static PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
{
AppCtx *user = (AppCtx*)ctx;
PetscErrorCode ierr;
PetscInt i,mx,xm,xs;
PetscScalar v[3],h,xlow,xhigh;
MatStencil row,col[3];
DM da;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,0,0,&xm,0,0);CHKERRQ(ierr);
h = 1.0/(mx-1);
for (i=xs; i<xs+xm; i++) {
row.i = i;
if (i==0 || i==mx-1) {
v[0] = 2.0;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
xlow = h*(PetscReal)i - .5*h;
xhigh = xlow + h;
v[0] = (-1.0 - user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xlow))/h;col[0].i = i-1;
v[1] = (2.0 + user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xlow) + user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xhigh))/h;col[1].i = row.i;
v[2] = (-1.0 - user->e*PetscSinScalar(2.0*PETSC_PI*user->k*xhigh))/h;col[2].i = i+1;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,MatStructure *str,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,mx,xm,xs;
PetscScalar v[7],Hx;
MatStencil row,col[7];
PetscScalar lambda;
DM da;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
ierr = PetscMemzero(col,7*sizeof(MatStencil));CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
Hx = 2.0*PETSC_PI / (PetscReal)(mx);
ierr = DMDAGetCorners(da,&xs,0,0,&xm,0,0);CHKERRQ(ierr);
lambda = 2.0*Hx;
for (i=xs; i<xs+xm; i++) {
row.i = i; row.j = 0; row.k = 0; row.c = 0;
v[0] = Hx; col[0].i = i; col[0].c = 0;
v[1] = lambda; col[1].i = i-1; col[1].c = 1;
v[2] = -lambda;col[2].i = i+1; col[2].c = 1;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
row.i = i; row.j = 0; row.k = 0; row.c = 1;
v[0] = lambda; col[0].i = i-1; col[0].c = 0;
v[1] = Hx; col[1].i = i; col[1].c = 1;
v[2] = -lambda;col[2].i = i+1; col[2].c = 0;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatView(jac,PETSC_VIEWER_BINARY_(PETSC_COMM_SELF));CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeJacobian(KSP ksp,Mat J, Mat jac,void *ctx)
{
PetscErrorCode ierr;
PetscInt i, j, M, N, xm, ym, xs, ys, num, numi, numj;
PetscScalar v[5], Hx, Hy, HydHx, HxdHy;
MatStencil row, col[5];
DM da;
MatNullSpace nullspace;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&M,&N,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
Hx = 1.0 / (PetscReal)(M);
Hy = 1.0 / (PetscReal)(N);
HxdHy = Hx/Hy;
HydHx = Hy/Hx;
ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
row.i = i; row.j = j;
if (i==0 || j==0 || i==M-1 || j==N-1) {
num=0; numi=0; numj=0;
if (j!=0) {
v[num] = -HxdHy; col[num].i = i; col[num].j = j-1;
num++; numj++;
}
if (i!=0) {
v[num] = -HydHx; col[num].i = i-1; col[num].j = j;
num++; numi++;
}
if (i!=M-1) {
v[num] = -HydHx; col[num].i = i+1; col[num].j = j;
num++; numi++;
}
if (j!=N-1) {
v[num] = -HxdHy; col[num].i = i; col[num].j = j+1;
num++; numj++;
}
v[num] = ((PetscReal)(numj)*HxdHy + (PetscReal)(numi)*HydHx); col[num].i = i; col[num].j = j;
num++;
ierr = MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
v[0] = -HxdHy; col[0].i = i; col[0].j = j-1;
v[1] = -HydHx; col[1].i = i-1; col[1].j = j;
v[2] = 2.0*(HxdHy + HydHx); col[2].i = i; col[2].j = j;
v[3] = -HydHx; col[3].i = i+1; col[3].j = j;
v[4] = -HxdHy; col[4].i = i; col[4].j = j+1;
ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
ierr = MatSetNullSpace(J,nullspace);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,mx,xm,xs;
PetscScalar v[3],h;
MatStencil row,col[3];
DM da,shell;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&shell);CHKERRQ(ierr);
