/// Calculates the absolute error between sln1 and sln2 using function fn
double calc_error(double (*fn)(MeshFunction*, MeshFunction*, int, QuadPt3D*), MeshFunction *sln1, MeshFunction *sln2) {
_F_
Mesh *meshes[2] = { sln1->get_mesh(), sln2->get_mesh() };
Transformable *tr[2] = { sln1, sln2 };
Traverse trav;
trav.begin(2, meshes, tr);
double error = 0.0;
Element **ee;
while ((ee = trav.get_next_state(NULL, NULL)) != NULL) {
ElementMode3D mode = ee[0]->get_mode();
RefMap *ru = sln1->get_refmap();
Ord3 order = max(sln1->get_fn_order(), sln2->get_fn_order()) + ru->get_inv_ref_order();
order.limit();
Quad3D *quad = get_quadrature(mode);
int np = quad->get_num_points(order);
QuadPt3D *pt = quad->get_points(order);
error += fn(sln1, sln2, np, pt);
}
trav.finish();
return error > H3D_TINY ? sqrt(error) : error; // do not ruin the precision by taking the sqrt
}
// l2 product
double l2_product(RealFunction *fu, RealFunction *fv) {
_F_
Quad3D *quad = get_quadrature(MODE);
// integrate with maximum order
Ord3 o = fu->get_fn_order() + fv->get_fn_order() + Ord3(2, 2, 2);
o.limit();
int np = quad->get_num_points(o);
QuadPt3D *pt = quad->get_points(o);
fu->precalculate(np, pt, FN_DEFAULT);
fv->precalculate(np, pt, FN_DEFAULT);
scalar *u0, *u1, *u2;
u0 = fu->get_fn_values(0);
u1 = fu->get_fn_values(1);
u2 = fu->get_fn_values(2);
scalar *v0, *v1, *v2;
v0 = fv->get_fn_values(0);
v1 = fv->get_fn_values(1);
v2 = fv->get_fn_values(2);
// integrating over reference brick -> jacobian is 1.0 (we do not have to bother with refmap)
double result = 0.0;
for (int i = 0; i < np; i++)
result += pt[i].w * (REAL(sqr(u0[i] - v0[i]) + sqr(u1[i] - v1[i]) + sqr(u2[i] - v2[i])));
return result;
}
/// Calculates the norm of sln using function fn
double calc_norm(double (*fn)(MeshFunction*, int, QuadPt3D*), MeshFunction *sln) {
_F_
double norm = 0.0;
Mesh *mesh = sln->get_mesh();
for(std::map<unsigned int, Element*>::iterator it = mesh->elements.begin(); it != mesh->elements.end(); it++)
if (it->second->used && it->second->active) {
Element *e = mesh->elements[it->first];
sln->set_active_element(e);
RefMap *ru = sln->get_refmap();
Ord3 o = sln->get_fn_order() + ru->get_inv_ref_order();
o.limit();
Quad3D *quad = get_quadrature(e->get_mode());
int np = quad->get_num_points(o);
QuadPt3D *pt = quad->get_points(o);
norm += fn(sln, np, pt);
}
return norm > H3D_TINY ? sqrt(norm) : norm; // do not ruin the precision by taking the sqrt
}
void H1ProjectionIpol::calc_bubble_proj(int split, int son, const Ord3 &order) {
_F_
int bubble_fns = (order.x - 1) * (order.y - 1) * (order.z - 1);
if (bubble_fns <= 0) return;
scalar *proj_rhs = new scalar[bubble_fns];
MEM_CHECK(proj_rhs);
memset(proj_rhs, 0, sizeof(scalar) * bubble_fns);
double **proj_mat = new_matrix<double>(bubble_fns, bubble_fns);
MEM_CHECK(proj_mat);
// get total number of functions (vertex + edge + face)
int ipol_fns = Hex::NUM_VERTICES;
