cpu.save("conv_cpu.gp");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait("Waiting for keyboard or mouse input.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("domain2.mesh", &mesh);
// initial uniform subdivision
//mesh.refine_all_elements();
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create an H1 space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(dir_bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form_iron), SYM, 3);
wf.add_biform(0, 0, callback(bilinear_form_wire), SYM, 2);
wf.add_biform(0, 0, callback(bilinear_form_air), SYM, 1);
wf.add_liform(0, callback(linear_form_wire), 2);
// visualize solution and mesh
ScalarView view("Vector potential A", 0, 0, 1000, 600);
OrderView oview("Polynomial orders", 1100, 0, 900, 600);
// matrix solver
UmfpackSolver solver;
// DOF and CPU convergence graphs
SimpleGraph graph_dof_est, graph_dof_exact, graph_cpu_est, graph_cpu_exact;
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
// time measurement
cpu += end_time();
// assemble the stiffness matrix and solve the system
sys.assemble();
sys.solve(1, &sln_coarse);
// visualize the solution
view.show(&sln_coarse, EPS_HIGH);
oview.show(&space);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&sys);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate element errors and total error estimate
H1OrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%%", err_est);
// add entries to DOF convergence graph
graph_dof_est.add_values(space.get_num_dofs(), err_est);
graph_dof_est.save("conv_dof.dat");
// add entries to CPU convergence graph
graph_cpu_est.add_values(cpu, err_est);
graph_cpu_est.save("conv_cpu.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
view.set_title("Final solution");
view.show(&sln_fine);
// wait for keyboard or mouse input
View::wait("Waiting for all views to be closed.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("lshape3q.mesh", &mesh);
// mloader.load("lshape3t.mesh", &mesh);
// initialize the shapeset and the cache
HcurlShapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
HcurlSpace space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form), SYM);
wf.add_biform_surf(0, 0, callback(bilinear_form_surf));
wf.add_liform_surf(0, linear_form_surf, linear_form_surf_ord);
// matrix solver
UmfpackSolver solver;
// convergence graph wrt. the number of degrees of freedom
GnuplotGraph graph;
graph.set_captions("Error Convergence for the Bessel Problem in H(curl)", "Degrees of Freedom", "Error [%]");
graph.add_row("exact error", "k", "-", "o");
graph.add_row("error estimate", "k", "--");
graph.set_log_y();
// convergence graph wrt. CPU time
GnuplotGraph graph_cpu;
graph_cpu.set_captions("Error Convergence for the Bessel Problem in H(curl)", "CPU Time", "Error [%]");
graph_cpu.add_row("exact error", "k", "-", "o");
graph_cpu.add_row("error estimate", "k", "--");
graph_cpu.set_log_y();
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem sys(&wf, &solver);
sys.set_spaces(1, &space);
sys.set_pss(1, &pss);
sys.assemble();
sys.solve(1, &sln_coarse);
// time measurement
cpu += end_time();
// calculating error wrt. exact solution
ExactSolution ex(&mesh, exact);
double err = 100 * hcurl_error(&sln_coarse, &ex);
info("Exact solution error: %g%%", err);
// time measurement
begin_time();
// solve the fine mesh problem
RefSystem rs(&sys);
rs.assemble();
rs.solve(1, &sln_fine);
// calculate error estimate wrt. fine mesh solution
HcurlOrthoHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%%", err_est);
// add entry to DOF convergence graph
graph.add_values(0, space.get_num_dofs(), err);
graph.add_values(1, space.get_num_dofs(), err_est);
graph.save("conv_dof.gp");
// add entry to CPU convergence graph
graph_cpu.add_values(0, cpu, err);
graph_cpu.add_values(1, cpu, err_est);
graph_cpu.save("conv_cpu.gp");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
verbose("Total running time: %g sec", cpu);
#define ERROR_SUCCESS 0
#define ERROR_FAILURE -1
int n_dof_allowed = 3000;
