int main(int argc, char* argv[])
{
hermes2d_initialize(&argc, argv);
info("SHAPESET TESTER");
info("num_components = %d", shapeset.get_num_components());
info("max_order = %d", shapeset.get_max_order());
precalc.set_quad_2d(&quad);
for (int mode = 0; mode <= 1; mode++)
{
shapeset.set_mode(mode);
quad.set_mode(mode);
precalc.set_mode(mode);
info(mode ? "\nTESTING QUADS\n" : "\nTESTING TRIANGLES\n");
//test_orders(&shapeset);
test_edge_rotation();
//test_edge_orientation(&shapeset);
//test_num_bubbles(&shapeset);
}
//info("\nALL OK!\n");
printf("\n");
hermes2d_finalize();
return 0;
}
static void precalculate_cholesky_projection_matrices_bubble()
{
// *** triangles ***
ref_map_pss.set_mode(MODE_TRIANGLE);
int order = ref_map_shapeset.get_max_order();
// calculate projection matrix of maximum order
int nb = ref_map_shapeset.get_num_bubbles(order);
int* indices = ref_map_shapeset.get_bubble_indices(order);
bubble_proj_matrix_tri = calculate_bubble_projection_matrix(nb, indices);
// cholesky factorization of the matrix
bubble_tri_p = new double[nb];
choldc(bubble_proj_matrix_tri, nb, bubble_tri_p);
// *** quads ***
ref_map_pss.set_mode(MODE_QUAD);
order = ref_map_shapeset.get_max_order();
order = make_quad_order(order, order);
// calculate projection matrix of maximum order
nb = ref_map_shapeset.get_num_bubbles(order);
indices = ref_map_shapeset.get_bubble_indices(order);
bubble_proj_matrix_quad = calculate_bubble_projection_matrix(nb, indices);
// cholesky factorization of the matrix
bubble_quad_p = new double[nb];
choldc(bubble_proj_matrix_quad, nb, bubble_quad_p);
}
void RefMap::calc_phys_y(int order)
{
// transform all y coordinates of the integration points
int i, j, np = quad_2d->get_num_points(order);
double* y = cur_node->phys_y[order] = new double[np];
memset(y, 0, np * sizeof(double));
ref_map_pss.force_transform(sub_idx, ctm);
for (i = 0; i < nc; i++)
{
ref_map_pss.set_active_shape(indices[i]);
ref_map_pss.set_quad_order(order);
double* fn = ref_map_pss.get_fn_values();
for (j = 0; j < np; j++)
y[j] += coeffs[i][1] * fn[j];
}
}
void RefMap::set_active_element(Element* e)
{
if (e != element) free();
ref_map_pss.set_active_element(e);
quad_2d->set_mode(e->get_mode());
num_tables = quad_2d->get_num_tables();
assert(num_tables <= H2D_MAX_TABLES);
if (e == element) return;
element = e;
reset_transform();
update_cur_node();
is_const = !element->is_curved() &&
(element->is_triangle() || is_parallelogram());
// prepare the shapes and coefficients of the reference map
int j, k = 0;
for (unsigned int i = 0; i < e->nvert; i++)
indices[k++] = ref_map_shapeset.get_vertex_index(i);
// straight-edged element
if (e->cm == NULL)
{
for (unsigned int i = 0; i < e->nvert; i++)
{
lin_coeffs[i][0] = e->vn[i]->x;
lin_coeffs[i][1] = e->vn[i]->y;
}
coeffs = lin_coeffs;
nc = e->nvert;
}
else // curvilinear element - edge and bubble shapes
{
int o = e->cm->order;
for (unsigned int i = 0; i < e->nvert; i++)
for (j = 2; j <= o; j++)
indices[k++] = ref_map_shapeset.get_edge_index(i, 0, j);
if (e->is_quad()) o = H2D_MAKE_QUAD_ORDER(o, o);
memcpy(indices + k, ref_map_shapeset.get_bubble_indices(o),
ref_map_shapeset.get_num_bubbles(o) * sizeof(int));