for (int iedge = 0; iedge < Hex::NUM_EDGES; iedge++) {
ipol_fns += order.get_edge_order(iedge) - 1;
}
for (int iface = 0; iface < Hex::NUM_FACES; iface++) {
Ord2 face_order = order.get_face_order(iface);
ipol_fns += (face_order.x - 1) * (face_order.y - 1);
}
ProjItem * ipol = new ProjItem[ipol_fns];
int mm = 0;
// vertex projection coefficients
for (int vtx = 0; vtx < Hex::NUM_VERTICES; vtx++, mm++)
ipol[mm] = vertex_proj[vtx];
// edge projection coefficients
for (int iedge = 0; iedge < Hex::NUM_EDGES; iedge++) {
Ord1 edge_order = order.get_edge_order(iedge);
int edge_fns = edge_order - 1;
for (int i = 0; i < edge_fns; i++, mm++)
ipol[mm] = edge_proj[iedge][i];
}
// face projection coefficients
for (int iface = 0; iface < Hex::NUM_FACES; iface++) {
Ord2 face_order = order.get_face_order(iface);
int face_fns = (face_order.x - 1) * (face_order.y - 1);
for (int i = 0; i < face_fns; i++, mm++)
ipol[mm] = face_proj[iface][i];
}
// do it //
int *bubble_fn_idx = ss->get_bubble_indices(order);
for (int i = 0; i < bubble_fns; i++) {
int iidx = bubble_fn_idx[i];
Ord3 oi = ss->get_dcmp(iidx);
for (int j = 0; j < bubble_fns; j++) {
int jidx = bubble_fn_idx[j];
Ord3 oj = ss->get_dcmp(jidx);
double val =
prod_fn[oi.x][oj.x] * prod_fn[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_dx[oi.x][oj.x] * prod_fn[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_fn[oi.x][oj.x] * prod_dx[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_fn[oi.x][oj.x] * prod_fn[oi.y][oj.y] * prod_dx[oi.z][oj.z];
proj_mat[i][j] += val;
}
}
for (int e = 0; e < int_ns[split]; e++) {
unsigned int son_idx = base_elem->get_son(int_son[son][e]);
sln->set_active_element(mesh->elements[son_idx]);
Trf *tr = get_trf(int_trf[split][e]);
for (int i = 0; i < bubble_fns; i++) {
int iidx = bubble_fn_idx[i];
fu->set_active_shape(iidx);
Ord3 order_rhs = ss->get_order(iidx) + order;
QuadPt3D *pt = quad->get_points(order_rhs);
int np = quad->get_num_points(order_rhs);
if (int_trf[split][e] != -1) fu->push_transform(int_trf[split][e]);
fu->precalculate(np, pt, FN_DEFAULT);
sln->precalculate(np, pt, FN_DEFAULT);
double *uval = fu->get_fn_values();
scalar *rval = sln->get_fn_values();
double *dudx, *dudy, *dudz;
scalar *drdx, *drdy, *drdz;
fu->get_dx_dy_dz_values(dudx, dudy, dudz);
sln->get_dx_dy_dz_values(drdx, drdy, drdz);
QuadPt3D *tpt = new QuadPt3D[np];
transform_points(np, pt, tr, tpt);
scalar *g = new scalar[np];
scalar *dgdx = new scalar[np];
scalar *dgdy = new scalar[np];
scalar *dgdz = new scalar[np];
memset(g, 0, np * sizeof(scalar));
memset(dgdx, 0, np * sizeof(scalar));
memset(dgdy, 0, np * sizeof(scalar));
memset(dgdz, 0, np * sizeof(scalar));
for (int l = 0; l < ipol_fns; l++) {
double *h = new double[np];
scalar *sch = new scalar[np];
ss->get_fn_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, g, 1);
ss->get_dx_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdx, 1);
