/* Scatter the points from u to U using the map in B->bmap */
static void ScatrBndry_Stokes(double *u, Element_List **V, Bsystem **B)
{
register int j,k;
int eDIM = V[0]->flist[0]->dim();
int nel = B[0]->nel, Nbmodes, *bmap;
double *hj;
double *sc = B[0]->signchange;
for(k = 0; k < nel; ++k)
{
bmap = B[eDIM]->bmap[k];
Nbmodes = V[0]->flist[k]->Nbmodes;
for(j = 0; j < eDIM; ++j)
{
hj = V[j]->flist[k]->vert->hj;
dgathr(Nbmodes, u, bmap + j*Nbmodes, hj);
dvmul (Nbmodes, sc, 1, hj, 1, hj,1);
}
V[eDIM]->flist[k]->vert[0].hj[0] = u[bmap[eDIM*Nbmodes]];
sc += Nbmodes;
}
}
void Quad::fillvec(Mode *v, double *f){
register int i;
for(i = 0; i < qb; ++i)
dcopy(qa,v->a,1,f+i*qa,1);
for(i = 0; i < qa; ++i)
dvmul(qb,v->b,1,f+i,qa,f+i,qa);
}
static void solve_pressure(Element_List **V, double *rhs, Bsystem **Vbsys)
{
register int i;
int eDIM = V[0]->flist[0]->dim();
int info,N,nbl,nblv,id,*bmap;
Bsystem *B = Vbsys[0], *PB = Vbsys[eDIM];
Element *E;
double *hj,*tmp;
double *sc = B->signchange;
if(eDIM == 2)
tmp = dvector(0,8*LGmax);
else
tmp = dvector(0,18*(LGmax-1)*(LGmax-1));
/* back solve for pressure */
for(E=V[eDIM]->fhead;E;E=E->next)
{
N = E->Nmodes - 1;
id = E->geom->id;
hj = E->vert->hj + 1;
E->state = 't';
/* solve interior and negate */
if(PB->lambda->wave)
{
dgetrs('N', N, 1, PB->Gmat->invc[id], N, PB->Gmat->cipiv[id],hj, N,
info);
}
else
{
dpptrs('L', N, 1, PB->Gmat->invc[id], hj, N, info);
dneg(N,hj,1);
}
bmap = PB->bmap[E->id];
nblv = V[0]->flist[E->id]->Nbmodes;
nbl = eDIM*nblv+1;
for(i = 0; i < nbl; ++i)
tmp[i] = rhs[bmap[i]];
for(i = 0; i < eDIM; ++i)
dvmul(nblv,sc,1,tmp+nblv*i,1,tmp+nblv*i,1);
if(PB->lambda->wave)
dgemv('N', N, nbl,-1.0, PB->Gmat->invcd[id], N, tmp, 1, 1.,hj,1);
else
dgemv('N', N, nbl,-1.0, PB->Gmat->binvc[id], N, tmp, 1, 1.,hj,1);
sc += nblv;
}
free(tmp);
}
void A_Stokes(Element_List **V, Bsystem **B, double *p, double *w, double **wk)
{
int eDIM = V[0]->flist[0]->dim();
int nel = B[0]->nel, Nbmodes;
double **a = B[eDIM]->Gmat->a;
int **bmap = B[eDIM]->bmap;
double *sc = B[0]->signchange;
register int i,j,k;
dzero(B[eDIM]->nsolve,w,1);
for(k = 0; k < nel; ++k)
{
Nbmodes = V[0]->flist[k]->Nbmodes;
/* Put p boundary modes into wk[0] and impose continuity */
dgathr(eDIM*Nbmodes+1, p, bmap[k], wk[0]);
for(j = 0; j < eDIM; ++j)
dvmul (Nbmodes, sc, 1, wk[0] + j*Nbmodes, 1, wk[0] + j*Nbmodes,1);
