// 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;
}
// 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 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];
}
}
void Linearizer::process_quad(MeshFunction<double>** fns, int iv0, int iv1, int iv2, int iv3, int level,
double* val, double* phx, double* phy, int* idx, bool curved)
{
double midval[3][5];
// try not to split through the vertex with the largest value
int a = (verts[iv0][2] > verts[iv1][2]) ? iv0 : iv1;
int b = (verts[iv2][2] > verts[iv3][2]) ? iv2 : iv3;
a = (verts[a][2] > verts[b][2]) ? a : b;
int flip = (a == iv1 || a == iv3) ? 1 : 0;
if(level < LinearizerBase::get_max_level(fns[0]->get_active_element(), fns[0]->get_fn_order(), fns[0]->get_mesh()))
{
int i;
if(!(level & 1)) // this is an optimization: do the following only every other time
{
// obtain solution values
fns[0]->set_quad_order(1, item);
val = fns[0]->get_values(component, value_type);
if(auto_max)
for (i = 0; i < lin_np_quad[1]; i++)
{
double v = val[i];
if(finite(v) && fabs(v) > max)
#pragma omp critical(max)
if(finite(v) && fabs(v) > max)
max = fabs(v);
}
// This is just to make some sense.
if(fabs(max) < Hermes::HermesSqrtEpsilon)
max = Hermes::HermesSqrtEpsilon;
idx = quad_indices[0];
if(curved)
{
RefMap* refmap = fns[0]->get_refmap();
phx = refmap->get_phys_x(1);
phy = refmap->get_phys_y(1);
double* dx = nullptr;
double* dy = nullptr;
if(this->xdisp != nullptr)
fns[1]->set_quad_order(1, H2D_FN_VAL);
if(this->ydisp != nullptr)
fns[this->xdisp == nullptr ? 1 : 2]->set_quad_order(1, H2D_FN_VAL);
if(this->xdisp != nullptr)
dx = fns[1]->get_fn_values();
if(this->ydisp != nullptr)
dy = fns[this->xdisp == nullptr ? 1 : 2]->get_fn_values();
for (i = 0; i < lin_np_quad[1]; i++)
{
if(this->xdisp != nullptr)
phx[i] += dmult*dx[i];
if(this->ydisp != nullptr)
phy[i] += dmult*dy[i];
}
}
}
// obtain linearized values and coordinates at the midpoints
for (i = 0; i < 3; i++)
{
midval[i][0] = (verts[iv0][i] + verts[iv1][i]) * 0.5;
midval[i][1] = (verts[iv1][i] + verts[iv2][i]) * 0.5;
midval[i][2] = (verts[iv2][i] + verts[iv3][i]) * 0.5;
midval[i][3] = (verts[iv3][i] + verts[iv0][i]) * 0.5;
midval[i][4] = (midval[i][0] + midval[i][2]) * 0.5;
};
// the value of the middle point is not the average of the four vertex values, since quad == 2 triangles
midval[2][4] = flip ? (verts[iv0][2] + verts[iv2][2]) * 0.5 : (verts[iv1][2] + verts[iv3][2]) * 0.5;
// determine whether or not to split the element
int split;
if(eps >= 1.0)
{
// if eps > 1, the user wants a fixed number of refinements (no adaptivity)
split = (level < eps) ? 3 : 0;
}
else
{
if(!auto_max && fabs(verts[iv0][2]) > max && fabs(verts[iv1][2]) > max
&& fabs(verts[iv2][2]) > max && fabs(verts[iv3][2]) > max)
{
// do not split if the whole quad is above the specified maximum value
split = 0;
}
else
{
// calculate the approximate error of linearizing the normalized solution
double herr = fabs(val[idx[1]] - midval[2][1]) + fabs(val[idx[3]] - midval[2][3]);
double verr = fabs(val[idx[0]] - midval[2][0]) + fabs(val[idx[2]] - midval[2][2]);
double err = fabs(val[idx[4]] - midval[2][4]) + herr + verr;
split = (!finite(err) || err > max*4*eps) ? 3 : 0;
// decide whether to split horizontally or vertically only
if(level > 0 && split)
{
if(herr > 5*verr)
split = 1; // h-split
else if(verr > 5*herr)
split = 2; // v-split
}
}
// also decide whether to split because of the curvature
if(split != 3 && curved)
{
double cm2 = sqr(fns[0]->get_active_element()->get_diameter()*this->get_curvature_epsilon());