ss->get_dy_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdy, 1);
ss->get_dz_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdz, 1);
delete [] h;
delete [] sch;
}
delete [] tpt;
scalar value = 0.0;
for (int k = 0; k < quad->get_num_points(order_rhs); k++) {
value += pt[k].w * (uval[k] * (rval[k] - g[k]) +
dudx[k] * ((drdx[k] * mdx[split]) - dgdx[k]) +
dudy[k] * ((drdy[k] * mdy[split]) - dgdy[k]) +
dudz[k] * ((drdz[k] * mdz[split]) - dgdz[k]));
}
delete [] g;
delete [] dgdx;
delete [] dgdy;
delete [] dgdz;
proj_rhs[i] += value * (1 / (double) int_ns[split]);
if (int_trf[split][e] != -1) fu->pop_transform();
}
}
delete [] ipol;
double d;
int *iperm = new int[bubble_fns];
ludcmp(proj_mat, bubble_fns, iperm, &d);
lubksb(proj_mat, bubble_fns, iperm, proj_rhs);
delete iperm;
bubble_proj = new ProjItem [bubble_fns];
for (int i = 0; i < bubble_fns; i++) {
bubble_proj[i].coef = proj_rhs[i];
bubble_proj[i].idx = bubble_fn_idx[i];
}
delete [] proj_mat;
delete [] proj_rhs;
}
void H1ProjectionIpol::calc_face_proj(int iface, int split, int son, const Ord3 &order)
{
_F_
Ord2 face_order = order.get_face_order(iface);
int face_fns = (face_order.x - 1) * (face_order.y - 1);
if (face_fns <= 0) return;
scalar *proj_rhs = new scalar[face_fns];
MEM_CHECK(proj_rhs);
memset(proj_rhs, 0, sizeof(scalar) * face_fns);
double **proj_mat = new_matrix<double>(face_fns, face_fns);
MEM_CHECK(proj_mat);
const int *face_vertex = RefHex::get_face_vertices(iface);
const int *face_edge = RefHex::get_face_edges(iface);
// get total number of functions for interpolant (vertex + edge functions)
int ipol_fns = RefHex::get_num_face_vertices(iface);
for (int iedge = 0; iedge < RefHex::get_num_face_edges(iface); iedge++)
ipol_fns += order.get_edge_order(face_edge[iedge]) - 1;
// interpolant
ProjItem * ipol = new ProjItem[ipol_fns];
int mm = 0;
for (int vtx = 0; vtx < RefHex::get_num_face_vertices(iface); vtx++, mm++)
ipol[mm] = vertex_proj[face_vertex[vtx]];
for (int iedge = 0; iedge < RefHex::get_num_face_edges(iface); iedge++) {
Ord1 edge_order = order.get_edge_order(face_edge[iedge]);
int edge_fns = edge_order - 1;
for (int i = 0; i < edge_fns; i++, mm++)
ipol[mm] = edge_proj[face_edge[iedge]][i];
}
int face_ori = 0;
int *face_fn_idx = ss->get_face_indices(iface, face_ori, face_order);
for (int i = 0; i < face_fns; i++) {
int iidx = face_fn_idx[i];
Ord3 oi = ss->get_dcmp(iidx);
for (int j = 0; j < face_fns; j++) {
int jidx = face_fn_idx[j];
Ord3 oj = ss->get_dcmp(jidx);
double val = 0.0;
if (iface == 0 || iface == 1) {
val =
prod_fn[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_dx[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_fn[oi.y][oj.y] * prod_dx[oi.z][oj.z];
}
else if (iface == 2 || iface == 3) {
val =
prod_fn[oi.x][oj.x] * prod_fn[oi.z][oj.z] +
prod_dx[oi.x][oj.x] * prod_fn[oi.z][oj.z] +
prod_fn[oi.x][oj.x] * prod_dx[oi.z][oj.z];
}
else if (iface == 4 || iface == 5) {
val =
prod_fn[oi.x][oj.x] * prod_fn[oi.y][oj.y] +
