void HcurlOrthoHP::calc_projection_errors(Element* e, int order, Solution* rsln, double herr[8][11], double perr[11]) { int i, j, k, son, s; int m = e->get_mode(); double error; scalar prod; if (!obase_ready) calc_ortho_base(); // select quadrature, obtain integration points and weights Quad2D* quad = &g_quad_2d_std; quad->set_mode(m); rsln->set_quad_2d(quad); double3* pt = quad->get_points(20); int np = quad->get_num_points(20); // everything is done on the reference domain // no reference mapping, no transformations rsln->enable_transform(false); // obtain reference solution values on all four refined sons scalar* rval0[4], *rval1[4], *rd1dx[4], *rd0dy[4]; Element* base = rsln->get_mesh()->get_element(e->id); assert(!base->active); for (son = 0; son < 4; son++) { Element* e = base->sons[son]; assert(e != NULL); rsln->set_active_element(e); rsln->set_quad_order(20); rval0[son] = rsln->get_fn_values(0); rval1[son] = rsln->get_fn_values(1); rd1dx[son] = rsln->get_dx_values(1); rd0dy[son] = rsln->get_dy_values(0); } // h-candidates: calculate products of the reference solution with orthonormal basis // functions on son elements, obtaining (partial) projections and their errors scalar proj_0[4][121]; scalar proj_1[4][121]; scalar proj_c[4][121]; for (son = 0; son < 4; son++) { memset(proj_0[0], 0, sizeof(proj_0[0])); memset(proj_1[0], 0, sizeof(proj_1[0])); memset(proj_c[0], 0, sizeof(proj_c[0])); for (i = 0; i <= order; i++) // h-candidates: max order equals to original element order { // update the projection to the current order for (j = basecnt[m][i]; j < basecnt[m][i+1]; j++) { for (k = 0, prod = 0.0; k < np; k++) { scalar rcurl = (rd1dx[son][k] - rd0dy[son][k]); scalar r0 = rval0[son][k]; scalar r1 = rval1[son][k]; prod += pt[k][2] * (( r0 * obase_0[m][8][j][k] ) + ( r1 * obase_1[m][8][j][k] ) + ( rcurl * obase_c[m][8][j][k] ) ); } for (k = 0; k < np; k++) { proj_0[0][k] += obase_0[m][8][j][k] * prod; proj_1[0][k] += obase_1[m][8][j][k] * prod; proj_c[0][k] += obase_c[m][8][j][k] * prod; } } // calculate the H(curl) error of the projection for (k = 0, error = 0.0; k < np; k++) { scalar rcurl = (rd1dx[son][k] - rd0dy[son][k]); scalar r0 = rval0[son][k]; scalar r1 = rval1[son][k]; error += pt[k][2] * ( sqr(r0 - proj_0[0][k]) + sqr(r1 - proj_1[0][k]) + sqr(rcurl - proj_c[0][k]) ); } herr[son][i] = error; } } // aniso-candidates: calculate projections and their errors (only quadrilaterals) if (m) { const double mx[4] = { 2.0, 2.0, 1.0, 1.0}; const double my[4] = { 1.0, 1.0, 2.0, 2.0}; const int sons[4][2] = {{0,1},{3,2},{0,3},{1,2}}; const int tr[4][2] = {{6,7},{6,7},{4,5},{4,5}}; for (son = 0; son < 4; son++) // 2 sons for vertical split, 2 sons for horizontal split { memset(proj_0, 0, sizeof(proj_0)); memset(proj_1, 0, sizeof(proj_1)); memset(proj_c, 0, sizeof(proj_c)); for (i = 0; i <= order+1; i++) // h-candidates: max order equals to original element order+1 { // update the projection to the current order for (j = basecnt[m][i]; j < basecnt[m][i+1]; j++) { for (s = 0, prod = 0.0; s < 2; s++) // each son has 2 subsons (regular square sons) { for (k = 0; k < np; k++) { scalar rcurl = 2.0 * (rd1dx[sons[son][s]][k] - rd0dy[sons[son][s]][k]); scalar r0 = mx[son] * rval0[sons[son][s]][k]; scalar r1 = my[son] * rval1[sons[son][s]][k]; prod += pt[k][2] * ((r0 * obase_0[m][tr[son][s]][j][k]) + (r1 * obase_1[m][tr[son][s]][j][k]) + (rcurl * obase_c[m][tr[son][s]][j][k])); } } prod *= 0.5; for (s = 0; s < 2; s++) for (k = 0; k < np; k++) { proj_0[s][k] += prod * obase_0[m][tr[son][s]][j][k]; proj_1[s][k] += prod * obase_1[m][tr[son][s]][j][k]; proj_c[s][k] += prod * obase_c[m][tr[son][s]][j][k]; } } // calculate the error of the projection for (s = 0, error = 0.0; s < 2; s++) { for (k = 0; k < np; k++) { scalar rcurl = 2.0 * (rd1dx[sons[son][s]][k] - rd0dy[sons[son][s]][k]); scalar r0 = mx[son] * rval0[sons[son][s]][k]; scalar r1 = my[son] * rval1[sons[son][s]][k]; error += pt[k][2] * (sqr(r0 - proj_0[s][k]) + sqr(r1 - proj_1[s][k]) + sqr(rcurl - proj_c[s][k])); } } herr[4 + son][i] = error * 0.5; } } } // p-candidates: calculate projections and their errors memset(proj_0, 0, sizeof(proj_0)); memset(proj_1, 0, sizeof(proj_1)); memset(proj_c, 0, sizeof(proj_c)); for (i = 0; i <= std::min(order+2, 9); i++) // p-candidate: max order = original order + 2 { // update the projection to the current order for (j = basecnt[m][i]; j < basecnt[m][i+1]; j++) { for (son = 0, prod = 0.0; son < 4; son++) { // transformations to the quarter of the reference element double mm = (e->is_triangle() && son == 3) ? -2.0 : 2.0; for (k = 0; k < np; k++) { scalar rcurl = 4.0 * (rd1dx[son][k] - rd0dy[son][k]); scalar r0 = mm * rval0[son][k]; scalar r1 = mm * rval1[son][k]; prod += pt[k][2] * ((r0 * obase_0[m][son][j][k]) + (r1 * obase_1[m][son][j][k]) + (rcurl * obase_c[m][son][j][k])); } } prod *= 0.25; for (son = 0; son < 4; son++) for (k = 0; k < np; k++) { proj_0[son][k] += prod * obase_0[m][son][j][k]; proj_1[son][k] += prod * obase_1[m][son][j][k]; proj_c[son][k] += prod * obase_c[m][son][j][k]; } } // calculate the error of the projection for (son = 0, error = 0.0; son < 4; son++) { double mm = (e->is_triangle() && son == 3) ? -2.0 : 2.0; for (k = 0; k < np; k++) { scalar rcurl = 4.0 * (rd1dx[son][k] - rd0dy[son][k]); scalar r0 = mm * rval0[son][k]; scalar r1 = mm * rval1[son][k]; error += pt[k][2] * (sqr(r0 - proj_0[son][k]) + sqr(r1 - proj_1[son][k]) + sqr(rcurl - proj_c[son][k])); } } perr[i] = error * 0.25; } }
void L2OrthoHP::calc_projection_errors(Element* e, int order, Solution* rsln, double herr[8][11], double perr[11]) { int i, j, s, k, r, son; int m = e->get_mode(); double error; Scalar prod; if (!obase_ready) calc_ortho_base(); // select quadrature, obtain integration points and weights Quad2D* quad = &g_quad_2d_std; quad->set_mode(m); rsln->set_quad_2d(quad); double3* pt = quad->get_points(20); int np = quad->get_num_points(20); // everything is done on the reference domain // -- no reference mapping, no transformations rsln->enable_transform(false); // obtain reference solution values on all four refined sons Scalar* rval[4][3]; Element* base = rsln->get_mesh()->get_element(e->id); assert(!base->active); for (son = 0; son < 4; son++) { Element* e = base->sons[son]; assert(e != NULL); rsln->set_active_element(e); rsln->set_quad_order(20); rval[son][0] = rsln->get_fn_values(); rval[son][1] = rsln->get_dx_values(); rval[son][2] = rsln->get_dy_values(); } // h-cadidates: calculate products of the reference solution with orthonormal basis // functions on son elements, obtaining (partial) projections and their errors Scalar3 proj[4][121]; for (son = 0; son < 4; son++) { memset(proj[0], 0, sizeof(proj[0])); for (i = 1; i <= order; i++) { // update the projection to the current order for (j = basecnt[m][i-1]; j < basecnt[m][i]; j++) { for (k = 0, prod = 0.0; k < np; k++) prod += pt[k][2] * (rval[son][0][k] * obase[m][8][j][k][0]); for (k = 0; k < np; k++) for (r = 0; r < 3; r++) proj[0][k][r] += obase[m][8][j][k][r] * prod; } // calculate the error of the projection for (k = 0, error = 0.0; k < np; k++) error += pt[k][2] * (sqr(rval[son][0][k] - proj[0][k][0])); herr[son][i] = error; } } // aniso-candidates: calculate projections and their errors (only quadrilaterals) if (m) { const double mx[4] = { 2.0, 2.0, 1.0, 1.0}; const double my[4] = { 1.0, 1.0, 2.0, 2.0}; const int sons[4][2] = { {0,1}, {3,2}, {0,3}, {1,2} }; const int tr[4][2] = { {6,7}, {6,7}, {4,5}, {4,5} }; for (son = 0; son < 4; son++) // 2 sons for vertical split, 2 sons for horizontal split { memset(proj, 0, sizeof(proj)); for (i = 1; i <= order+1; i++) // h-candidates: max order equals to original element order+1 { // update the projection to the current order for (j = basecnt[m][i-1]; j < basecnt[m][i]; j++) { for (s = 0, prod = 0.0; s < 2; s++) // each son has 2 subsons (regular square sons) for (k = 0; k < np; k++) prod += pt[k][2] * rval[sons[son][s]][0][k] * obase[m][tr[son][s]][j][k][0]; prod *= 0.5; for (s = 0; s < 2; s++) for (k = 0; k < np; k++) for (r = 0; r < 1; r++) proj[s][k][r] += prod * obase[m][tr[son][s]][j][k][r]; } // calculate the error of the projection for (s = 0, error = 0.0; s < 2; s++) for (k = 0; k < np; k++) error += pt[k][2] * sqr(rval[sons[son][s]][0][k] - proj[s][k][0]); herr[4 + son][i] = error * 0.5; } } } // p-candidates: calculate projections and their errors memset(proj, 0, sizeof(proj)); for (i = 1; i <= std::min(order+2, 10); i++) { // update the projection to the current order for (j = basecnt[m][i-1]; j < basecnt[m][i]; j++) { for (son = 0, prod = 0.0; son < 4; son++) { // (transforming to the quarter of the reference element) double mm = (e->is_triangle() && son == 3) ? -2.0 : 2.0; for (k = 0; k < np; k++) { prod += pt[k][2] * rval[son][0][k] * obase[m][son][j][k][0]; } } prod *= 0.25; for (son = 0; son < 4; son++) for (k = 0; k < np; k++) for (r = 0; r < 1; r++) proj[son][k][r] += prod * obase[m][son][j][k][r]; } // calculate the error of the projection for (son = 0, error = 0.0; son < 4; son++) { double mm = (e->is_triangle() && son == 3) ? -2.0 : 2.0; for (k = 0; k < np; k++) error += pt[k][2] * sqr(rval[son][0][k] - proj[son][k][0]); } perr[i] = error * 0.25; } }