if(sqr(phx[idx[1]] - midval[0][1]) + sqr(phy[idx[1]] - midval[1][1]) > cm2 ||
sqr(phx[idx[3]] - midval[0][3]) + sqr(phy[idx[3]] - midval[1][3]) > cm2) split |= 1;
if(sqr(phx[idx[0]] - midval[0][0]) + sqr(phy[idx[0]] - midval[1][0]) > cm2 ||
sqr(phx[idx[2]] - midval[0][2]) + sqr(phy[idx[2]] - midval[1][2]) > cm2) split |= 2;
}
// do extra tests at level 0, so as not to miss some functions with zero error at edge midpoints
if(level == 0 && !split)
{
split = ((fabs(val[13] - 0.5*(midval[2][0] + midval[2][1])) +
fabs(val[17] - 0.5*(midval[2][1] + midval[2][2])) +
fabs(val[20] - 0.5*(midval[2][2] + midval[2][3])) +
fabs(val[9] - 0.5*(midval[2][3] + midval[2][0]))) > max*4*eps) ? 3 : 0;
}
}
// split the quad if the error is too large, otherwise produce two linear triangles
if(split)
{
if(curved)
for (i = 0; i < 5; i++)
{
midval[0][i] = phx[idx[i]];
midval[1][i] = phy[idx[i]];
}
// obtain mid-edge and mid-element vertices
int mid0, mid1, mid2, mid3, mid4;
if(split != 1) mid0 = get_vertex(iv0, iv1, midval[0][0], midval[1][0], val[idx[0]]);
if(split != 2) mid1 = get_vertex(iv1, iv2, midval[0][1], midval[1][1], val[idx[1]]);
if(split != 1) mid2 = get_vertex(iv2, iv3, midval[0][2], midval[1][2], val[idx[2]]);
if(split != 2) mid3 = get_vertex(iv3, iv0, midval[0][3], midval[1][3], val[idx[3]]);
if(split == 3) mid4 = get_vertex(mid0, mid2, midval[0][4], midval[1][4], val[idx[4]]);
if(!this->exceptionMessageCaughtInParallelBlock.empty())
return;
// recur to sub-elements
if(split == 3)
{
this->push_transforms(fns, 0);
process_quad(fns, iv0, mid0, mid4, mid3, level + 1, val, phx, phy, quad_indices[1], curved);
this->pop_transforms(fns);
this->push_transforms(fns, 1);
process_quad(fns, mid0, iv1, mid1, mid4, level + 1, val, phx, phy, quad_indices[2], curved);
this->pop_transforms(fns);
this->push_transforms(fns, 2);
process_quad(fns, mid4, mid1, iv2, mid2, level + 1, val, phx, phy, quad_indices[3], curved);
this->pop_transforms(fns);
this->push_transforms(fns, 3);
process_quad(fns, mid3, mid4, mid2, iv3, level + 1, val, phx, phy, quad_indices[4], curved);
this->pop_transforms(fns);
}
else
if(split == 1) // h-split
{
this->push_transforms(fns, 4);
process_quad(fns, iv0, iv1, mid1, mid3, level + 1, val, phx, phy, quad_indices[5], curved);
this->pop_transforms(fns);
this->push_transforms(fns, 5);
process_quad(fns, mid3, mid1, iv2, iv3, level + 1, val, phx, phy, quad_indices[6], curved);
this->pop_transforms(fns);
}
else // v-split
{
this->push_transforms(fns, 6);
process_quad(fns, iv0, mid0, mid2, iv3, level + 1, val, phx, phy, quad_indices[7], curved);
this->pop_transforms(fns);
this->push_transforms(fns, 7);
process_quad(fns, mid0, iv1, iv2, mid2, level + 1, val, phx, phy, quad_indices[8], curved);
this->pop_transforms(fns);
}
return;
}
}
// output two linear triangles,
if(!flip)
{
add_triangle(iv3, iv0, iv1, fns[0]->get_active_element()->marker);
add_triangle(iv1, iv2, iv3, fns[0]->get_active_element()->marker);
}
else
{
add_triangle(iv0, iv1, iv2, fns[0]->get_active_element()->marker);
add_triangle(iv2, iv3, iv0, fns[0]->get_active_element()->marker);
}
}
void Orderizer::process_space(SpaceSharedPtr<Scalar> space, bool show_edge_orders)
{
// sanity check
if (space == nullptr)
throw Hermes::Exceptions::Exception("Space is nullptr in Orderizer:process_space().");
if (!space->is_up_to_date())
throw Hermes::Exceptions::Exception("The space is not up to date.");
MeshSharedPtr mesh = space->get_mesh();
// Reallocate.
