void PrecalcShapeset::precalculate(int order, int mask)
{
int i, j, k;
// initialization
Quad2D* quad = get_quad_2d();
quad->set_mode(mode);
H2D_CHECK_ORDER(quad, order);
int np = quad->get_num_points(order);
double3* pt = quad->get_points(order);
int oldmask = (cur_node != NULL) ? cur_node->mask : 0;
int newmask = mask | oldmask;
Node* node = new_node(newmask, np);
// precalculate all required tables
for (j = 0; j < num_components; j++)
{
for (k = 0; k < 6; k++)
{
if (newmask & idx2mask[k][j]) {
if (oldmask & idx2mask[k][j])
memcpy(node->values[j][k], cur_node->values[j][k], np * sizeof(double));
else
for (i = 0; i < np; i++)
node->values[j][k][i] = shapeset->get_value(k, index, ctm->m[0] * pt[i][0] + ctm->t[0],
ctm->m[1] * pt[i][1] + ctm->t[1], j);
}
}
}
if(nodes->present(order)) {
assert(nodes->get(order) == cur_node);
::free(nodes->get(order));
}
nodes->add(node, order);
cur_node = node;
}
void ProjBasedSelector::calc_projection_errors(Element* e, const CandsInfo& info_h, const CandsInfo& info_p, const CandsInfo& info_aniso, Solution* rsln, CandElemProjError herr[4], CandElemProjError perr, CandElemProjError anisoerr[4]) {
assert_msg(info_h.is_empty() || (H2D_GET_H_ORDER(info_h.max_quad_order) <= H2DRS_MAX_ORDER && H2D_GET_V_ORDER(info_h.max_quad_order) <= H2DRS_MAX_ORDER), "Maximum allowed order of a son of H-candidate is %d but order (H:%d,V:%d) requested.", H2DRS_MAX_ORDER, H2D_GET_H_ORDER(info_h.max_quad_order), H2D_GET_V_ORDER(info_h.max_quad_order));
assert_msg(info_p.is_empty() || (H2D_GET_H_ORDER(info_p.max_quad_order) <= H2DRS_MAX_ORDER && H2D_GET_V_ORDER(info_p.max_quad_order) <= H2DRS_MAX_ORDER), "Maximum allowed order of a son of P-candidate is %d but order (H:%d,V:%d) requested.", H2DRS_MAX_ORDER, H2D_GET_H_ORDER(info_p.max_quad_order), H2D_GET_V_ORDER(info_p.max_quad_order));
assert_msg(info_aniso.is_empty() || (H2D_GET_H_ORDER(info_aniso.max_quad_order) <= H2DRS_MAX_ORDER && H2D_GET_V_ORDER(info_aniso.max_quad_order) <= H2DRS_MAX_ORDER), "Maximum allowed order of a son of ANISO-candidate is %d but order (H:%d,V:%d) requested.", H2DRS_MAX_ORDER, H2D_GET_H_ORDER(info_aniso.max_quad_order), H2D_GET_V_ORDER(info_aniso.max_quad_order));
int mode = e->get_mode();
// select quadrature, obtain integration points and weights
Quad2D* quad = &g_quad_2d_std;
quad->set_mode(mode);
rsln->set_quad_2d(quad);
double3* gip_points = quad->get_points(H2DRS_INTR_GIP_ORDER);
int num_gip_points = quad->get_num_points(H2DRS_INTR_GIP_ORDER);
// everything is done on the reference domain
rsln->enable_transform(false);
// obtain reference solution values on all four refined sons
scalar** rval[H2D_MAX_ELEMENT_SONS];
Element* base_element = rsln->get_mesh()->get_element(e->id);
assert(!base_element->active);
for (int son = 0; son < H2D_MAX_ELEMENT_SONS; son++)
{
//set element
Element* e = base_element->sons[son];
assert(e != NULL);
//obtain precalculated values
rval[son] = precalc_ref_solution(son, rsln, e, H2DRS_INTR_GIP_ORDER);
}
//retrieve transformations
Trf* trfs = NULL;
int num_noni_trfs = 0;
if (mode == HERMES_MODE_TRIANGLE) {
trfs = tri_trf;
num_noni_trfs = H2D_TRF_TRI_NUM;
}
else {
trfs = quad_trf;
num_noni_trfs = H2D_TRF_QUAD_NUM;
}
// precalculate values of shape functions