dspmv('U',eDIM*Nbmodes+1,1.0,a[V[0]->flist[k]->geom->id],
wk[0],1,0.0,wk[1],1);
/* do sign change back and put into w */
for(j = 0; j < eDIM; ++j)
for(i = 0; i < Nbmodes; ++i)
w[bmap[k][i+j*Nbmodes]] += sc[i]*wk[1][i+j*Nbmodes];
w[bmap[k][eDIM*Nbmodes]] += wk[1][eDIM*Nbmodes];
sc += Nbmodes;
}
/* set first pressure constant to zero */
if(B[eDIM]->singular)
w[eDIM*B[0]->nsolve] = 0.0;
}
double Quad::get_1diag_massmat(int ID){
double *wa, *wb;
double *wvec = dvector(0, qtot-1), vmmat;
Mode mw,*m;
#ifndef PCONTBASE
double **ba, **bb;
Mode m1;
get_moda_GL (qa, &ba);
get_moda_GL (qb, &bb);
m1.a = ba[ID];
m1.b = bb[ID];
m = &m1;
#else
Basis *b = getbasis();
m = b->vert+ID;
#endif
getzw(qa,&wa,&wa,'a');
getzw(qb,&wb,&wb,'a');
mw.a = wa; mw.b = wb;
fillvec(&mw, wvec);
if(curvX)
dvmul(qtot, wvec, 1, geom->jac.p, 1, wvec, 1);
else
dscal(qtot, geom->jac.d, wvec, 1);
vmmat = Quad_mass_mprod(this, m, wvec);
free(wvec);
return vmmat;
}
// ============================================================================
void Tri::BET_Mat(Element *P, LocMatDiv *bet, double *beta, double *sigma)
{
register int i,j,n;
const int nbl = Nbmodes, N = Nmodes - Nbmodes;
int L;
Basis *b = getbasis();
double **dxb = bet->Dxb, // MSB: dx corresponds to bar(beta)
**dxi = bet->Dxi,
**dyb = bet->Dyb, // MSB: dy corresponds to sigma
**dyi = bet->Dyi;
char orig_state = state;
/* fill boundary systems */
for(i = 0,n=0; i < Nverts; ++i,++n)
{
fillElmt(b->vert+i);
dvmul(qtot,beta,1,*h,1,*P->h,1);
#ifndef PCONTBASE
P->Ofwd(*P->h,P->vert->hj,P->dgL);
#else
P->Iprod(P);
#endif
dcopy(P->Nmodes,P->vert->hj,1,*dxb + n,nbl);
dvmul(qtot,sigma,1,*h,1,*P->h,1);
#ifndef PCONTBASE
P->Ofwd(*P->h,P->vert->hj,P->dgL);
#else
P->Iprod(P);
#endif
dcopy(P->Nmodes,P->vert->hj,1,*dyb + n,nbl);
}
for(i = 0; i < Nedges; ++i)
for(j = 0; j < edge[i].l; ++j, ++n)
{
fillElmt(b->edge[i]+j);
dvmul(qtot,beta,1,*h,1,*P->h,1);
#ifndef PCONTBASE
P->Ofwd(*P->h,P->vert->hj,P->dgL);
#else
P->Iprod(P);
#endif
dcopy(P->Nmodes,P->vert->hj,1,*dxb + n,nbl);
dvmul(qtot,sigma,1,*h,1,*P->h,1);
#ifndef PCONTBASE
P->Ofwd(*P->h,P->vert->hj,P->dgL);
#else
P->Iprod(P);
#endif
dcopy(P->Nmodes,P->vert->hj,1,*dyb + n,nbl);
}
L = face->l;
for(i = 0,n=0; i < L;++i)
for(j = 0; j < L-i; ++j,++n)
{
fillElmt(b->face[0][i]+j);
dvmul(qtot,beta,1,*h,1,*P->h,1);
#ifndef PCONTBASE
P->Ofwd(*P->h,P->vert->hj,P->dgL);
#else