coeffs = e->cm->coeffs;
nc = e->cm->nc;
}
// calculate the order of the inverse reference map
if (element->iro_cache == -1 && quad_2d->get_max_order() > 1)
{
element->iro_cache = is_const ? 0 : calc_inv_ref_order();
}
inv_ref_order = element->iro_cache;
// constant inverse reference map
if (is_const) calc_const_inv_ref_map(); else const_jacobian = 0.0;
}
static void calc_edge_projection(Element* e, int edge, Nurbs** nurbs, int order, double2* proj)
{
ref_map_pss.set_active_element(e);
int i, j, k;
int mo1 = quad1d.get_max_order();
int np = quad1d.get_num_points(mo1);
int ne = order - 1;
int mode = e->get_mode();
assert(np <= 15 && ne <= 10);
double2 fn[15];
double rhside[2][10];
memset(fn, 0, sizeof(double2) * np);
memset(rhside[0], 0, sizeof(double) * ne);
memset(rhside[1], 0, sizeof(double) * ne);
double a_1, a_2, b_1, b_2;
a_1 = ctm.m[0] * ref_vert[mode][edge][0] + ctm.t[0];
a_2 = ctm.m[1] * ref_vert[mode][edge][1] + ctm.t[1];
b_1 = ctm.m[0] * ref_vert[mode][e->next_vert(edge)][0] + ctm.t[0];
b_2 = ctm.m[1] * ref_vert[mode][e->next_vert(edge)][1] + ctm.t[1];
// values of nonpolynomial function in two vertices
double2 fa, fb;
calc_ref_map(e, nurbs, a_1, a_2, fa);
calc_ref_map(e, nurbs, b_1, b_2, fb);
double2* pt = quad1d.get_points(mo1);
for (j = 0; j < np; j++) // over all integration points
{
double2 x, v;
double t = pt[j][0];
edge_coord(e, edge, t, x, v);
calc_ref_map(e, nurbs, x[0], x[1], fn[j]);
for (k = 0; k < 2; k++)
fn[j][k] = fn[j][k] - (fa[k] + (t+1)/2.0 * (fb[k] - fa[k]));
}
double2* result = proj + e->nvert + edge * (order - 1);
for (k = 0; k < 2; k++)
{
for (i = 0; i < ne; i++)
{
for (j = 0; j < np; j++)
{
double t = pt[j][0];
double fi = lob[i+2](t);
rhside[k][i] += pt[j][1] * (fi * fn[j][k]);
}
}
// solve
cholsl(edge_proj_matrix, ne, edge_p, rhside[k], rhside[k]);
for (i = 0; i < ne; i++)
result[i][k] = rhside[k][i];
}
}
void RefMap::calc_inv_ref_map(int order)
{
assert(quad_2d != NULL);
int i, j, np = quad_2d->get_num_points(order);
// construct jacobi matrices of the direct reference map for all integration points
AUTOLA_OR(double2x2, m, np);
memset(m, 0, m.size);
ref_map_pss.force_transform(sub_idx, ctm);
for (i = 0; i < nc; i++)
{
double *dx, *dy;
ref_map_pss.set_active_shape(indices[i]);
ref_map_pss.set_quad_order(order);
ref_map_pss.get_dx_dy_values(dx, dy);
for (j = 0; j < np; j++)
{
m[j][0][0] += coeffs[i][0] * dx[j];
m[j][0][1] += coeffs[i][0] * dy[j];
m[j][1][0] += coeffs[i][1] * dx[j];
m[j][1][1] += coeffs[i][1] * dy[j];
}
}
// calculate the jacobian and inverted matrix
double trj = get_transform_jacobian();
double2x2* irm = cur_node->inv_ref_map[order] = new double2x2[np];
double* jac = cur_node->jacobian[order] = new double[np];
for (i = 0; i < np; i++)
{
jac[i] = (m[i][0][0] * m[i][1][1] - m[i][0][1] * m[i][1][0]);
double ij = 1.0 / jac[i];
error_if(!finite(ij), "1/jac[%d] is infinity when calculating inv. ref. map for order %d (jac=%g)", i, order);
assert_msg(ij == ij, "1/jac[%d] is NaN when calculating inv. ref. map for order %d (jac=%g)", i, order);
// invert and transpose the matrix
irm[i][0][0] = m[i][1][1] * ij;
irm[i][0][1] = -m[i][1][0] * ij;