printf("n_dof_actual = %d\n", ndofs);
printf("n_dof_allowed = %d\n", n_dof_allowed);// ndofs was 2680 at the time this test was created
if (ndofs <= n_dof_allowed) {
printf("Success!\n");
return ERROR_SUCCESS;
}
else {
printf("Failure!\n");
return ERROR_FAILURE;
}
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh, basemesh;
basemesh.load("square.mesh");
for(int i = 0; i < REF_INIT; i++) basemesh.refine_all_elements();
mesh.copy(&basemesh);
mesh.refine_towards_boundary(1,3);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
space.assign_dofs();
// enumerate basis functions
space.assign_dofs();
Solution Tprev, // previous time step solution, for the time integration method
Titer; // solution converging during the Newton's iteration
// initialize the weak formulation
WeakForm wf(1);
if(TIME_DISCR == 1) {
wf.add_biform(0, 0, callback(J_euler), UNSYM, ANY, 1, &Titer);
wf.add_liform(0, callback(F_euler), ANY, 2, &Titer, &Tprev);
}
else {
wf.add_biform(0, 0, callback(J_cranic), UNSYM, ANY, 1, &Titer);
wf.add_liform(0, callback(F_cranic), ANY, 2, &Titer, &Tprev);
}
// matrix solver
UmfpackSolver solver;
// nonlinear system class
NonlinSystem nls(&wf, &solver);
nls.set_spaces(1, &space);
nls.set_pss(1, &pss);
// visualize solution and mesh
ScalarView view("", 0, 0, 700, 600);
view.fix_scale_width(80);
OrderView ordview("", 700, 0, 700, 600);
// error estimate as a function of physical time
GnuplotGraph graph_err;
graph_err.set_captions("","Time step","Error");
graph_err.add_row();
// error estimate as a function of DOF
GnuplotGraph graph_dofs;
graph_dofs.set_captions("","Time step","DOFs");
graph_dofs.add_row();
// initial condition at zero time level
//Tprev.set_const(&mesh, 0.0);
Tprev.set_dirichlet_lift(&space, &pss);
Titer.set_dirichlet_lift(&space, &pss);
nls.set_ic(&Titer, &Titer, PROJ_TYPE);
// view initial guess for Newton's method
// satisfies BC conditions
char title[100];
sprintf(title, "Initial iteration");
view.set_title(title);
view.show(&Titer);
ordview.show(&space);
//view.wait_for_keypress(); // this may cause graphics problems
// time stepping loop
int nstep = (int)(T_FINAL/TAU + 0.5);
double cpu = 0.0;
Solution sln_coarse, sln_fine;
for(int n = 1; n <= nstep; n++)
{
info("\n---- Time step %d -----------------------------------------------------------------", n);
// time measurement
begin_time();
// perform periodic unrefinements
if (n % UNREF_FREQ == 0) {
mesh.copy(&basemesh);
space.set_uniform_order(P_INIT);
space.assign_dofs();
}
// adaptivity loop
int at = 0, ndofs;
bool done = false;
double err_est, cpu;
do
{
info("\n---- Time step %d, adaptivity step %d ---------------------------------------------\n", n, ++at);
// Newton's loop for coarse mesh solution
int it = 1;
double res_l2_norm;
if (n > 1 || at > 1) nls.set_ic(&sln_fine, &Titer);
else nls.set_ic(&Titer, &Titer);
do
{
info("\n---- Time step %d, adaptivity step %d, Newton step %d (Coarse mesh solution)-------\n", n, at, it++);
nls.assemble();
nls.solve(1, &sln_coarse);
res_l2_norm = nls.get_residuum_l2_norm();
info("Residuum L2 norm: %g", res_l2_norm);
Titer.copy(&sln_coarse);
}
while (res_l2_norm > NEWTON_TOL_COARSE);
// Newton's loop for fine mesh solution
it = 1;
RefNonlinSystem rs(&nls);
rs.prepare();
if (n > 1 || at > 1) rs.set_ic(&sln_fine, &Titer);
else rs.set_ic(&Titer, &Titer);
do
{
info("\n---- Time step %d, adaptivity step %d, Newton step %d (Fine mesh solution) --------\n", n, at, it++);
rs.assemble();
rs.solve(1, &sln_fine);
res_l2_norm = rs.get_residuum_l2_norm();
info("Residuum L2 norm: %g", res_l2_norm);
Titer.copy(&sln_fine);
}
while (res_l2_norm > NEWTON_TOL_REF);
// calculate error estimate wrt. fine mesh solution
H1OrthoHP hp(1, &space);
err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Error estimate: %g%", err_est);
// visualization of solution on the n-th time level
sprintf(title, "Temperature, time level %d", n);
//view.set_min_max_range(0,100);
view.set_title(title);
//view.show(&Titer); // to see reference solution