P->Iprod(P);
#endif
dcopy(P->Nmodes,P->vert->hj,1,*dxi + n,N);
dvmul(qtot,sigma,1,*h,1,*P->h,1);
#ifndef PCONTBASE
P->Ofwd(*P->h,P->vert->hj,P->dgL);
#else
P->Iprod(P);
#endif
dcopy(P->Nmodes,P->vert->hj,1,*dyi + n,N);
}
state = orig_state;
/* negate all systems to that the whole operator can be treated
as positive when condensing */
/*
dneg(nbl*P->Nmodes,*dxb,1);
dneg(nbl*P->Nmodes,*dyb,1);
dneg(N *P->Nmodes,*dxi,1);
dneg(N *P->Nmodes,*dyi,1);
*/
}
// ============================================================================
void Tri::PSE_Mat(Element *E, LocMat *pse, double *DU)
{
register int i,j,n;
int nbl, L, N, Nm, qt, asize = pse->asize, csize = pse->csize;
Basis *B = E->getbasis();
double *Eh;
double **a = pse->a;
double **b = pse->b;
double **c = pse->c;
double **d = pse->d;
// This routine is placed within the for loop for each element
// at around line 30 in the code. Therefore, this is within an element
nbl = E->Nbmodes;
N = E->Nmodes - nbl;
Nm = E->Nmodes;
qt = E->qa*E->qb;
Eh = dvector(0, qt - 1); // Temporary storage for E->h[0] ------
dcopy(qt, E->h[0], 1, Eh, 1);
// Fill A and D ----------------------------------------------------
for(i = 0, n = 0; i < E->Nverts; ++i, ++n)
{
E->fillElmt(B->vert + i);
// ROUTINE THAT DOES INNERPRODUCT AND EVALUATES TERM--------------
dvmul(qt, DU, 1, E->h[0], 1, E->h[0], 1);
E->Iprod(E);
// ---------------------------------------------------------------
dcopy(nbl, E->vert->hj, 1, *a + n, asize);
dcopy(N, E->vert->hj + nbl, 1, d[n], 1);
}
dcopy(qt, Eh, 1, E->h[0], 1);
for(i = 0; i < E->Nedges; ++i)
{
for(j = 0; j < (L = E->edge[i].l); ++j, ++n)
{
E->fillElmt(B->edge[i] + j);
// ROUTINE THAT DOES INNERPRODUCT AND EVALUATES TERM------------
dvmul(qt, DU, 1, E->h[0], 1, E->h[0], 1);
E->Iprod(E);
// -------------------------------------------------------------
dcopy(nbl, E->vert->hj, 1, *a + n, asize);
dcopy(N, E->vert->hj + nbl, 1, d[n], 1);
}
}
dcopy(qt, Eh, 1, E->h[0], 1);
// Fill B and C ----------------------------------------------------
L = E->face->l;
for(i = 0, n = 0; i < L; ++i)
{
for(j = 0; j < L-i; ++j, ++n)
{
E->fillElmt(B->face[0][i]+j);
// ROUTINE THAT DOES INNERPRODUCT AND EVALUATES TERM-----------
dvmul(qt, DU, 1, E->h[0], 1, E->h[0], 1);
E->Iprod(E);
// ------------------------------------------------------------
dcopy(nbl, E->vert->hj , 1, *b + n, csize);