ierr = DMShellGetContext(shell,(void**)&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&mx,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,0,0,&xm,0,0);CHKERRQ(ierr);
h = 1.0/(mx-1);
for (i=xs; i<xs+xm; i++) {
row.i = i;
if (i==0 || i==mx-1) {
v[0] = 2.0/h;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
v[0] = (-1.0)/h;col[0].i = i-1;
v[1] = (2.0)/h;col[1].i = row.i;
v[2] = (-1.0)/h;col[2].i = i+1;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FillMatrix(DM da,Mat A)
{
PetscErrorCode ierr;
PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,idx;
PetscScalar v[7];
MatStencil row,col[7];
PetscFunctionBeginUser;
ierr = DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
for (k=zs;k<zs+zm;k++) {
for (j=ys;j<ys+ym;j++) {
for (i=xs;i<xs+xm;i++) {
row.i=i; row.j=j; row.k=k;
col[0].i=row.i; col[0].j=row.j; col[0].k=row.k;
v[0]=6.0;
idx=1;
if (k>0) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j; col[idx].k=k-1; idx++; }
if (j>0) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j-1; col[idx].k=k; idx++; }
if (i>0) { v[idx]=-1.0; col[idx].i=i-1; col[idx].j=j; col[idx].k=k; idx++; }
if (i<mx-1) { v[idx]=-1.0; col[idx].i=i+1; col[idx].j=j; col[idx].k=k; idx++; }
if (j<my-1) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j+1; col[idx].k=k; idx++; }
if (k<mz-1) { v[idx]=-1.0; col[idx].i=i; col[idx].j=j; col[idx].k=k+1; idx++; }
ierr = MatSetValuesStencil(A,1,&row,idx,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Produces the second order centered difference diffusion operator on a one dimensional periodic domain
*/
static PetscErrorCode FormDiffusionJacobian(TS ts,PetscReal t,Vec X,Mat Amat,Mat Pmat,void *ptr)
{
User user = (User)ptr;
PetscErrorCode ierr;
DM dm;
PetscInt i,xs,xm,j,dof;
PetscReal idx,values[3];
MatStencil row,col[3];
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&dm);CHKERRQ(ierr);
ierr = DMDAGetInfo(dm,NULL,NULL,NULL,NULL,NULL,NULL,NULL,&dof,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = DMDAGetCorners(dm,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
idx = 1.0*user->diffus/user->dx;
values[0] = idx;
values[1] = -2.0*idx;
values[2] = idx;
for (i=xs; i<xs+xm; i++) {
for (j=0; j<dof; j++) {
row.i = i; row.c = j;
col[0].i = i-1; col[0].c = j;
col[1].i = i; col[1].c = j;
col[2].i = i+1; col[2].c = j;
ierr = MatSetValuesStencil(Pmat,1,&row,3,col,values,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(Pmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Pmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode update_dirichlet_sym_3d(ef_bc *bc, Mat A, DM da)
{
PetscErrorCode ierr;
PetscInt i,j,k,cnt;
PetscInt ngx, ngy, ngz;
PetscScalar v[6];
MatStencil row[6], col;
PetscInt level;
ef_patch *patch = bc->patch;
ierr = DMGetCoarsenLevel(da, &level);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &ngx, &ngy, &ngz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
for (i = 0; i < 6; i++) v[i] = 0;
for (k = patch->corners[level].is[2]; k <= patch->corners[level].ie[2]; k++) {
for (j = patch->corners[level].is[1]; j <= patch->corners[level].ie[1]; j++) {
for (i = patch->corners[level].is[0]; i <= patch->corners[level].ie[0]; i++) {
col.i = i; col.j = j; col.k = k;
cnt = 0;
if (i-1 < patch->corners[level].is[0] &&
i-1 >= 0) {
row[cnt].i = i-1; row[cnt].j = j; row[cnt].k = k;
cnt++;
}
if (i+1 > patch->corners[level].ie[0] &&
i+1 <= ngx-1) {
row[cnt].i = i+1; row[cnt].j = j; row[cnt].k = k;
cnt++;
}