this->reallocate(mesh);
RefMap refmap;
int oo, o[6];
// make a mesh illustrating the distribution of polynomial orders over the space
Element* e;
for_all_active_elements(e, mesh)
{
oo = o[4] = o[5] = space->get_element_order(e->id);
if (show_edge_orders)
for (unsigned int k = 0; k < e->get_nvert(); k++)
o[k] = space->get_edge_order(e, k);
else if (e->is_curved())
{
if (e->is_triangle())
for (unsigned int k = 0; k < e->get_nvert(); k++)
o[k] = oo;
else
for (unsigned int k = 0; k < e->get_nvert(); k++)
o[k] = H2D_GET_H_ORDER(oo);
}
double3* pt;
int np;
double* x;
double* y;
if (show_edge_orders || e->is_curved())
{
refmap.set_quad_2d(&quad_ord);
refmap.set_active_element(e);
x = refmap.get_phys_x(1);
y = refmap.get_phys_y(1);
pt = quad_ord.get_points(1, e->get_mode());
np = quad_ord.get_num_points(1, e->get_mode());
}
else
{
refmap.set_quad_2d(&quad_ord_simple);
refmap.set_active_element(e);
x = refmap.get_phys_x(1);
y = refmap.get_phys_y(1);
pt = quad_ord_simple.get_points(1, e->get_mode());
np = quad_ord_simple.get_num_points(1, e->get_mode());
}
int id[80];
assert(np <= 80);
int mode = e->get_mode();
if (e->is_quad())
{
o[4] = H2D_GET_H_ORDER(oo);
o[5] = H2D_GET_V_ORDER(oo);
}
if (show_edge_orders || e->is_curved())
{
make_vert(lvert[label_count], x[0], y[0], o[4]);
for (int i = 1; i < np; i++)
make_vert(id[i - 1], x[i], y[i], o[(int)pt[i][2]]);
for (int i = 0; i < num_elem[mode][1]; i++)
this->add_triangle(id[ord_elem[mode][1][i][0]], id[ord_elem[mode][1][i][1]], id[ord_elem[mode][1][i][2]], e->marker);
for (int i = 0; i < num_edge[mode][1]; i++)
{
if (e->en[ord_edge[mode][1][i][2]]->bnd || (y[ord_edge[mode][1][i][0] + 1] < y[ord_edge[mode][1][i][1] + 1]) ||
((y[ord_edge[mode][1][i][0] + 1] == y[ord_edge[mode][1][i][1] + 1]) &&
(x[ord_edge[mode][1][i][0] + 1] < x[ord_edge[mode][1][i][1] + 1])))
{
add_edge(id[ord_edge[mode][1][i][0]], id[ord_edge[mode][1][i][1]], e->en[ord_edge[mode][1][i][2]]->marker);
}
}
}
else
{
make_vert(lvert[label_count], x[0], y[0], o[4]);
for (int i = 1; i < np; i++)
make_vert(id[i - 1], x[i], y[i], o[(int)pt[i][2]]);
for (int i = 0; i < num_elem_simple[mode][1]; i++)
this->add_triangle(id[ord_elem_simple[mode][1][i][0]], id[ord_elem_simple[mode][1][i][1]], id[ord_elem_simple[mode][1][i][2]], e->marker);
for (int i = 0; i < num_edge_simple[mode][1]; i++)
add_edge(id[ord_edge_simple[mode][1][i][0]], id[ord_edge_simple[mode][1][i][1]], e->en[ord_edge_simple[mode][1][i][2]]->marker);
}
double xmin = 1e100, ymin = 1e100, xmax = -1e100, ymax = -1e100;
for (unsigned int k = 0; k < e->get_nvert(); k++)
{
if (e->vn[k]->x < xmin) xmin = e->vn[k]->x;
if (e->vn[k]->x > xmax) xmax = e->vn[k]->x;
if (e->vn[k]->y < ymin) ymin = e->vn[k]->y;
if (e->vn[k]->y > ymax) ymax = e->vn[k]->y;
}
lbox[label_count][0] = xmax - xmin;
lbox[label_count][1] = ymax - ymin;
ltext[label_count++] = labels[o[4]][o[5]];
}
void Orderizer::process_solution(Space* space)
{
// sanity check
if (space == NULL) error("Space is NULL in Orderizer:process_solution().");
if (!space->is_up_to_date())
error("The space is not up to date.");
int type = 1;
nv = nt = ne = nl = 0;
del_slot = -1;
// estimate the required number of vertices and triangles
Mesh* mesh = space->get_mesh();
if (mesh == NULL) {
error("Mesh is NULL in Orderizer:process_solution().");
}
int nn = mesh->get_num_active_elements();
int ev = 77 * nn, et = 64 * nn, ee = 16 * nn, el = nn + 10;
// 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);
lin_init_array(lvert, int, cl1, el);
lin_init_array(ltext, char*, cl2, el);
lin_init_array(lbox, double2, cl3, el);
info = NULL;
int oo, o[6];