dcopy(N, E->vert->hj + nbl, 1, *c + n, csize);
}
}
// -----------------------------------------------------------------
free(Eh);
}
void Tri_setup_iprodlap()
{
int qa = QGmax;
int qb;
if(LZero) // use extra points if have Legendre zeros in 'b' direction
qb = QGmax;
else
qb = QGmax-1;
int qc = 0;
int L = LGmax;
// Set up dummy element with maximum quadrature/edge order
Coord X;
X.x = dvector(0,NTri_verts-1);
X.y = dvector(0,NTri_verts-1);
X.x[0] = 0.0;
X.x[1] = 1.0;
X.x[2] = 0.0;
X.y[0] = 0.0;
X.y[1] = 0.0;
X.y[2] = 1.0;
Tri *T = (Tri*) new Tri(0,'T', L, qa, qb, qc, &X);
free(X.x);
free(X.y);
int i,j,k,n;
int facs = Tri_DIM*Tri_DIM;
Tri_ipmodes = T->Nmodes;
Tri_iplap = (double***) calloc(facs,sizeof(double**));
for(i = 0; i < facs; ++i)
{
Tri_iplap[i] = dmatrix(0, T->Nmodes-1, 0, T->Nmodes-1);
dzero(T->Nmodes*T->Nmodes, Tri_iplap[i][0], 1);
}
// Set up gradient basis
Basis *B,*DB;
Mode *w,*m,*m1,*md,*md1,**gb,**gb1,*fac;
double *z;
B = T->getbasis();
DB = T->derbasis();
fac = B->vert;
w = mvector(0,0);
gb = (Mode **) malloc(T->Nmodes*sizeof(Mode *));
gb[0] = mvecset(0,Tri_DIM*T->Nmodes,qa, qb, qc);
gb1 = (Mode **) malloc(T->Nmodes*sizeof(Mode *));
gb1[0] = mvecset(0,Tri_DIM*T->Nmodes,qa, qb, qc);
for(i = 1; i < T->Nmodes; ++i)
gb[i] = gb[i-1]+Tri_DIM;
for(i = 1; i < T->Nmodes; ++i)
gb1[i] = gb1[i-1]+Tri_DIM;
getzw(qa,&z,&w[0].a,'a');
getzw(qb,&z,&w[0].b,'b');
/* fill gb with basis info for laplacian calculation */
// vertex modes
m = B->vert;
md = DB->vert;
for(i = 0,n=0; i < T->Nverts; ++i,++n)
T->fill_gradbase(gb[n],m+i,md+i,fac);
// edge modes
for(i = 0; i < T->Nedges; ++i)
{
m1 = B ->edge[i];
md1 = DB->edge[i];
for(j = 0; j < T->edge[i].l; ++j,++n)
T->fill_gradbase(gb[n],m1+j,md1+j,fac);
}
// face modes
for(i = 0; i < T->Nfaces; ++i)
for(j = 0; j < T->face[0].l; ++j)
{
m1 = B ->face[i][j];
md1 = DB->face[i][j];
for(k = 0; k < T->face[0].l-j; ++k,++n)
T->fill_gradbase(gb[n],m1+k,md1+k,fac);
}
/* multiply by weights */
for(i = 0; i < T->Nmodes; ++i)
{
Tri_mvmul2d(qa,qb,qc,gb[i] ,w,gb1[i]);
Tri_mvmul2d(qa,qb,qc,gb[i]+1,w,gb1[i]+1);
}
// Calculate Laplacian inner products
double s1, s2, s3, s4, s5, s6, s7, s8;
double *tmp = dvector(0, QGmax-1);
fac = B->vert+1;
for(i = 0; i < T->Nmodes; ++i)
for(j = 0; j < T->Nmodes; ++j)
{
s1 = ddot(qa,gb[i][0].a,1,gb1[j][0].a,1);
s1 *= ddot(qb,gb[i][0].b,1,gb1[j][0].b,1);
