/*
dR_dx has shape (dim, n_efun), transposed w.r.t. the Python version!
*/
int32 eval_nurbs_basis_tp(FMField *R, FMField *dR_dx, FMField *det,
FMField *dR_dxi,
FMField *dx_dxi, FMField *dxi_dx,
FMField *B, FMField *dB_dxi,
FMField *N, FMField *dN_dxi,
FMField *qp, uint32 ie, FMField *control_points,
FMField *weights, int32 *degrees, int32 dim,
FMField *cs,
int32 *conn, int32 n_el, int32 n_ep)
{
int32 ret = RET_OK;
uint32 ii, jj, a, i0, i1, i2;
uint32 n_efuns[3];
uint32 n_efun = 1;
uint32 n_els[3];
uint32 ic[3];
int32 *ec;
FMField *C, *N0, *N1, *N2, *dN0_dxi, *dN1_dxi, *dN2_dxi;
float64 w, W, P;
float64 dw_dxi[3];
#ifdef DEBUG_FMF
if (!((dim == qp->nCol) && (dim <= 3))) {
errput(ErrHead "inconsistent dimension! (%d == $d <= 3)", dim, qp->nCol);
ERR_CheckGo(ret);
}
#endif
for (ii = 0; ii < dim; ii++) {
n_efuns[ii] = degrees[ii] + 1;
n_efun *= n_efuns[ii];
}
#ifdef DEBUG_FMF
if (n_efun != n_ep) {
errput(ErrHead "inconsistent number of bases! (%d == $d)", n_efun, n_ep);
ERR_CheckGo(ret);
}
#endif
// Element connectivity.
ec = conn + n_ep * ie;
// 1D Bernstein basis B, dB/dxi.
for (ii = 0; ii < dim; ii++) {
eval_bernstein_basis(B + ii, dB_dxi + ii, qp->val[ii], degrees[ii]);
}
// 1D B-spline basis N = CB, dN/dxi = C dB/dxi.
for (ii = 0; ii < dim; ii++) {
n_els[ii] = (cs + ii)->nCell;
}
unravel_index(ic, ie, n_els, dim);
for (ii = 0; ii < dim; ii++) {
C = cs + ii;
FMF_SetCell(C, ic[ii]);
fmf_mulAB_nn(N + ii, C, B + ii);
fmf_mulAB_nn(dN_dxi + ii, C, dB_dxi + ii);
}
ERR_CheckGo(ret);
// Numerators and denominator for tensor-product NURBS basis R, dR/dxi.
w = 0; // w_b
for (ii = 0; ii < dim; ii++) {
dw_dxi[ii] = 0.0; // dw_b/dxi
}
a = 0; // Basis function index.
if (dim == 3) {
N0 = N + 0;
N1 = N + 1;
N2 = N + 2;
dN0_dxi = dN_dxi + 0;
dN1_dxi = dN_dxi + 1;
dN2_dxi = dN_dxi + 2;
for (i0 = 0; i0 < n_efuns[0]; i0++) {
for (i1 = 0; i1 < n_efuns[1]; i1++) {
for (i2 = 0; i2 < n_efuns[2]; i2++) {
W = weights->val[ec[a]];
R->val[a] = N0->val[i0] * N1->val[i1] * N2->val[i2] * W;
w += R->val[a];
dR_dxi->val[a+n_ep*0] = dN0_dxi->val[i0] * N1->val[i1] * N2->val[i2] * W;
dw_dxi[0] += dR_dxi->val[a+n_ep*0];
dR_dxi->val[a+n_ep*1] = N0->val[i0] * dN1_dxi->val[i1] * N2->val[i2] * W;
dw_dxi[1] += dR_dxi->val[a+n_ep*1];
dR_dxi->val[a+n_ep*2] = N0->val[i0] * N1->val[i1] * dN2_dxi->val[i2] * W;
dw_dxi[2] += dR_dxi->val[a+n_ep*2];
a += 1;
}
}
}
} else if (dim == 2) {
N0 = N + 0;
N1 = N + 1;
dN0_dxi = dN_dxi + 0;
dN1_dxi = dN_dxi + 1;
for (i0 = 0; i0 < n_efuns[0]; i0++) {
for (i1 = 0; i1 < n_efuns[1]; i1++) {
W = weights->val[ec[a]];
R->val[a] = N0->val[i0] * N1->val[i1] * W;
w += R->val[a];
dR_dxi->val[a+n_ep*0] = dN0_dxi->val[i0] * N1->val[i1] * W;
dw_dxi[0] += dR_dxi->val[a+n_ep*0];
dR_dxi->val[a+n_ep*1] = N0->val[i0] * dN1_dxi->val[i1] * W;
dw_dxi[1] += dR_dxi->val[a+n_ep*1];
a += 1;
}
}
} else {
N0 = N + 0;
dN0_dxi = dN_dxi + 0;
for (i0 = 0; i0 < n_efuns[0]; i0++) {
W = weights->val[ec[a]];
R->val[a] = N0->val[i0] * W;
w += R->val[a];
dR_dxi->val[a+n_ep*0] = dN0_dxi->val[i0] * W;
dw_dxi[0] += dR_dxi->val[a+n_ep*0];
a += 1;
}
}
// Finish R <- R / w_b.