RefMap refmap;
refmap.set_quad_2d(&quad_ord);
// make a mesh illustrating the distribution of polynomial orders over the space
Element* e;
for_all_active_elements(e, mesh)
{
oo = o[4] = o[5] = space->get_element_order(e->id);
for (unsigned int k = 0; k < e->nvert; k++)
o[k] = space->get_edge_order(e, k);
refmap.set_active_element(e);
double* x = refmap.get_phys_x(type);
double* y = refmap.get_phys_y(type);
double3* pt = quad_ord.get_points(type);
int np = quad_ord.get_num_points(type);
int id[80];
assert(np <= 80);
#define make_vert(index, x, y, val) \
{ (index) = add_vertex(); \
verts[index][0] = (x); \
verts[index][1] = (y); \
verts[index][2] = (val); }
int mode = e->get_mode();
if (e->is_quad())
{
o[4] = H2D_GET_H_ORDER(oo);
o[5] = H2D_GET_V_ORDER(oo);
}
make_vert(lvert[nl], x[0], y[0], o[4]);
for (int i = 1; i < np; i++)
make_vert(id[i-1], x[i], y[i], o[(int) pt[i][2]]);
for (int i = 0; i < num_elem[mode][type]; i++)
add_triangle(id[ord_elem[mode][type][i][0]], id[ord_elem[mode][type][i][1]], id[ord_elem[mode][type][i][2]]);
for (int i = 0; i < num_edge[mode][type]; i++)
{
if (e->en[ord_edge[mode][type][i][2]]->bnd || (y[ord_edge[mode][type][i][0] + 1] < y[ord_edge[mode][type][i][1] + 1]) ||
((y[ord_edge[mode][type][i][0] + 1] == y[ord_edge[mode][type][i][1] + 1]) &&
(x[ord_edge[mode][type][i][0] + 1] < x[ord_edge[mode][type][i][1] + 1])))
{
add_edge(id[ord_edge[mode][type][i][0]], id[ord_edge[mode][type][i][1]], 0);
}
}
double xmin = 1e100, ymin = 1e100, xmax = -1e100, ymax = -1e100;
for (unsigned int k = 0; k < e->nvert; k++)
{
if (e->vn[k]->x < xmin) xmin = e->vn[k]->x;
if (e->vn[k]->x > xmax) xmax = e->vn[k]->x;
if (e->vn[k]->y < ymin) ymin = e->vn[k]->y;
if (e->vn[k]->y > ymax) ymax = e->vn[k]->y;
}
lbox[nl][0] = xmax - xmin;
lbox[nl][1] = ymax - ymin;
ltext[nl++] = labels[o[4]][o[5]];
}
void Linearizer::process_quad(int iv0, int iv1, int iv2, int iv3, int level,
scalar* val, double* phx, double* phy, int* idx)
{
double midval[3][5];
// try not to split through the vertex with the largest value
int a = (verts[iv0][2] > verts[iv1][2]) ? iv0 : iv1;
int b = (verts[iv2][2] > verts[iv3][2]) ? iv2 : iv3;
a = (verts[a][2] > verts[b][2]) ? a : b;
int flip = (a == iv1 || a == iv3) ? 1 : 0;
if (level < LIN_MAX_LEVEL)
{
int i;
if (!(level & 1)) // this is an optimization: do the following only every other time
{
// obtain solution values
sln->set_quad_order(1, item);
val = sln->get_values(ia, ib);
if (auto_max)
for (i = 0; i < lin_np_quad[1]; i++) {
double v = getval(i);
if (finite(v) && fabs(v) > max) max = fabs(v);
}
// obtain physical element coordinates
if (curved || disp)
{
RefMap* refmap = sln->get_refmap();
phx = refmap->get_phys_x(1);
phy = refmap->get_phys_y(1);
if (disp)
{
xdisp->force_transform(sln);
ydisp->force_transform(sln);
xdisp->set_quad_order(1, FN_VAL);
ydisp->set_quad_order(1, FN_VAL);
scalar* dx = xdisp->get_fn_values();
scalar* dy = ydisp->get_fn_values();
for (i = 0; i < lin_np_quad[1]; i++) {
phx[i] += dmult*realpart(dx[i]);
phy[i] += dmult*realpart(dy[i]);
}
}
}
idx = quad_indices[0];
}
// obtain linearized values and coordinates at the midpoints
for (i = 0; i < 3; i++)
{
midval[i][0] = (verts[iv0][i] + verts[iv1][i]) * 0.5;
midval[i][1] = (verts[iv1][i] + verts[iv2][i]) * 0.5;
midval[i][2] = (verts[iv2][i] + verts[iv3][i]) * 0.5;
midval[i][3] = (verts[iv3][i] + verts[iv0][i]) * 0.5;
midval[i][4] = (midval[i][0] + midval[i][2]) * 0.5;
};
// the value of the middle point is not the average of the four vertex values, since quad == 2 triangles
midval[2][4] = flip ? (verts[iv0][2] + verts[iv2][2]) * 0.5 : (verts[iv1][2] + verts[iv3][2]) * 0.5;