TrfShape empty_shape_vals;
if (!cached_shape_vals_valid[mode]) {
precalc_ortho_shapes(gip_points, num_gip_points, trfs, num_noni_trfs, shape_indices[mode], max_shape_inx[mode], cached_shape_ortho_vals[mode]);
precalc_shapes(gip_points, num_gip_points, trfs, num_noni_trfs, shape_indices[mode], max_shape_inx[mode], cached_shape_vals[mode]);
cached_shape_vals_valid[mode] = true;
//issue a warning if ortho values are defined and the selected cand_list might benefit from that but it cannot because elements do not have uniform orders
if (!warn_uniform_orders && mode == HERMES_MODE_QUAD && !cached_shape_ortho_vals[mode][H2D_TRF_IDENTITY].empty()) {
warn_uniform_orders = true;
if (cand_list == H2D_H_ISO || cand_list == H2D_H_ANISO || cand_list == H2D_P_ISO || cand_list == H2D_HP_ISO || cand_list == H2D_HP_ANISO_H) {
warn_if(!info_h.uniform_orders || !info_aniso.uniform_orders || !info_p.uniform_orders, "Possible inefficiency: %s might be more efficient if the input mesh contains elements with uniform orders strictly.", get_cand_list_str(cand_list));
}
}
}
TrfShape& svals = cached_shape_vals[mode];
TrfShape& ortho_svals = cached_shape_ortho_vals[mode];
//H-candidates
if (!info_h.is_empty()) {
Trf* p_trf_identity[1] = { &trfs[H2D_TRF_IDENTITY] };
std::vector<TrfShapeExp>* p_trf_svals[1] = { &svals[H2D_TRF_IDENTITY] };
std::vector<TrfShapeExp>* p_trf_ortho_svals[1] = { &ortho_svals[H2D_TRF_IDENTITY] };
for(int son = 0; son < H2D_MAX_ELEMENT_SONS; son++) {
scalar **sub_rval[1] = { rval[son] };
calc_error_cand_element(mode, gip_points, num_gip_points
, 1, &base_element->sons[son], p_trf_identity, sub_rval
, p_trf_svals, p_trf_ortho_svals
, info_h, herr[son]);
}
}
//ANISO-candidates
if (!info_aniso.is_empty()) {
const int sons[4][2] = { {0,1}, {3,2}, {0,3}, {1,2} }; //indices of sons for sub-areas
const int tr[4][2] = { {6,7}, {6,7}, {4,5}, {4,5} }; //indices of ref. domain transformations for sub-areas
for(int version = 0; version < 4; version++) { // 2 elements for vertical split, 2 elements for horizontal split
Trf* sub_trfs[2] = { &trfs[tr[version][0]], &trfs[tr[version][1]] };
Element* sub_domains[2] = { base_element->sons[sons[version][0]], base_element->sons[sons[version][1]] };
scalar **sub_rval[2] = { rval[sons[version][0]], rval[sons[version][1]] };
std::vector<TrfShapeExp>* sub_svals[2] = { &svals[tr[version][0]], &svals[tr[version][1]] };
std::vector<TrfShapeExp>* sub_ortho_svals[2] = { &ortho_svals[tr[version][0]], &ortho_svals[tr[version][1]] };
calc_error_cand_element(mode, gip_points, num_gip_points
, 2, sub_domains, sub_trfs, sub_rval
, sub_svals, sub_ortho_svals
, info_aniso, anisoerr[version]);
}
}
//P-candidates
if (!info_p.is_empty()) {
Trf* sub_trfs[4] = { &trfs[0], &trfs[1], &trfs[2], &trfs[3] };
scalar **sub_rval[4] = { rval[0], rval[1], rval[2], rval[3] };
std::vector<TrfShapeExp>* sub_svals[4] = { &svals[0], &svals[1], &svals[2], &svals[3] };
std::vector<TrfShapeExp>* sub_ortho_svals[4] = { &ortho_svals[0], &ortho_svals[1], &ortho_svals[2], &ortho_svals[3] };
calc_error_cand_element(mode, gip_points, num_gip_points
, 4, base_element->sons, sub_trfs, sub_rval
, sub_svals, sub_ortho_svals
, info_p, perr);
}
}
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;
}
}