dvmul(qa, fac->a, 1, gb[i][0].a, 1, tmp, 1);
s2 = ddot(qa, tmp,1,gb1[j][0].a,1);
s2 *= ddot(qb,gb[i][0].b,1,gb1[j][0].b,1);
s3 = ddot(qa, tmp,1,gb1[j][1].a,1);
s3 *= ddot(qb,gb[i][0].b,1,gb1[j][1].b,1);
dvmul(qa, fac->a, 1, tmp, 1, tmp, 1);
s4 = ddot(qa, tmp,1,gb1[j][0].a,1);
s4 *= ddot(qb,gb[i][0].b,1,gb1[j][0].b,1);
s5 = ddot(qa,gb[i][0].a,1,gb1[j][1].a,1);
s5 *= ddot(qb,gb[i][0].b,1,gb1[j][1].b,1);
s6 = ddot(qa,gb[i][1].a,1,gb1[j][0].a,1);
s6 *= ddot(qb,gb[i][1].b,1,gb1[j][0].b,1);
dvmul(qa, fac->a, 1, gb[i][1].a, 1, tmp, 1);
s7 = ddot(qa, tmp,1,gb1[j][0].a,1);
s7 *= ddot(qb,gb[i][1].b,1,gb1[j][0].b,1);
s8 = ddot(qa,gb[i][1].a,1,gb1[j][1].a,1);
s8 *= ddot(qb,gb[i][1].b,1,gb1[j][1].b,1);
Tri_iplap[0][i][j] = s1;
Tri_iplap[1][i][j] = s5 + 2*s2 + s6;
Tri_iplap[2][i][j] = s3 + s4 + s7 + s8;
}
/* fill gb with basis info for mass matrix calculation */
// vertex modes
m = B->vert;
for(i = 0,n=0; i < T->Nverts; ++i,++n)
{
dcopy(qa, m[i].a, 1, gb[n]->a, 1);
dcopy(qb, m[i].b, 1, gb[n]->b, 1);
}
// edge modes
for(i = 0; i < T->Nedges; ++i)
{
m1 = B ->edge[i];
for(j = 0; j < T->edge[i].l; ++j,++n)
{
dcopy(qa, m1[j].a, 1, gb[n]->a, 1);
dcopy(qb, m1[j].b, 1, gb[n]->b, 1);
}
}
// face modes
for(i = 0; i < T->Nfaces; ++i)
for(j = 0; j < T->face[i].l; ++j)
{
m1 = B ->face[i][j];
for(k = 0; k < T->face[i].l-j; ++k,++n)
{
dcopy(qa, m1[k].a, 1, gb[n]->a, 1);
dcopy(qb, m1[k].b, 1, gb[n]->b, 1);
}
}
/* multiply by weights */
for(i = 0; i < T->Nmodes; ++i)
Tri_mvmul2d(qa,qb,qc,gb[i] ,w,gb1[i]);
for(i = 0; i < T->Nmodes; ++i)
for(j = 0; j < T->Nmodes; ++j)
{
s1 = ddot(qa,gb[i][0].a,1,gb1[j][0].a,1);
s1 *= ddot(qb,gb[i][0].b,1,gb1[j][0].b,1);
Tri_iplap[3][i][j] = s1;
}
free_mvec(gb[0]) ;
free((char *) gb);
free_mvec(gb1[0]);
free((char *) gb1);
free((char*)w);
free(tmp);
delete (T);
}
void Precon_Stokes(Element_List *U, Bsystem *B, double *r, double *z){
switch(B->Precon){
case Pre_Diag:
dvmul(B->Pmat->info.diag.ndiag,B->Pmat->info.diag.idiag,1,r,1,z,1);
break;
case Pre_Block:{
register int i;
int eDIM = U->fhead->dim();
int nedge = B->Pmat->info.block.nedge;
int info,l,cnt;
double *tmp = dvector(0,LGmax-1);
static double *pinv;
dcopy(B->nsolve,r,1,z,1);
#ifdef BVERT
dpptrs('U',B->Pmat->info.block.nvert,1,B->Pmat->info.block.ivert,
z,B->Pmat->info.block.nvert,info);
#else
dvmul(B->Pmat->info.block.nvert,B->Pmat->info.block.ivert,1,z,1,z,1);