// determine whether or not to split the element
int split;
if (eps >= 1.0)
{
// if eps > 1, the user wants a fixed number of refinements (no adaptivity)
split = (level < eps) ? 3 : 0;
}
else
{
if (!auto_max && fabs(verts[iv0][2]) > max && fabs(verts[iv1][2]) > max
&& fabs(verts[iv2][2]) > max && fabs(verts[iv3][2]) > max)
{
// do not split if the whole quad is above the specified maximum value
split = 0;
}
else
{
// calculate the approximate error of linearizing the normalized solution
double herr = fabs(getval(idx[1]) - midval[2][1]) + fabs(getval(idx[3]) - midval[2][3]);
double verr = fabs(getval(idx[0]) - midval[2][0]) + fabs(getval(idx[2]) - midval[2][2]);
double err = fabs(getval(idx[4]) - midval[2][4]) + herr + verr;
split = (!finite(err) || err > max*4*eps) ? 3 : 0;
// decide whether to split horizontally or vertically only
if (level > 0 && split)
if (herr > 5*verr)
split = 1; // h-split
else if (verr > 5*herr)
split = 2; // v-split
}
// also decide whether to split because of the curvature
if (split != 3 && (curved || disp))
{
double cm2 = sqr(cmax*5e-4);
if (sqr(phx[idx[1]] - midval[0][1]) + sqr(phy[idx[1]] - midval[1][1]) > cm2 ||
sqr(phx[idx[3]] - midval[0][3]) + sqr(phy[idx[3]] - midval[1][3]) > cm2) split |= 1;
if (sqr(phx[idx[0]] - midval[0][0]) + sqr(phy[idx[0]] - midval[1][0]) > cm2 ||
sqr(phx[idx[2]] - midval[0][2]) + sqr(phy[idx[2]] - midval[1][2]) > cm2) split |= 2;
/*for (i = 0; i < 5; i++)
if (sqr(phx[idx[i]] - midval[0][i]) + sqr(phy[idx[i]] - midval[1][i]) > sqr(cmax*1e-3))
{ split = 1; break; }*/
}
// do extra tests at level 0, so as not to miss some functions with zero error at edge midpoints
if (level == 0 && !split)
{
split = ((fabs(getval(13) - 0.5*(midval[2][0] + midval[2][1])) +
fabs(getval(17) - 0.5*(midval[2][1] + midval[2][2])) +
fabs(getval(20) - 0.5*(midval[2][2] + midval[2][3])) +
fabs(getval(9) - 0.5*(midval[2][3] + midval[2][0]))) > max*4*eps) ? 3 : 0;
}
}
// split the quad if the error is too large, otherwise produce two linear triangles
if (split)
{
if (curved || disp)
for (i = 0; i < 5; i++) {
midval[0][i] = phx[idx[i]];
midval[1][i] = phy[idx[i]];
}
// obtain mid-edge and mid-element vertices
int mid0, mid1, mid2, mid3, mid4;
if (split != 1) mid0 = get_vertex(iv0, iv1, midval[0][0], midval[1][0], getval(idx[0]));
if (split != 2) mid1 = get_vertex(iv1, iv2, midval[0][1], midval[1][1], getval(idx[1]));
if (split != 1) mid2 = get_vertex(iv2, iv3, midval[0][2], midval[1][2], getval(idx[2]));
if (split != 2) mid3 = get_vertex(iv3, iv0, midval[0][3], midval[1][3], getval(idx[3]));
if (split == 3) mid4 = get_vertex(mid0, mid2, midval[0][4], midval[1][4], getval(idx[4]));
// recur to sub-elements
if (split == 3)
{
sln->push_transform(0); process_quad(iv0, mid0, mid4, mid3, level+1, val, phx, phy, quad_indices[1]); sln->pop_transform();
sln->push_transform(1); process_quad(mid0, iv1, mid1, mid4, level+1, val, phx, phy, quad_indices[2]); sln->pop_transform();
sln->push_transform(2); process_quad(mid4, mid1, iv2, mid2, level+1, val, phx, phy, quad_indices[3]); sln->pop_transform();
sln->push_transform(3); process_quad(mid3, mid4, mid2, iv3, level+1, val, phx, phy, quad_indices[4]); sln->pop_transform();
}
else if (split == 1) // h-split
{
sln->push_transform(4); process_quad(iv0, iv1, mid1, mid3, level+1, val, phx, phy, quad_indices[5]); sln->pop_transform();
sln->push_transform(5); process_quad(mid3, mid1, iv2, iv3, level+1, val, phx, phy, quad_indices[6]); sln->pop_transform();
}
else // v-split
{
sln->push_transform(6); process_quad(iv0, mid0, mid2, iv3, level+1, val, phx, phy, quad_indices[7]); sln->pop_transform();
