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 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); } } } } } } }
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 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::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 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_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]; } }