prod_dx[oi.x][oj.x] * prod_fn[oi.y][oj.y] +
prod_fn[oi.x][oj.x] * prod_dx[oi.y][oj.y];
}
else
EXIT("Local face number out of range.");
proj_mat[i][j] += val;
}
}
for (int e = 0; e < face_ns[split][iface]; e++) {
unsigned int son_idx = base_elem->get_son(face_son[son][iface][e]);
sln->set_active_element(mesh->elements[son_idx]);
Trf *tr = get_trf(face_trf[split][iface][e]);
for (int i = 0; i < face_fns; i++) {
int iidx = face_fn_idx[i];
fu->set_active_shape(iidx);
Ord2 ord = (ss->get_order(iidx) + order).get_face_order(iface);
QuadPt3D *pt = quad->get_face_points(iface, ord);
int np = quad->get_face_num_points(iface, ord);
if (face_trf[split][iface][e] != -1) fu->push_transform(face_trf[split][iface][e]);
fu->precalculate(np, pt, FN_DEFAULT);
sln->precalculate(np, pt, FN_DEFAULT);
double *uval = fu->get_fn_values();
scalar *rval = sln->get_fn_values();
double *dudx, *dudy;
scalar *drdx, *drdy;
double md, me;
if (iface == 0 || iface == 1) {
dudx = fu->get_dy_values();
drdx = sln->get_dy_values();
dudy = fu->get_dz_values();
drdy = sln->get_dz_values();
md = mdy[split];
me = mdz[split];
}
else if (iface == 2 || iface == 3) {
dudx = fu->get_dx_values();
drdx = sln->get_dx_values();
dudy = fu->get_dz_values();
drdy = sln->get_dz_values();
md = mdx[split];
me = mdz[split];
}
else if (iface == 4 || iface == 5) {
dudx = fu->get_dx_values();
drdx = sln->get_dx_values();
dudy = fu->get_dy_values();
drdy = sln->get_dy_values();
md = mdx[split];
me = mdy[split];
}
else
EXIT("Local face number out of range.");
QuadPt3D *tpt = new QuadPt3D[np];
transform_points(np, pt, tr, tpt);
scalar * g = new scalar[np];
scalar * dgdx = new scalar[np];
scalar * dgdy = new scalar[np];
memset(g, 0, np * sizeof(scalar));
memset(dgdx, 0, np * sizeof(scalar));
memset(dgdy, 0, np * sizeof(scalar));
for (int l = 0; l < ipol_fns; l++) {
double * h = new double[np];
scalar * sch = new scalar[np];
ss->get_fn_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, g, 1);
if (iface == 0 || iface == 1) {
ss->get_dy_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdx, 1);
ss->get_dz_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdy, 1);
}
else if (iface == 2 || iface == 3) {
ss->get_dx_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdx, 1);
ss->get_dz_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdy, 1);
}
else if (iface == 4 || iface == 5) {
ss->get_dx_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdx, 1);
ss->get_dy_values(ipol[l].idx, np, tpt, 0, h);
for (int ii = 0; ii < np; ii++) sch[ii] = h[ii];
blas_axpy(np, ipol[l].coef, sch, 1, dgdy, 1);
}
else
EXIT("Local face number out of range.");
delete [] h;
delete [] sch;
}
delete tpt;
scalar value = 0.0;
for (int k = 0; k < np; k++)
value += pt[k].w * (uval[k] * (rval[k] - g[k]) + dudx[k] * ((drdx[k] * md) - dgdx[k]) + dudy[k] * ((drdy[k] * me) - dgdy[k]));
proj_rhs[i] += value * (1 / (double) face_ns[split][iface]);