sln->push_transform(7); process_quad(mid0, iv1, iv2, mid2, level+1, val, phx, phy, quad_indices[8]); sln->pop_transform();
}
return;
}
}
// output two linear triangles,
if (!flip)
{
add_triangle(iv3, iv0, iv1);
add_triangle(iv1, iv2, iv3);
}
else
{
add_triangle(iv0, iv1, iv2);
add_triangle(iv2, iv3, iv0);
}
}
void Linearizer::process_triangle(int iv0, int iv1, int iv2, int level,
scalar* val, double* phx, double* phy, int* idx)
{
double midval[3][3];
if (level < LIN_MAX_LEVEL)
{
int i;
if (!(level & 1))
{
// obtain solution values
sln->set_quad_order(1, item);
val = sln->get_values(ia, ib);
if (auto_max)
for (i = 0; i < lin_np_tri[1]; i++) {
double v = getval(i);
if (finite(v) && fabs(v) > max) max = fabs(v);
}
// obtain physical element coordinates
if (curved || disp)
{
RefMap* refmap = sln->get_refmap();
phx = refmap->get_phys_x(1);
phy = refmap->get_phys_y(1);
if (disp)
{
xdisp->force_transform(sln);
ydisp->force_transform(sln);
xdisp->set_quad_order(1, FN_VAL);
ydisp->set_quad_order(1, FN_VAL);
scalar* dx = xdisp->get_fn_values();
scalar* dy = ydisp->get_fn_values();
for (i = 0; i < lin_np_tri[1]; i++) {
phx[i] += dmult*realpart(dx[i]);
phy[i] += dmult*realpart(dy[i]);
}
}
}
idx = tri_indices[0];
}
// obtain linearized values and coordinates at the midpoints
for (i = 0; i < 3; i++)
{
midval[i][0] = (verts[iv0][i] + verts[iv1][i])*0.5;
midval[i][1] = (verts[iv1][i] + verts[iv2][i])*0.5;
midval[i][2] = (verts[iv2][i] + verts[iv0][i])*0.5;
};
// determine whether or not to split the element
bool split;
if (eps >= 1.0)
{
// if eps > 1, the user wants a fixed number of refinements (no adaptivity)
split = (level < eps);
}
else
{
if (!auto_max && fabs(verts[iv0][2]) > max && fabs(verts[iv1][2]) > max && fabs(verts[iv2][2]) > max)
{
// do not split if the whole triangle is above the specified maximum value
split = false;
}
else
{
// calculate the approximate error of linearizing the normalized solution
double err = fabs(getval(idx[0]) - midval[2][0]) +
fabs(getval(idx[1]) - midval[2][1]) +
fabs(getval(idx[2]) - midval[2][2]);
split = !finite(err) || err > max*3*eps;
}
// do the same for the curvature
if (!split && (curved || disp))
{
for (i = 0; i < 3; i++)
if (sqr(phx[idx[i]] - midval[0][i]) + sqr(phy[idx[i]] - midval[1][i]) > sqr(cmax*1.5e-3))
{ split = true; break; }
}
// do extra tests at level 0, so as not to miss some functions with zero error at edge midpoints
if (level == 0 && !split)
{
split = (fabs(getval(8) - 0.5*(midval[2][0] + midval[2][1])) +
fabs(getval(9) - 0.5*(midval[2][1] + midval[2][2])) +
fabs(getval(4) - 0.5*(midval[2][2] + midval[2][0]))) > max*3*eps;
}
}
// split the triangle if the error is too large, otherwise produce a linear triangle
if (split)
{
if (curved || disp)
for (i = 0; i < 3; i++) {
midval[0][i] = phx[idx[i]];
midval[1][i] = phy[idx[i]];
}
// obtain mid-edge vertices
int mid0 = get_vertex(iv0, iv1, midval[0][0], midval[1][0], getval(idx[0]));
int mid1 = get_vertex(iv1, iv2, midval[0][1], midval[1][1], getval(idx[1]));
int mid2 = get_vertex(iv2, iv0, midval[0][2], midval[1][2], getval(idx[2]));
// recur to sub-elements
sln->push_transform(0); process_triangle(iv0, mid0, mid2, level+1, val, phx, phy, tri_indices[1]); sln->pop_transform();
sln->push_transform(1); process_triangle(mid0, iv1, mid1, level+1, val, phx, phy, tri_indices[2]); sln->pop_transform();
sln->push_transform(2); process_triangle(mid2, mid1, iv2, level+1, val, phx, phy, tri_indices[3]); sln->pop_transform();
sln->push_transform(3); process_triangle(mid1, mid2, mid0, level+1, val, phx, phy, tri_indices[4]); sln->pop_transform();