fmf_mulC(R, 1.0 / w);
// Finish dR/dxi. D == W C dB/dxi, dR/dxi = (D - R dw_b/dxi) / w_b.
for (a = 0; a < dR_dxi->nCol; a++) {
for (ii = 0; ii < dim; ii++) {
dR_dxi->val[a+n_ep*ii] = (dR_dxi->val[a+n_ep*ii]
- R->val[a] * dw_dxi[ii]) / w;
}
}
// Mapping reference -> physical domain dxi/dx.
// x = sum P_a R_a, dx/dxi = sum P_a dR_a/dxi, invert.
for (ii = 0; ii < dim; ii++) {
for (jj = 0; jj < dim; jj++) {
dx_dxi->val[dim*ii+jj] = 0.0;
for (a = 0; a < dR_dxi->nCol; a++) {
P = control_points->val[dim*ec[a]+ii];
dx_dxi->val[dim*ii+jj] += P * dR_dxi->val[a+n_ep*jj];
}
}
}
geme_det3x3(det->val, dx_dxi);
geme_invert3x3(dxi_dx, dx_dxi);
// dR/dx.
fmf_mulATB_nn(dR_dx, dxi_dx, dR_dxi);
end_label:
return(ret);
}
/*!
@par Revision history:
- 11.10.2005, c
- 12.10.2005
- 05.06.2006
- 06.06.2006
*/
int32 vg_describe( VolumeGeometry *obj,
float64 *coorIn, int32 nNod, int32 dim,
int32 *conn, int32 nEl, int32 nEP,
FMField *bfGR, FMField *weight )
{
int32 iel, inod, idim, pos, iqp, nQP, ret = RET_OK;
FMField *mtxMR = 0, *mtxMRI = 0, *coor = 0;
nQP = bfGR->nLev;
if (!((nEl == obj->nEl) &&
(dim == obj->dim) &&
(nQP == obj->nQP) &&
(nEP == obj->nEP))) {
output( "nNod: %d, dim: %d, nEl: %d, nEP: %d\n", nNod, dim, nEl, nEP );
fmf_print( obj->bfGM, stdout, 1 );
fmf_print( bfGR, stdout, 1 );
fmf_print( weight, stdout, 1 );
errput( "size mismatch!\n" );
return( RET_Fail );
}
fmf_createAlloc( &mtxMR, 1, nQP, dim, dim );
fmf_createAlloc( &mtxMRI, 1, nQP, dim, dim );
fmf_createAlloc( &coor, 1, 1, nEP, dim );
obj->totalVolume = 0.0;
/* output( "nCell %d\n", obj->bfGM->nCell ); */
for (iel = 0; iel < obj->bfGM->nCell; iel++) {
FMF_SetCell( obj->bfGM, iel );
FMF_SetCell( obj->det, iel );
FMF_SetCell( obj->volume, iel );
for (inod = 0; inod < nEP; inod++) {
pos = dim*conn[inod];
for (idim = 0; idim < dim; idim++ ) {
coor->val[dim*inod+idim] = coorIn[idim+pos];
}
}
// Jacobi matrix from reference to material system.
fmf_mulATBT_1n( mtxMR, coor, bfGR );
// Its determinant, preweighted.
geme_det3x3( obj->det->val, mtxMR );
for (iqp = 0; iqp < nQP; iqp++) {
if (obj->det->val[iqp] <= MachEps) {
errput( "warp violation %e at (iel: %d, iqp: %d)!\n",
obj->det->val[iqp], iel, iqp );
}
}
fmf_mul( obj->det, weight->val );
// Element volume.
geme_elementVolume( obj->volume->val, obj->det->val, nQP );
obj->totalVolume += obj->volume->val[0];
// Inverse of Jacobi matrix reference to material system.
geme_invert3x3( mtxMRI, mtxMR );
// Base function gradient w.r.t. material system.
fmf_mulATB_nn( obj->bfGM, mtxMRI, bfGR );
conn += nEP;
/* output( "cell %d\n", iel ); */
/* fmf_print( coor, stdout, 0 ); */
/* fmf_print( obj->det, stdout, 0 ); */
ERR_CheckGo( ret );
}
end_label:
fmf_freeDestroy( &mtxMR );
fmf_freeDestroy( &mtxMRI );
fmf_freeDestroy( &coor );
return( ret );
}