if (j-1 < patch->corners[level].is[1] &&
j-1 >= 0) {
row[cnt].i = i; row[cnt].j = j-1; row[cnt].k = k;
cnt++;
}
if (j+1 > patch->corners[level].ie[1] &&
j+1 <= ngy-1) {
row[cnt].i = i; row[cnt].j = j+1; row[cnt].k = k;
cnt++;
}
if (k-1 < patch->corners[level].is[2] &&
k-1 >= 0) {
row[cnt].i = i; row[cnt].j = j; row[cnt].k = k-1;
cnt++;
}
if (k+1 > patch->corners[level].ie[2] &&
k+1 <= ngz-1) {
row[cnt].i = i; row[cnt].j = j; row[cnt].k = k+1;
cnt++;
}
ierr = MatSetValuesStencil(A, cnt, row, 1, &col, v, INSERT_VALUES);CHKERRQ(ierr);
}
}
}
return 0;
}
PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,j,Mx,My,xs,ys,xm,ym,nc;
AppCtx *user = (AppCtx*)ctx;
DM da = (DM)user->da;
MatStencil col[5],row;
PetscScalar vals[5],hx,hy,sx,sy;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
ierr = DMDAGetCorners(da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy);
for (j=ys; j<ys+ym; j++){
for (i=xs; i<xs+xm; i++){
nc = 0;
row.j = j; row.i = i;
if (user->boundary == 0 && (i == 0 || i == Mx-1 || j == 0 || j == My-1)) {
col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
} else if (user->boundary > 0 && i == 0) { /* Left Neumann */
col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
col[nc].j = j; col[nc].i = i+1; vals[nc++] = -1.0;
} else if (user->boundary > 0 && i == Mx-1){/* Right Neumann */
col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
col[nc].j = j; col[nc].i = i-1; vals[nc++] = -1.0;
} else if (user->boundary > 0 && j == 0) { /* Bottom Neumann */
col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
col[nc].j = j+1; col[nc].i = i; vals[nc++] = -1.0;
} else if (user->boundary > 0 && j == My-1){/* Top Neumann */
col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0;
col[nc].j = j-1; col[nc].i = i; vals[nc++] = -1.0;
} else { /* Interior */
col[nc].j = j-1; col[nc].i = i; vals[nc++] = -sy;
col[nc].j = j; col[nc].i = i-1; vals[nc++] = -sx;
col[nc].j = j; col[nc].i = i; vals[nc++] = 2.0*(sx + sy) + a;
col[nc].j = j; col[nc].i = i+1; vals[nc++] = -sx;
col[nc].j = j+1; col[nc].i = i; vals[nc++] = -sy;
}
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (*J != *Jpre) {
ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
if (user->viewJacobian){
ierr = PetscPrintf(((PetscObject)*Jpre)->comm,"Jpre:\n");CHKERRQ(ierr);
ierr = MatView(*Jpre,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info, PetscScalar ***u,
Mat J, Mat Jpre, Ctx *usr) {
PetscErrorCode ierr;
PetscInt i,j,q;
PetscReal v[5],diag,x,y;
const PetscReal e = usr->eps;
MatStencil col[5],row;
Spacings s;
Wind W;
getSpacings(info,&s);
diag = e * 2.0 * (1.0/s.hx2 + 1.0/s.hy2);
for (j=info->ys; j<info->ys+info->ym; j++) {
y = -1.0 + j * s.hy;
row.j = j;
col[0].j = j;
for (i=info->xs; i<info->xs+info->xm; i++) {
x = -1.0 + i * s.hx;
row.i = i;
col[0].i = i;
q = 1;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
v[0] = 1.0;
} else {
W = getWind(x,y);
v[0] = diag;
if (i-1 != 0) {
v[q] = - e / s.hx2 - W.x / (2.0 * s.hx);
col[q].j = j; col[q].i = i-1;
q++;
}
if (i+1 != info->mx-1) {
v[q] = - e / s.hx2 + W.x / (2.0 * s.hx);
col[q].j = j; col[q].i = i+1;
q++;
}
if (j-1 != 0) {
v[q] = - e / s.hy2 - W.y / (2.0 * s.hy);
col[q].j = j-1; col[q].i = i;
q++;
}
if (j+1 != info->my-1) {
v[q] = - e / s.hy2 + W.y / (2.0 * s.hy);
col[q].j = j+1; col[q].i = i;
q++;
}
}
ierr = MatSetValuesStencil(Jpre,1,&row,q,col,v,INSERT_VALUES); CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (J != Jpre) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