irm[i][1][0] = -m[i][0][1] * ij;
irm[i][1][1] = m[i][0][0] * ij;
jac[i] *= trj;
}
}
void test_edge_rotation()
{
info("Testing edge rotation...");
int mode = shapeset.get_mode();
int ne = mode ? 4 : 3;
for (int ori = 0; ori <= 1; ori++)
{
for (int order = 0; order <= shapeset.get_max_order(); order++)
{
double *e01, *e02, *ee1, *ee2;
precalc.set_active_shape(shapeset.get_edge_index(0, ori, order));
precalc.set_quad_order(quad.get_edge_points(0));
e01 = precalc.get_fn_values(0);
if (nc > 1) e02 = precalc.get_fn_values(1);
for (int e = 1; e < ne; e++)
{
precalc.set_active_shape(shapeset.get_edge_index(e, ori, order));
precalc.set_quad_order(quad.get_edge_points(e));
ee1 = precalc.get_fn_values(0);
if (nc > 1) ee2 = precalc.get_fn_values(1);
int np = quad.get_num_points(quad.get_edge_points(0));
if (nc == 1)
{
for (int i = 0; i < np; i++)
if (!eq(e01[i], ee1[i]))
{
info("order=%d, ori=%d, edge=%d -- not equal to edge 0", order, ori, e);
}
}
else
{
for (int i = 0; i < np; i++)
{
double x = rot[mode][e][0][0] * ee1[i] + rot[mode][e][0][1] * ee2[i];
double y = rot[mode][e][1][0] * ee1[i] + rot[mode][e][1][1] * ee2[i];
if (!eq(e01[i], x) || !eq(e02[i], y))
{
info("order=%d, ori=%d, edge=%d -- not equal to edge 0", order, ori, e);
printf("x comp: 0-ta %g, %d-ta %g\n", e01[i], e, x);
printf("y comp: 0-ta %g, %d-ta %g\n\n", e02[i], e, y);
}
}
}
}
}
}
}
static void old_projection(Element* e, int order, double2* proj, double* old[2])
{
int mo2 = quad2d.get_max_order();
int np = quad2d.get_num_points(mo2);
for (unsigned int k = 0; k < e->nvert; k++) // loop over vertices
{
// vertex basis functions in all integration points
double* vd;
int index_v = ref_map_shapeset.get_vertex_index(k);
ref_map_pss.set_active_shape(index_v);
ref_map_pss.set_quad_order(mo2);
vd = ref_map_pss.get_fn_values();
for (int m = 0; m < 2; m++) // part 0 or 1
for (int j = 0; j < np; j++)
old[m][j] += proj[k][m] * vd[j];
for (int ii = 0; ii < order - 1; ii++)
{
// edge basis functions in all integration points
double* ed;
int index_e = ref_map_shapeset.get_edge_index(k,0,ii+2);
ref_map_pss.set_active_shape(index_e);
ref_map_pss.set_quad_order(mo2);
ed = ref_map_pss.get_fn_values();
for (int m = 0; m < 2; m++) //part 0 or 1
for (int j = 0; j < np; j++)
old[m][j] += proj[e->nvert + k * (order-1) + ii][m] * ed[j];
}
}
}
void DiscreteProblem::precalc_equi_coefs()
{
int i, m;
memset(equi, 0, sizeof(double) * ndofs);
verbose("Precalculating equilibration coefficients...");
RefMap refmap;
AsmList al;
Element* e;
for (m = 0; m < neq; m++)
{
PrecalcShapeset* fu = pss[m];
BiForm* bf = biform[m] + m;
Mesh* mesh = spaces[m]->get_mesh();
for_all_active_elements(e, mesh)
{
update_limit_table(e->get_mode());
fu->set_active_element(e);
refmap.set_active_element(e);
spaces[m]->get_element_assembly_list(e, &al);
for (i = 0; i < al.cnt; i++)
{
if (al.dof[i] < 0) continue;
fu->set_active_shape(al.idx[i]);
scalar sy = 0.0, un = 0.0;
if (bf->unsym) un = bf->unsym(fu, fu, &refmap, &refmap);
if (bf->sym) sy = bf->sym (fu, fu, &refmap, &refmap);
#ifndef COMPLEX
equi[al.dof[i]] += (sy + un) * sqr(al.coef[i]);
#else
equi[al.dof[i]] += 0;//std::norm(sy + un) * sqr(al.coef[i]);
