/// Calculates the absolute error between sln1 and sln2 using function fn
double calc_error(double (*fn)(MeshFunction*, MeshFunction*, int, QuadPt3D*), MeshFunction *sln1, MeshFunction *sln2) {
_F_
Mesh *meshes[2] = { sln1->get_mesh(), sln2->get_mesh() };
Transformable *tr[2] = { sln1, sln2 };
Traverse trav;
trav.begin(2, meshes, tr);
double error = 0.0;
Element **ee;
while ((ee = trav.get_next_state(NULL, NULL)) != NULL) {
ElementMode3D mode = ee[0]->get_mode();
RefMap *ru = sln1->get_refmap();
Ord3 order = max(sln1->get_fn_order(), sln2->get_fn_order()) + ru->get_inv_ref_order();
order.limit();
Quad3D *quad = get_quadrature(mode);
int np = quad->get_num_points(order);
QuadPt3D *pt = quad->get_points(order);
error += fn(sln1, sln2, np, pt);
}
trav.finish();
return error > H3D_TINY ? sqrt(error) : error; // do not ruin the precision by taking the sqrt
}
// Integral over the active core.
double integrate(MeshFunction* sln, int marker)
{
Quad2D* quad = &g_quad_2d_std;
sln->set_quad_2d(quad);
double integral = 0.0;
Element* e;
Mesh* mesh = sln->get_mesh();
for_all_active_elements(e, mesh)
{
if (e->marker == marker)
{
update_limit_table(e->get_mode());
sln->set_active_element(e);
RefMap* ru = sln->get_refmap();
int o = sln->get_fn_order() + ru->get_inv_ref_order();
limit_order(o);
sln->set_quad_order(o, H2D_FN_VAL);
scalar *uval = sln->get_fn_values();
double* x = ru->get_phys_x(o);
double result = 0.0;
h1_integrate_expression(x[i] * uval[i]);
integral += result;
}
}
return 2.0 * M_PI * integral;
}
// Calculates maximum of a given function, including its coordinates.
Extremum get_peak(MeshFunction *sln)
{
Quad2D* quad = &g_quad_2d_std;
sln->set_quad_2d(quad);
Element* e;
Mesh* mesh = sln->get_mesh();
scalar peak = 0.0;
double pos_x = 0.0;
double pos_y = 0.0;
for_all_active_elements(e, mesh)
{
update_limit_table(e->get_mode());
sln->set_active_element(e);
RefMap* ru = sln->get_refmap();
int o = sln->get_fn_order() + ru->get_inv_ref_order();
limit_order(o);
sln->set_quad_order(o, H2D_FN_VAL);
scalar *uval = sln->get_fn_values();
int np = quad->get_num_points(o);
double* x = ru->get_phys_x(o);
double* y = ru->get_phys_y(o);
for (int i = 0; i < np; i++)
if (uval[i] > peak) {
peak = uval[i];
pos_x = x[i];
pos_y = y[i];
}
}
// Integral over the active core.
double integrate(MeshFunction<double>* sln, std::string area)
{
Quad2D* quad = &g_quad_2d_std;
sln->set_quad_2d(quad);
double integral = 0.0;
Element* e;
Mesh* mesh = const_cast<Mesh*>(sln->get_mesh());
int marker = mesh->get_element_markers_conversion().get_internal_marker(area).marker;
for_all_active_elements(e, mesh)
{
if (e->marker == marker)
{
update_limit_table(e->get_mode());
sln->set_active_element(e);
RefMap* ru = sln->get_refmap();
int o = sln->get_fn_order() + ru->get_inv_ref_order();
limit_order(o, e->get_mode());
sln->set_quad_order(o, H2D_FN_VAL);
double *uval = sln->get_fn_values();
double* x = ru->get_phys_x(o);
double result = 0.0;
h1_integrate_expression(x[i] * uval[i]);
integral += result;
}
}
return 2.0 * M_PI * integral;
}
/// Calculates the norm of sln using function fn
double calc_norm(double (*fn)(MeshFunction*, int, QuadPt3D*), MeshFunction *sln) {
_F_
double norm = 0.0;
Mesh *mesh = sln->get_mesh();
FOR_ALL_ACTIVE_ELEMENTS(eid, mesh) {
Element *e = mesh->elements[eid];
sln->set_active_element(e);
RefMap *ru = sln->get_refmap();
order3_t o = sln->get_fn_order() + ru->get_inv_ref_order();
o.limit();
Quad3D *quad = get_quadrature(e->get_mode());
int np = quad->get_num_points(o);
QuadPt3D *pt = quad->get_points(o);
norm += fn(sln, np, pt);
}
/// Calculates the norm of sln using function fn
double calc_norm(double (*fn)(MeshFunction*, int, QuadPt3D*), MeshFunction *sln) {
_F_
double norm = 0.0;
Mesh *mesh = sln->get_mesh();
for(std::map<unsigned int, Element*>::iterator it = mesh->elements.begin(); it != mesh->elements.end(); it++)
if (it->second->used && it->second->active) {
Element *e = mesh->elements[it->first];
sln->set_active_element(e);
RefMap *ru = sln->get_refmap();
Ord3 o = sln->get_fn_order() + ru->get_inv_ref_order();
o.limit();
Quad3D *quad = get_quadrature(e->get_mode());
int np = quad->get_num_points(o);
QuadPt3D *pt = quad->get_points(o);
norm += fn(sln, np, pt);
}
return norm > H3D_TINY ? sqrt(norm) : norm; // do not ruin the precision by taking the sqrt
}
/// Calculate number of negative solution values.
int get_num_of_neg(MeshFunction *sln)
{
Quad2D* quad = &g_quad_2d_std;
sln->set_quad_2d(quad);
Element* e;
Mesh* mesh = sln->get_mesh();
int n = 0;
for_all_active_elements(e, mesh)
{
update_limit_table(e->get_mode());
sln->set_active_element(e);
RefMap* ru = sln->get_refmap();
int o = sln->get_fn_order() + ru->get_inv_ref_order();
limit_order(o);
sln->set_quad_order(o, H2D_FN_VAL);
scalar *uval = sln->get_fn_values();
int np = quad->get_num_points(o);
for (int i = 0; i < np; i++)
if (uval[i] < -1e-12)
n++;
}