return;
}
}
// no splitting: output a linear triangle
add_triangle(iv0, iv1, iv2);
}
void Vectorizer::process_triangle(int iv0, int iv1, int iv2, int level,
scalar* xval, scalar* yval, double* phx, double* phy, int* idx)
{
if (level < LIN_MAX_LEVEL)
{
int i;
if (!(level & 1))
{
// obtain solution values and physical element coordinates
xsln->set_quad_order(1, xitem);
ysln->set_quad_order(1, yitem);
xval = xsln->get_values(xia, xib);
yval = ysln->get_values(yia, yib);
for (i = 0; i < lin_np_tri[1]; i++) {
double m = getmag(i);
if (finite(m) && fabs(m) > max) max = fabs(m);
}
if (curved)
{
RefMap* refmap = xsln->get_refmap();
phx = refmap->get_phys_x(1);
phy = refmap->get_phys_y(1);
}
idx = tri_indices[0];
}
// obtain linearized values and coordinates at the midpoints
double midval[4][3];
for (i = 0; i < 4; i++)
{
midval[i][0] = (verts[iv0][i] + verts[iv1][i])*0.5;
midval[i][1] = (verts[iv1][i] + verts[iv2][i])*0.5;
midval[i][2] = (verts[iv2][i] + verts[iv0][i])*0.5;
};
// determine whether or not to split the element
bool split;
if (eps >= 1.0)
{
//if eps > 1, the user wants a fixed number of refinements (no adaptivity)
split = (level < eps);
}
else
{
// calculate the approximate error of linearizing the normalized solution
double err = fabs(getmag(idx[0]) - midmag(0)) +
fabs(getmag(idx[1]) - midmag(1)) +
fabs(getmag(idx[2]) - midmag(2));
split = !finite(err) || err > max*3*eps;
// do the same for the curvature
if (curved && !split)
{
double cerr = 0.0, cden = 0.0; // fixme
for (i = 0; i < 3; i++)
{
cerr += fabs(phx[idx[i]] - midval[0][i]) + fabs(phy[idx[i]] - midval[1][i]);
cden += fabs(phx[idx[i]]) + fabs(phy[idx[i]]);
}
split = (cerr > cden*2.5e-4);
}
// do extra tests at level 0, so as not to miss some functions with zero error at edge midpoints
if (level == 0 && !split)
{
split = (fabs(getmag(8) - 0.5*(midmag(0) + midmag(1))) +
fabs(getmag(9) - 0.5*(midmag(1) + midmag(2))) +
fabs(getmag(4) - 0.5*(midmag(2) + midmag(0)))) > max*3*eps;
}
}
// split the triangle if the error is too large, otherwise produce a linear triangle
if (split)
{
if (curved)
for (i = 0; i < 3; i++) {
midval[0][i] = phx[idx[i]];
midval[1][i] = phy[idx[i]];
}
// obtain mid-edge vertices
int mid0 = get_vertex(iv0, iv1, midval[0][0], midval[1][0], getvalx(idx[0]), getvaly(idx[0]));
int mid1 = get_vertex(iv1, iv2, midval[0][1], midval[1][1], getvalx(idx[1]), getvaly(idx[1]));
int mid2 = get_vertex(iv2, iv0, midval[0][2], midval[1][2], getvalx(idx[2]), getvaly(idx[2]));
// recur to sub-elements
push_transform(0); process_triangle(iv0, mid0, mid2, level+1, xval, yval, phx, phy, tri_indices[1]); pop_transform();
push_transform(1); process_triangle(mid0, iv1, mid1, level+1, xval, yval, phx, phy, tri_indices[2]); pop_transform();
push_transform(2); process_triangle(mid2, mid1, iv2, level+1, xval, yval, phx, phy, tri_indices[3]); pop_transform();
push_transform(3); process_triangle(mid1, mid2, mid0, level+1, xval, yval, phx, phy, tri_indices[4]); pop_transform();
return;
}
}
// no splitting: output a linear triangle
add_triangle(iv0, iv1, iv2);
}
void Vectorizer::process_quad(int iv0, int iv1, int iv2, int iv3, int level,
scalar* xval, scalar* yval, double* phx, double* phy, int* idx)
{
// try not to split through the vertex with the largest value
int a = (magvert(iv0) > magvert(iv1)) ? iv0 : iv1;
int b = (magvert(iv2) > magvert(iv3)) ? iv2 : iv3;
a = (magvert(a) > magvert(b)) ? a : b;
int flip = (a == iv1 || a == iv3) ? 1 : 0;
if (level < LIN_MAX_LEVEL)
{
int i;
if (!(level & 1))
{
// obtain solution values and physical element coordinates