#endif
cnt = B->Pmat->info.block.nvert;
for(i = 0; i < nedge; ++i){
l = B->Pmat->info.block.Ledge[i];
dpptrs('U',l,1,B->Pmat->info.block.iedge[i],z+cnt,l,info);
cnt += l;
}
if(!pinv){
pinv = dvector(0,B->nsolve-cnt-1);
for(i = 0; i < B->nsolve-cnt; ++i)
pinv[i] = U->flist[i]->get_1diag_massmat(0);
dvrecp(B->nsolve-cnt,pinv,1,pinv,1);
}
/* finally multiply pressure dof by inverse of mass matrix */
dvmul(B->nsolve-cnt,pinv,1,r+cnt,1,z+cnt,1);
free(tmp);
}
break;
case Pre_None:
dcopy(B->nsolve,r,1,z,1);
break;
case Pre_Diag_Stokes:{
register int i,j,k;
double *tmp = dvector(0,B->nglobal-1),*sc,*b,*p,*wk;
int eDIM = U->fhead->dim();
int **bmap = B->bmap;
int nel = B->nel,asize,Nbmodes,info;
if(eDIM == 2)
wk = dvector(0,eDIM*4*LGmax);
else
wk = dvector(0,eDIM*6*LGmax*LGmax);
dzero(B->nglobal,tmp,1);
dcopy(B->nsolve-nel,r,1,tmp,1);
/* multiply by invc */
dvmul(B->nsolve-nel,B->Pmat->info.diagst.idiag,1,tmp,1,tmp,1);
/* multiply by b^T */
sc = B->signchange;
p = z + B->nsolve-nel;
dcopy(nel,r+B->nsolve-nel,1,p,1);
dneg (nel-1,p+1,1);
/* start at 1 to omit singular pressure point */
if(!(B->singular))
error_msg(issue in setting singular modes in Stokes_Precon not resolved);
for(j = 1; j < nel; ++j){
Nbmodes = U->flist[j]->Nbmodes;
asize = Nbmodes*eDIM+1;
dzero (asize,wk,1);
dgathr(eDIM*Nbmodes, tmp, bmap[j], wk);
dvmul (eDIM*Nbmodes, sc, 1, wk, 1, wk, 1);
b = B->Gmat->a[U->flist[j]->geom->id] + asize*(asize-1)/2;
p[j] += ddot(asize-1,b,1,wk,1);
sc += asize;
}
/* solve for p */
dpptrs('L', nel, 1, B->Pmat->info.diagst.binvcb,p,nel,info);
/* generate initial vector as tmp = B p */
sc = B->signchange;
dzero(B->nglobal,tmp,1);
/* start from 1 due to singular pressure system */
for(k = 1; k < nel; ++k){
Nbmodes = U->flist[k]->Nbmodes;
asize = Nbmodes*eDIM+1;
b = B->Gmat->a[U->flist[k]->geom->id] + asize*(asize-1)/2;
dsmul(asize-1,p[k],b,1,wk,1);
for(i = 0; i < eDIM*Nbmodes; ++i)
tmp[bmap[k][i]] += sc[i]*wk[i];
sc += asize;
}
/* set z = r - tmp */
dvsub(B->nsolve-nel,r,1,tmp,1,z,1);
/* u = invc*z */
dvmul(B->nsolve-nel,B->Pmat->info.diagst.idiag,1,z,1,z,1);
free(tmp); free(wk);
}
break;
case Pre_Block_Stokes:{
register int i,j,k;
double *tmp = dvector(0,B->nglobal-1),*sc,*b,*p,*wk;
int eDIM = U->fhead->dim(),cnt,l;
int **bmap = B->bmap;
int nel = B->nel,asize,Nbmodes,info;
int nedge = B->Pmat->info.blockst.nedge;
if(eDIM == 2)