#endif
}
}
}
void RefMap::calc_second_ref_map(int order)
{
assert(quad_2d != NULL);
int i, j, np = quad_2d->get_num_points(order);
AUTOLA_OR(double3x2, k, np);
memset(k, 0, k.size);
ref_map_pss.force_transform(sub_idx, ctm);
for (i = 0; i < nc; i++)
{
double *dxy, *dxx, *dyy;
ref_map_pss.set_active_shape(indices[i]);
ref_map_pss.set_quad_order(order, H2D_FN_ALL);
dxx = ref_map_pss.get_dxx_values();
dyy = ref_map_pss.get_dyy_values();
dxy = ref_map_pss.get_dxy_values();
for (j = 0; j < np; j++)
{
k[j][0][0] += coeffs[i][0] * dxx[j];
k[j][0][1] += coeffs[i][1] * dxx[j];
k[j][1][0] += coeffs[i][0] * dxy[j];
k[j][1][1] += coeffs[i][1] * dxy[j];
k[j][2][0] += coeffs[i][0] * dyy[j];
k[j][2][1] += coeffs[i][1] * dyy[j];
}
}
double3x2* mm = cur_node->second_ref_map[order] = new double3x2[np];
double2x2* m = get_inv_ref_map(order);
for (j = 0; j < np; j++)
{
double a, b;
// coefficients in second derivative with respect to xx
a = sqr(m[j][0][0])*k[j][0][0] + 2*m[j][0][0]*m[j][0][1]*k[j][1][0] + sqr(m[j][0][1])*k[j][2][0];
b = sqr(m[j][0][0])*k[j][0][1] + 2*m[j][0][0]*m[j][0][1]*k[j][1][1] + sqr(m[j][0][1])*k[j][2][1];
mm[j][0][0] = -(a * m[j][0][0] + b * m[j][1][0]); // du/dx
mm[j][0][1] = -(a * m[j][0][1] + b * m[j][1][1]); // du/dy
// coefficients in second derivative with respect to xy
a = m[j][0][0]*m[j][1][0]*k[j][0][0] + (m[j][0][1]*m[j][1][0] + m[j][0][0]*m[j][1][1])*k[j][1][0] + m[j][0][1]*m[j][1][1]*k[j][2][0];
b = m[j][0][0]*m[j][1][0]*k[j][0][1] + (m[j][0][1]*m[j][1][0] + m[j][0][0]*m[j][1][1])*k[j][1][1] + m[j][0][1]*m[j][1][1]*k[j][2][1];
mm[j][1][0] = -(a * m[j][0][0] + b * m[j][1][0]); // du/dx
mm[j][1][1] = -(a * m[j][0][1] + b * m[j][1][1]); // du/dy
// coefficients in second derivative with respect to yy
a = sqr(m[j][1][0])*k[j][0][0] + 2*m[j][1][0]*m[j][1][1]*k[j][1][0] + sqr(m[j][1][1])*k[j][2][0];
b = sqr(m[j][1][0])*k[j][0][1] + 2*m[j][1][0]*m[j][1][1]*k[j][1][1] + sqr(m[j][1][1])*k[j][2][1];
mm[j][2][0] = -(a * m[j][0][0] + b * m[j][1][0]); // du/dx
mm[j][2][1] = -(a * m[j][0][1] + b * m[j][1][1]); // du/dy
}
}
void CurvMap::update_refmap_coefs(Element* e)
{
ref_map_pss.set_quad_2d(&quad2d);
//ref_map_pss.set_active_element(e);
// calculation of projection matrices
if (edge_proj_matrix == NULL) precalculate_cholesky_projection_matrix_edge();
if (bubble_proj_matrix_tri == NULL) precalculate_cholesky_projection_matrices_bubble();
ref_map_pss.set_mode(e->get_mode());
ref_map_shapeset.set_mode(e->get_mode());
// allocate projection coefficients
int nv = e->nvert;
int ne = order - 1;
int qo = e->is_quad() ? make_quad_order(order, order) : order;
int nb = ref_map_shapeset.get_num_bubbles(qo);
nc = nv + nv*ne + nb;
if (coefs != NULL) delete [] coefs;
coefs = new double2[nc];
// WARNING: do not change the format of the array 'coefs'. If it changes,
// RefMap::set_active_element() has to be changed too.
Nurbs** nurbs;
if (toplevel == false)
{
ref_map_pss.set_active_element(e);
ref_map_pss.set_transform(part);
nurbs = parent->cm->nurbs;
}
else
{
ref_map_pss.reset_transform();
nurbs = e->cm->nurbs;
}
ctm = *(ref_map_pss.get_ctm());
ref_map_pss.reset_transform(); // fixme - do we need this?