delete [] g;
delete [] dgdx;
delete [] dgdy;
if (face_trf[split][iface][e] != -1) fu->pop_transform();
}
}
delete [] ipol;
double d;
int * iperm = new int[face_fns];
ludcmp(proj_mat, face_fns, iperm, &d);
lubksb(proj_mat, face_fns, iperm, proj_rhs);
delete [] iperm;
face_proj[iface] = new ProjItem [face_fns];
for (int i = 0; i < face_fns; i++) {
face_proj[iface][i].coef = proj_rhs[i];
face_proj[iface][i].idx = face_fn_idx[i];
}
delete [] proj_mat;
delete [] proj_rhs;
}
void H1ProjectionIpol::calc_edge_proj(int iedge, int split, int son, const Ord3 &order)
{
_F_
Ord1 edge_order = order.get_edge_order(iedge);
int edge_fns = edge_order - 1;
if (edge_fns <= 0) return;
scalar *proj_rhs = new scalar[edge_fns];
MEM_CHECK(proj_rhs);
memset(proj_rhs, 0, sizeof(scalar) * edge_fns);
double **proj_mat = new_matrix<double>(edge_fns, edge_fns);
MEM_CHECK(proj_rhs);
// local edge vertex numbers
const int *edge_vtx = RefHex::get_edge_vertices(iedge);
ProjItem vtxp[] = { vertex_proj[edge_vtx[0]], vertex_proj[edge_vtx[1]] };
int *edge_fn_idx = ss->get_edge_indices(iedge, 0, edge_order); // indices of edge functions
for (int i = 0; i < edge_fns; i++) {
int iidx = edge_fn_idx[i];
Ord3 oi = ss->get_dcmp(iidx);
for (int j = 0; j < edge_fns; j++) {
int jidx = edge_fn_idx[j];
Ord3 oj = ss->get_dcmp(jidx);
double val = 0.0;
if (iedge == 0 || iedge == 2 || iedge == 8 || iedge == 10) {
val = prod_fn[oi.x][oj.x] + prod_dx[oi.x][oj.x];
}
else if (iedge == 1 || iedge == 3 || iedge == 9 || iedge == 11) {
val = prod_fn[oi.y][oj.y] + prod_dx[oi.y][oj.y];
}
else if (iedge == 4 || iedge == 5 || iedge == 6 || iedge == 7) {
val = prod_fn[oi.z][oj.z] + prod_dx[oi.z][oj.z];
}
else
EXIT("Local edge number out of range.");
proj_mat[i][j] += val;
}
}
for (int e = 0; e < edge_ns[split][iedge]; e++) {
edge_fn_idx = ss->get_edge_indices(iedge, 0, edge_order); // indices of edge functions
unsigned int son_idx = base_elem->get_son(edge_son[son][iedge][e]);
sln->set_active_element(mesh->elements[son_idx]);
Trf *tr = get_trf(edge_trf[split][iedge][e]);
for (int i = 0; i < edge_fns; i++) {
int iidx = edge_fn_idx[i];
fu->set_active_shape(iidx);
Ord1 ord = (ss->get_order(iidx) + order).get_edge_order(iedge);
QuadPt3D *pt = quad->get_edge_points(iedge, ord);
int np = quad->get_edge_num_points(iedge, ord);
if (edge_trf[split][iedge][e] != -1) fu->push_transform(edge_trf[split][iedge][e]);
fu->precalculate(np, pt, FN_DEFAULT);
sln->precalculate(np, pt, FN_DEFAULT);
double *uval = fu->get_fn_values();
scalar *rval = sln->get_fn_values();
double *du, md;
scalar *dr;
if (iedge == 0 || iedge == 2 || iedge == 8 || iedge == 10) {
du = fu->get_dx_values();
dr = sln->get_dx_values();
md = mdx[split];
}
else if (iedge == 1 || iedge == 3 || iedge == 9 || iedge == 11) {
du = fu->get_dy_values();
dr = sln->get_dy_values();
md = mdy[split];
}
else if (iedge == 4 || iedge == 5 || iedge == 6 || iedge == 7) {
du = fu->get_dz_values();