xsln->set_quad_order(1, xitem);
ysln->set_quad_order(1, yitem);
xval = xsln->get_values(xia, xib);
yval = ysln->get_values(yia, yib);
for (i = 0; i < lin_np_quad[1]; i++) {
double m = getmag(i);
if (finite(m) && fabs(m) > max) max = fabs(m);
}
if (curved)
{
RefMap* refmap = xsln->get_refmap();
phx = refmap->get_phys_x(1);
phy = refmap->get_phys_y(1);
}
idx = quad_indices[0];
}
// obtain linearized values and coordinates at the midpoints
double midval[4][5];
for (i = 0; i < 4; i++)
{
midval[i][0] = (verts[iv0][i] + verts[iv1][i]) * 0.5;
midval[i][1] = (verts[iv1][i] + verts[iv2][i]) * 0.5;
midval[i][2] = (verts[iv2][i] + verts[iv3][i]) * 0.5;
midval[i][3] = (verts[iv3][i] + verts[iv0][i]) * 0.5;
midval[i][4] = (midval[i][0] + midval[i][2]) * 0.5;
};
// determine whether or not to split the element
bool split;
if (eps >= 1.0)
{
//if eps > 1, the user wants a fixed number of refinements (no adaptivity)
split = (level < eps);
}
else
{
// the value of the middle point is not the average of the four vertex values, since quad == 2 triangles
midval[2][4] = flip ? (verts[iv0][2] + verts[iv2][2]) * 0.5 : (verts[iv1][2] + verts[iv3][2]) * 0.5;
midval[3][4] = flip ? (verts[iv0][3] + verts[iv2][3]) * 0.5 : (verts[iv1][3] + verts[iv3][3]) * 0.5;
// calculate the approximate error of linearizing the normalized solution
double err = fabs(getmag(idx[0]) - midmag(0)) +
fabs(getmag(idx[1]) - midmag(1)) +
fabs(getmag(idx[2]) - midmag(2)) +
fabs(getmag(idx[3]) - midmag(3)) +
fabs(getmag(idx[4]) - midmag(4));
split = !finite(err) || err > max*4*eps;
// do the same for the curvature
if (curved && !split)
{
double cerr = 0.0, cden = 0.0; // fixme
for (i = 0; i < 5; i++)
{
cerr += fabs(phx[idx[i]] - midval[0][i]) + fabs(phy[idx[i]] - midval[1][i]);
cden += fabs(phx[idx[i]]) + fabs(phy[idx[i]]);
}
split = (cerr > cden*2.5e-4);
}
// do extra tests at level 0, so as not to miss functions with zero error at edge midpoints
if (level == 0 && !split)
{
err = fabs(getmag(13) - 0.5*(midmag(0) + midmag(1))) +
fabs(getmag(17) - 0.5*(midmag(1) + midmag(2))) +
fabs(getmag(20) - 0.5*(midmag(2) + midmag(3))) +
fabs(getmag(9) - 0.5*(midmag(3) + midmag(0)));
split = !finite(err) || (err) > max*2*eps; //?
}
}
// split the quad if the error is too large, otherwise produce two linear triangles
if (split)
{
if (curved)
for (i = 0; i < 5; i++) {
midval[0][i] = phx[idx[i]];
midval[1][i] = phy[idx[i]];
}
// obtain mid-edge and mid-element vertices
int mid0 = get_vertex(iv0, iv1, midval[0][0], midval[1][0], getvalx(idx[0]), getvaly(idx[0]));
int mid1 = get_vertex(iv1, iv2, midval[0][1], midval[1][1], getvalx(idx[1]), getvaly(idx[1]));
int mid2 = get_vertex(iv2, iv3, midval[0][2], midval[1][2], getvalx(idx[2]), getvaly(idx[2]));
int mid3 = get_vertex(iv3, iv0, midval[0][3], midval[1][3], getvalx(idx[3]), getvaly(idx[3]));
int mid4 = get_vertex(mid0, mid2, midval[0][4], midval[1][4], getvalx(idx[4]), getvaly(idx[4]));
// recur to sub-elements
push_transform(0); process_quad(iv0, mid0, mid4, mid3, level+1, xval, yval, phx, phy, quad_indices[1]); pop_transform();
push_transform(1); process_quad(mid0, iv1, mid1, mid4, level+1, xval, yval, phx, phy, quad_indices[2]); pop_transform();
push_transform(2); process_quad(mid4, mid1, iv2, mid2, level+1, xval, yval, phx, phy, quad_indices[3]); pop_transform();
push_transform(3); process_quad(mid3, mid4, mid2, iv3, level+1, xval, yval, phx, phy, quad_indices[4]); pop_transform();
return;
}
}
// output two linear triangles,
if (!flip)
{
add_triangle(iv3, iv0, iv1);
add_triangle(iv1, iv2, iv3);
}
else
{
add_triangle(iv0, iv1, iv2);
add_triangle(iv2, iv3, iv0);
}
}