view.show(&sln_fine); // to see the solution
// visualization of mesh on the n-th time level
sprintf(title, "hp-mesh, time level %d", n);
ordview.set_title(title);
ordview.show(&space); // to see hp-mesh
//view.wait_for_keypress();
// if err_est too large, adapt the mesh
if (err_est < SPACE_H1_TOL) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, ADAPT_TYPE, ISO_ONLY, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (!done);
// add entry to both time and DOF error graphs
graph_err.add_values(0, n, err_est);
graph_err.save("error.txt");
graph_dofs.add_values(0, n, space.get_num_dofs());
graph_dofs.save("dofs.txt");
// copying result of the Newton's iteration into Tprev
Tprev.copy(&Titer);
}
// time measurement
cpu += end_time();
verbose("Total running time: %g sec", cpu);
// wait for keyboard or mouse input
View::wait("Waiting for keyboard or mouse input.");
return 0;
}
int main(int argc, char* argv[])
{
// load the mesh
Mesh mesh;
H2DReader mloader;
mloader.load("square_quad.mesh", &mesh);
// mloader.load("square_tri.mesh", &mesh);
for (int i=0; i<INIT_REF_NUM; i++) mesh.refine_all_elements();
mesh.refine_towards_boundary(2, INIT_REF_NUM_BDY);
// initialize the shapeset and the cache
H1Shapeset shapeset;
PrecalcShapeset pss(&shapeset);
// create finite element space
H1Space space(&mesh, &shapeset);
space.set_bc_types(bc_types);
space.set_bc_values(bc_values);
space.set_uniform_order(P_INIT);
// enumerate basis functions
space.assign_dofs();
// initialize the weak formulation
WeakForm wf(1);
wf.add_biform(0, 0, callback(bilinear_form));
if (STABILIZATION_ON == true) {
wf.add_biform(0, 0, bilinear_form_stabilization,
bilinear_form_stabilization_order);
}
if (SHOCK_CAPTURING_ON == true) {
wf.add_biform(0, 0, bilinear_form_shock_capturing, bilinear_form_shock_capturing_order);
}
// visualize solution and mesh
OrderView oview("Coarse mesh", 0, 0, 500, 400);
ScalarView sview("Coarse mesh solution", 510, 0, 500, 400);
ScalarView sview2("Fine mesh solution", 1020, 0, 500, 400);
// matrix solver
UmfpackSolver solver;
// DOF convergence graph
SimpleGraph graph_dof_est, graph_cpu_est;
// prepare selector
RefinementSelectors::H1NonUniformHP selector(ISO_ONLY, ADAPT_TYPE, CONV_EXP, H2DRS_DEFAULT_ORDER, &shapeset);
// adaptivity loop
int it = 1, ndofs;
bool done = false;
double cpu = 0.0;
Solution sln_coarse, sln_fine;
do
{
info("\n---- Adaptivity step %d ---------------------------------------------\n", it++);
// time measurement
begin_time();
// solve the coarse mesh problem
LinSystem ls(&wf, &solver);
ls.set_spaces(1, &space);
ls.set_pss(1, &pss);
ls.assemble();
ls.solve(1, &sln_coarse);
// solve the fine mesh problem
int p_increase;
if (ADAPT_TYPE == RefinementSelectors::H2DRS_CAND_HP) p_increase = 1;
else p_increase = 0;
RefSystem rs(&ls, p_increase, 1); // the '1' is for one level of global refinement in space
rs.assemble();
rs.solve(1, &sln_fine);
// time measurement
cpu += end_time();
// show fine mesh solution
// view the solution and mesh
oview.show(&space);
sview.show(&sln_coarse);
sview2.show(&sln_fine);
//sview.wait_for_keypress();
// time measurement
begin_time();
// calculate error estimate wrt. fine mesh solution
H1AdaptHP hp(1, &space);
double err_est = hp.calc_error(&sln_coarse, &sln_fine) * 100;
info("Estimate of error: %g%%", err_est);
// add entries to DOF and CPU convergence graphs
graph_dof_est.add_values(space.get_num_dofs(), err_est);
graph_dof_est.save("conv_dof_est.dat");
graph_cpu_est.add_values(cpu, err_est);
graph_cpu_est.save("conv_cpu_est.dat");
// if err_est too large, adapt the mesh
if (err_est < ERR_STOP) done = true;
else {
hp.adapt(THRESHOLD, STRATEGY, &selector, MESH_REGULARITY);
ndofs = space.assign_dofs();
if (ndofs >= NDOF_STOP) done = true;
}
// time measurement
cpu += end_time();
}
while (done == false);
verbose("Total running time: %g sec", cpu);
// show the fine solution - this is the final result
sview.set_title("Final solution");
sview.show(&sln_fine);
// wait for keyboard or mouse input
View::wait();
return 0;
}