dr = sln->get_dz_values();
md = mdz[split];
}
else
EXIT("Local edge number out of range.");
QuadPt3D *tpt = new QuadPt3D[np];
transform_points(np, pt, tr, tpt);
double *tmp = new double[np];
scalar *sctmp = new scalar[np];
scalar *g = new scalar[np]; // interpolant
memset(g, 0, np * sizeof(scalar));
#ifndef H3D_COMPLEX
ss->get_fn_values(vtxp[0].idx, np, tpt, 0, tmp);
blas_axpy(np, vtxp[0].coef, tmp, 1, g, 1);
ss->get_fn_values(vtxp[1].idx, np, tpt, 0, tmp);
blas_axpy(np, vtxp[1].coef, tmp, 1, g, 1);
#else
ss->get_fn_values(vtxp[0].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[0].coef, sctmp, 1, g, 1);
ss->get_fn_values(vtxp[1].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[1].coef, sctmp, 1, g, 1);
#endif
scalar *dg = new scalar[np];
memset(dg, 0, np * sizeof(scalar));
if (iedge == 0 || iedge == 2 || iedge == 8 || iedge == 10) {
ss->get_dx_values(vtxp[0].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[0].coef, sctmp, 1, dg, 1);
ss->get_dx_values(vtxp[1].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[1].coef, sctmp, 1, dg, 1);
}
else if (iedge == 1 || iedge == 3 || iedge == 9 || iedge == 11) {
ss->get_dy_values(vtxp[0].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[0].coef, sctmp, 1, dg, 1);
ss->get_dy_values(vtxp[1].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[1].coef, sctmp, 1, dg, 1);
}
else if (iedge == 4 || iedge == 5 || iedge == 6 || iedge == 7) {
ss->get_dz_values(vtxp[0].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[0].coef, sctmp, 1, dg, 1);
ss->get_dz_values(vtxp[1].idx, np, tpt, 0, tmp);
for (int ii = 0; ii < np; ii++) sctmp[ii] = tmp[ii];
blas_axpy(np, vtxp[1].coef, sctmp, 1, dg, 1);
}
else
EXIT("Local edge number out of range.");
delete [] tmp;
delete [] sctmp;
delete [] tpt;
scalar value = 0.0;
for (int k = 0; k < np; k++)
value += pt[k].w * (uval[k] * (rval[k] - g[k]) + du[k] * ((dr[k] * md) - dg[k]));
proj_rhs[i] += value * (1 / (double) edge_ns[split][iedge]);
delete [] g;
delete [] dg;
if (edge_trf[split][iedge][e] != -1) fu->pop_transform();
}
}
double d;
int * iperm = new int[edge_fns];
ludcmp(proj_mat, edge_fns, iperm, &d);
lubksb(proj_mat, edge_fns, iperm, proj_rhs);
delete [] iperm;
// copy functions and coefficients to the basis
edge_proj[iedge] = new ProjItem[edge_fns];
for (int i = 0; i < edge_fns; i++) {
edge_proj[iedge][i].coef = proj_rhs[i];
edge_proj[iedge][i].idx = edge_fn_idx[i];
}
delete [] proj_mat;
delete [] proj_rhs;
}
void H1Projection::calc_projection(int split, int son, const Ord3 &order)
{
_F_
n_fns = (order.x + 1) * (order.y + 1) * (order.z + 1);
delete [] fn_idx;
fn_idx = new int [n_fns];
int mm = 0;
// vertex functions
for (int vtx = 0; vtx < Hex::NUM_VERTICES; vtx++, mm++)
fn_idx[mm] = ss->get_vertex_index(vtx);
// edge functions
for (int iedge = 0; iedge < Hex::NUM_EDGES; iedge++) {
Ord1 edge_order = order.get_edge_order(iedge);
int n_edge_fns = ss->get_num_edge_fns(edge_order);