wk = dvector(0,eDIM*4*LGmax);
else
wk = dvector(0,eDIM*6*LGmax*LGmax);
dzero(B->nglobal,tmp,1);
dcopy(B->nsolve-nel,r,1,tmp,1);
/* multiply by invc */
#ifdef BVERT
dpptrs('U',B->Pmat->info.blockst.nvert,1,B->Pmat->info.blockst.ivert,
tmp,B->Pmat->info.blockst.nvert,info);
#else
dvmul(B->Pmat->info.blockst.nvert,B->Pmat->info.blockst.ivert,1,
tmp,1,tmp,1);
#endif
cnt = B->Pmat->info.blockst.nvert;
for(i = 0; i < nedge; ++i){
l = B->Pmat->info.blockst.Ledge[i];
dpptrs('U',l,1,B->Pmat->info.blockst.iedge[i],tmp+cnt,l,info);
cnt += l;
}
/* multiply by b^T */
sc = B->signchange;
p = z + B->nsolve-nel;
dcopy(nel,r+B->nsolve-nel,1,p,1);
dneg(nel-1,p+1,1);
if(!(B->singular))
error_msg(issue in setting singular modes in Stokes_Precon not resolved);
/* start at 1 to omit singular pressure point */
for(j = 1; j < nel; ++j){
Nbmodes = U->flist[j]->Nbmodes;
asize = Nbmodes*eDIM+1;
dzero (asize,wk,1);
dgathr(eDIM*Nbmodes, tmp, bmap[j], wk);
dvmul (eDIM*Nbmodes, sc, 1, wk, 1, wk, 1);
b = B->Gmat->a[U->flist[j]->geom->id] + asize*(asize-1)/2;
p[j] += ddot(asize-1,b,1,wk,1);
sc += asize;
}
/* solve for p */
dpptrs('L', nel, 1, B->Pmat->info.blockst.binvcb,p,nel,info);
/* generate initial vector as tmp = B p */
sc = B->signchange;
dzero(B->nglobal,tmp,1);
/* start from 1 due to singular pressure system */
for(k = 1; k < nel; ++k){
Nbmodes = U->flist[k]->Nbmodes;
asize = Nbmodes*eDIM+1;
b = B->Gmat->a[U->flist[k]->geom->id] + asize*(asize-1)/2;
dsmul(asize-1,p[k],b,1,wk,1);
for(i = 0; i < eDIM*Nbmodes; ++i)
tmp[bmap[k][i]] += sc[i]*wk[i];
sc += asize;
}
/* set z = r - tmp */
dvsub(B->nsolve-nel,r,1,tmp,1,z,1);
/* u = invc*z */
#ifdef BVERT
dpptrs('U',B->Pmat->info.blockst.nvert,1,B->Pmat->info.blockst.ivert,
z,B->Pmat->info.blockst.nvert,info);
#else
dvmul(B->Pmat->info.blockst.nvert,B->Pmat->info.blockst.ivert,1,z,1,z,1);
#endif
cnt = B->Pmat->info.blockst.nvert;
for(i = 0; i < nedge; ++i){
l = B->Pmat->info.blockst.Ledge[i];
dpptrs('U',l,1,B->Pmat->info.blockst.iedge[i],z+cnt,l,info);
cnt += l;
}
free(tmp); free(wk);
}
break;
default:
fprintf(stderr,"Preconditioner (Precon=%d) not known\n",B->Precon);
exit(-1);
}
}
static void divergence_free_init(Element_List **V, double *u0, double *r,
Bsystem **B, double **wk){
register int i,j,k,cnt;
int eDIM = V[0]->fhead->dim();
int asize,info,Nbmodes;
int **bmap = B[eDIM]->bmap;
int nel = B[eDIM]->nel;