// calculation of new projection coefficients
ref_map_projection(e, nurbs, order, coefs);
}
void RefMap::set_quad_2d(Quad2D* quad_2d)
{
free();
this->quad_2d = quad_2d;
ref_map_pss.set_quad_2d(quad_2d);
}
void RefMap::calc_tangent(int edge, int eo)
{
int i, j;
int np = quad_2d->get_num_points(eo);
double3* tan = cur_node->tan[edge] = new double3[np];
int a = edge, b = element->next_vert(edge);
if (!element->is_curved())
{
// straight edges: the tangent at each point is just the edge length
tan[0][0] = element->vn[b]->x - element->vn[a]->x;
tan[0][1] = element->vn[b]->y - element->vn[a]->y;
tan[0][2] = sqrt(sqr(tan[0][0]) + sqr(tan[0][1]));
double inorm = 1.0 / tan[0][2];
tan[0][0] *= inorm;
tan[0][1] *= inorm;
tan[0][2] *= (edge == 0 || edge == 2) ? ctm->m[0] : ctm->m[1];
for (i = 1; i < np; i++)
memcpy(tan+i, tan, sizeof(double3));
}
else
{
// construct jacobi matrices of the direct reference map at integration points along the edge
static double2x2 m[15];
assert(np <= 15);
memset(m, 0, np*sizeof(double2x2));
ref_map_pss.force_transform(sub_idx, ctm);
for (i = 0; i < nc; i++)
{
double *dx, *dy;
ref_map_pss.set_active_shape(indices[i]);
ref_map_pss.set_quad_order(eo);
ref_map_pss.get_dx_dy_values(dx, dy);
for (j = 0; j < np; j++)
{
m[j][0][0] += coeffs[i][0] * dx[j];
m[j][0][1] += coeffs[i][0] * dy[j];
m[j][1][0] += coeffs[i][1] * dx[j];
m[j][1][1] += coeffs[i][1] * dy[j];
}
}
// multiply them by the vector of the reference edge
double2* v1 = ref_map_shapeset.get_ref_vertex(a);
double2* v2 = ref_map_shapeset.get_ref_vertex(b);
double ex = (*v2)[0] - (*v1)[0];
double ey = (*v2)[1] - (*v1)[1];
for (i = 0; i < np; i++)
{
double3& t = tan[i];
t[0] = m[i][0][0]*ex + m[i][0][1]*ey;
t[1] = m[i][1][0]*ex + m[i][1][1]*ey;
t[2] = sqrt(sqr(t[0]) + sqr(t[1]));
double inorm = 1.0 / t[2];
t[0] *= inorm;
t[1] *= inorm;
t[2] *= (edge == 0 || edge == 2) ? ctm->m[0] : ctm->m[1];
}
}
}
static void calc_bubble_projection(Element* e, Nurbs** nurbs, int order, double2* proj)
{
ref_map_pss.set_active_element(e);
int i, j, k;
int mo2 = quad2d.get_max_order();
int np = quad2d.get_num_points(mo2);
int qo = e->is_quad() ? make_quad_order(order, order) : order;
int nb = ref_map_shapeset.get_num_bubbles(qo);
AUTOLA_OR(double2, fn, np);
memset(fn, 0, sizeof(double2) * np);
double* rhside[2];
double* old[2];
for (i = 0; i < 2; i++) {
rhside[i] = new double[nb];
old[i] = new double[np];
memset(rhside[i], 0, sizeof(double) * nb);
memset(old[i], 0, sizeof(double) * np);
}
// compute known part of projection (vertex and edge part)
old_projection(e, order, proj, old);
// fn values of both components of nonpolynomial function
double3* pt = quad2d.get_points(mo2);
for (j = 0; j < np; j++) // over all integration points
{
double2 a;
a[0] = ctm.m[0] * pt[j][0] + ctm.t[0];
a[1] = ctm.m[1] * pt[j][1] + ctm.t[1];
calc_ref_map(e, nurbs, a[0], a[1], fn[j]);
}
double2* result = proj + e->nvert + e->nvert * (order - 1);
for (k = 0; k < 2; k++)
{
for (i = 0; i < nb; i++) // loop over bubble basis functions
{
// bubble basis functions in all integration points
double *bfn;
int index_i = ref_map_shapeset.get_bubble_indices(qo)[i];
ref_map_pss.set_active_shape(index_i);
ref_map_pss.set_quad_order(mo2);
bfn = ref_map_pss.get_fn_values();
for (j = 0; j < np; j++) // over all integration points
rhside[k][i] += pt[j][2] * (bfn[j] * (fn[j][k] - old[k][j]));
}
// solve
if (e->nvert == 3)
cholsl(bubble_proj_matrix_tri, nb, bubble_tri_p, rhside[k], rhside[k]);
else
cholsl(bubble_proj_matrix_quad, nb, bubble_quad_p, rhside[k], rhside[k]);
for (i = 0; i < nb; i++)
result[i][k] = rhside[k][i];
}
for (i = 0; i < 2; i++) {
delete [] rhside[i];
delete [] old[i];
}
}