if (n_edge_fns > 0) {
const int *edge_fn_idx = ss->get_edge_indices(iedge, 0, edge_order);
for (int i = 0; i < n_edge_fns; i++, mm++)
fn_idx[mm] = edge_fn_idx[i];
}
}
// face functions
for (int iface = 0; iface < Hex::NUM_FACES; iface++) {
Ord2 face_order = order.get_face_order(iface);
int n_face_fns = ss->get_num_face_fns(face_order);
if (n_face_fns > 0) {
const int *face_fn_idx = ss->get_face_indices(iface, 0, face_order);
for (int i = 0; i < n_face_fns; i++, mm++)
fn_idx[mm] = face_fn_idx[i];
}
}
{
// bubble functions
int n_bubble_fns = ss->get_num_bubble_fns(order);
if (n_bubble_fns > 0) {
const int *bubble_fn_idx = ss->get_bubble_indices(order);
for (int i = 0; i < n_bubble_fns; i++, mm++)
fn_idx[mm] = bubble_fn_idx[i];
}
}
double **proj_mat = new_matrix<double>(n_fns, n_fns);
scalar *proj_rhs = new scalar[n_fns];
memset(proj_rhs, 0, sizeof(scalar) * n_fns);
// proj matrix
for (int i = 0; i < n_fns; i++) {
int iidx = fn_idx[i];
Ord3 oi = ss->get_dcmp(iidx);
for (int j = 0; j < n_fns; j++) {
int jidx = fn_idx[j];
Ord3 oj = ss->get_dcmp(jidx);
double val =
prod_fn[oi.x][oj.x] * prod_fn[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_dx[oi.x][oj.x] * prod_fn[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_fn[oi.x][oj.x] * prod_dx[oi.y][oj.y] * prod_fn[oi.z][oj.z] +
prod_fn[oi.x][oj.x] * prod_fn[oi.y][oj.y] * prod_dx[oi.z][oj.z];
proj_mat[i][j] += val;
}
}
// rhs
for (int e = 0; e < int_ns[split]; e++) {
unsigned int son_idx = base_elem->get_son(int_son[son][e]);
sln->set_active_element(mesh->elements[son_idx]);
Trf *tr = get_trf(int_trf[split][e]);
for (int i = 0; i < n_fns; i++) {
int iidx = fn_idx[i];
fu->set_active_shape(iidx);
Ord3 order_rhs = ss->get_order(iidx) + order;
QuadPt3D *pt = quad->get_points(order_rhs);
int np = quad->get_num_points(order_rhs);
if (int_trf[split][e] != -1) fu->push_transform(int_trf[split][e]);
fu->precalculate(np, pt, FN_DEFAULT);
sln->precalculate(np, pt, FN_DEFAULT);
double *uval = fu->get_fn_values();
scalar *rval = sln->get_fn_values();
double *dudx, *dudy, *dudz;
scalar *drdx, *drdy, *drdz;
fu->get_dx_dy_dz_values(dudx, dudy, dudz);
sln->get_dx_dy_dz_values(drdx, drdy, drdz);
QuadPt3D *tpt = new QuadPt3D[np];
transform_points(np, pt, tr, tpt); // tpt is not used further, if this changes, the call to the destructor can be moved.
delete tpt;
scalar value = 0.0;
for (int k = 0; k < np; k++) {
value += pt[k].w * (uval[k] * rval[k] +
dudx[k] * drdx[k] * mdx[split] +
dudy[k] * drdy[k] * mdy[split] +
dudz[k] * drdz[k] * mdz[split]);
}
proj_rhs[i] += value * (1 / (double) int_ns[split]);
if (int_trf[split][e] != -1) fu->pop_transform();
}
}
double d;
int * iperm = new int[n_fns];
ludcmp(proj_mat, n_fns, iperm, &d);
lubksb(proj_mat, n_fns, iperm, proj_rhs);
delete [] iperm;
proj_coef = new double [n_fns];
memcpy(proj_coef, proj_rhs, n_fns * sizeof(double));
delete [] proj_mat;
delete [] proj_rhs;
}