int nglobal = B[eDIM]->nglobal;
int nsolve = B[eDIM]->nsolve;
int vsolve = B[0]->nsolve;
double **a = B[eDIM]->Gmat->a,*x,*b,*sc,*sc1;
static double *invb;
x = dvector(0,nel-1);
/* form and invert B' B system */
if(!invb){
invb = dvector(0,nel*(nel+1)/2-1);
sc = B[0]->signchange;
for(cnt = 0,k = 0; k < nel; ++k){
/* gather B from local systems */
Nbmodes = V[0]->flist[k]->Nbmodes;
asize = Nbmodes*eDIM+1;
b = a[V[0]->flist[k]->geom->id] + asize*(asize-1)/2;
dzero(nglobal,u0,1);
for(j = 0; j < eDIM; ++j){
for(i = 0; i < Nbmodes; ++i)
u0[bmap[k][i+j*Nbmodes]] += sc[i]*b[i+j*Nbmodes];
}
dzero(nglobal-nsolve,u0+nsolve,1);
/* take inner product with B' */
sc1 = B[0]->signchange;
for(j = k; j < nel; ++j,cnt++){
dzero(asize,wk[0],1);
dgathr(asize-1, u0, bmap[j], wk[0]);
for(i = 0; i < eDIM; ++i)
dvmul (Nbmodes, sc1, 1, wk[0]+i*Nbmodes, 1, wk[0]+i*Nbmodes, 1);
Nbmodes = V[0]->flist[j]->Nbmodes;
asize = Nbmodes*eDIM+1;
b = a[V[0]->flist[j]->geom->id] + asize*(asize-1)/2;
invb[cnt] = ddot(asize-1,b,1,wk[0],1);
sc1 += Nbmodes;
}
sc += V[0]->flist[k]->Nbmodes;
}
/* take out first row to deal with singularity */
if(B[eDIM]->singular)
dzero(nel,invb,1); invb[0] = 1.0;
dpptrf('L', nel, invb, info);
}
/* solve B' B x = r */
dcopy (nel,r+eDIM*vsolve,1,x,1);
dpptrs('L', nel, 1, invb, x, nel, info);
dzero(B[eDIM]->nglobal,u0,1);
/* generate initial vector as u0 = B x */
sc = B[0]->signchange;
for(k = 0; k < nel; ++k){
Nbmodes = V[0]->flist[k]->Nbmodes;
asize = Nbmodes*eDIM+1;
b = a[V[0]->flist[k]->geom->id] + asize*(asize-1)/2;
dsmul(asize-1,x[k],b,1,wk[0],1);
for(j = 0; j < eDIM; ++j){
for(i = 0; i < Nbmodes; ++i)
u0[bmap[k][i+j*Nbmodes]] += sc[i]*wk[0][i+j*Nbmodes];
}
sc += Nbmodes;
}
dzero(nglobal-eDIM*vsolve, u0 + eDIM*vsolve, 1);
/* subtract off a*u0 from r */
sc = B[0]->signchange;
for(k = 0; k < nel; ++k){
Nbmodes = V[0]->flist[k]->Nbmodes;
dzero(eDIM*Nbmodes+1,wk[0],1);
dgathr(eDIM*Nbmodes+1, u0, bmap[k], wk[0]);
for(j = 0; j < eDIM; ++j)
dvmul (Nbmodes, sc, 1, wk[0] + j*Nbmodes, 1, wk[0] + j*Nbmodes,1);
dspmv('U',eDIM*Nbmodes+1,1.0,a[V[0]->flist[k]->geom->id],
wk[0],1,0.0,wk[1],1);
for(j = 0; j < eDIM; ++j)
for(i = 0; i < Nbmodes; ++i)
r[bmap[k][i+j*Nbmodes]] -= sc[i]*wk[1][i+j*Nbmodes];
r[bmap[k][eDIM*Nbmodes]] -= wk[1][eDIM*Nbmodes];
sc += Nbmodes;
}
r[eDIM*vsolve] = 0.0;
dzero(nglobal-nsolve, r + nsolve, 1);
free(x);
}