return 0;
}
/* FormJacobianLocal - Evaluates Jacobian matrix on local process patch */
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat A,Mat jac, MatStructure *str,ObsCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
MatStencil col[5],row;
PetscReal v[5],dx,dy,oxx,oyy;
PetscFunctionBeginUser;
dx = 4.0 / (PetscReal)(info->mx-1);
dy = 4.0 / (PetscReal)(info->my-1);
oxx = 1.0 / (dx * dx);
oyy = 1.0 / (dy * dy);
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
row.j = j; row.i = i;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { /* boundary */
v[0] = 1.0;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else { /* interior grid points */
v[0] = -oyy; col[0].j = j - 1; col[0].i = i;
v[1] = -oxx; col[1].j = j; col[1].i = i - 1;
v[2] = 2.0 * (oxx + oyy); col[2].j = j; col[2].i = i;
v[3] = -oxx; col[3].j = j; col[3].i = i + 1;
v[4] = -oyy; col[4].j = j + 1; col[4].i = i;
ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
/* Assemble matrix, using the 2-step process: */
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (A != jac) {
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
*str = SAME_NONZERO_PATTERN;
/* Tell the matrix we will never add a new nonzero location to the
matrix. If we do, it will generate an error. */
ierr = MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscLogFlops(2.0*info->ym*info->xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode apply_dirichlet_3d(ef_bc *bc, Mat A, DM da)
{
PetscErrorCode ierr;
PetscInt i,j,k,cnt;
PetscInt ngx, ngy, ngz;
PetscScalar v[7];
MatStencil row, col[7];
PetscInt level;
ef_patch *patch = bc->patch;
ierr = DMGetCoarsenLevel(da, &level);CHKERRQ(ierr);
ierr = DMDAGetInfo(da, 0, &ngx, &ngy, &ngz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
v[0] = 1.0;
for (k = patch->corners[level].is[2]; k <= patch->corners[level].ie[2]; k++) {
for (j = patch->corners[level].is[1]; j <= patch->corners[level].ie[1]; j++) {
for (i = patch->corners[level].is[0]; i <= patch->corners[level].ie[0]; i++) {
row.i = i; row.j = j; row.k = k;
col[0].i = i; col[0].j = j; col[0].k = k;
cnt = 1;
if (i != 0) {
col[cnt].i = i-1; col[cnt].j = j; col[cnt].k = k;
v[cnt] = 0; cnt++;
}
if (j != 0) {
col[cnt].i = i; col[cnt].j = j-1; col[cnt].k = k;
v[cnt] = 0; cnt++;
}
if (k != 0) {
col[cnt].i = i; col[cnt].j = j; col[cnt].k = k-1;
v[cnt] = 0; cnt++;
}
if (i != ngx - 1) {
col[cnt].i = i+1; col[cnt].j = j; col[cnt].k = k;
v[cnt] = 0; cnt++;
}
if (j != ngy - 1) {
col[cnt].i = i; col[cnt].j = j+1; col[cnt].k = k;
v[cnt] = 0; cnt++;
}
if (k != ngz - 1) {
col[cnt].i = i; col[cnt].j = j; col[cnt].k = k+1;
v[cnt] = 0; cnt++;
}
ierr = MatSetValuesStencil(A, 1, &row, cnt, col, v, INSERT_VALUES);CHKERRQ(ierr);
}
}
}
return 0;
}
/* FormJacobianLocal - Evaluates Jacobian matrix on local process patch */
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat A,Mat jac, ObsCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
MatStencil col[5],row;
PetscReal v[5],dx,dy,oxx,oyy;
PetscFunctionBeginUser;
dx = 4.0 / (PetscReal)(info->mx-1);
dy = 4.0 / (PetscReal)(info->my-1);
oxx = dy / dx;
oyy = dx / dy;
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
row.j = j; row.i = i;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { /* boundary */
v[0] = 4.0;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else { /* interior grid points */
v[0] = -oyy; col[0].j = j - 1; col[0].i = i;
v[1] = -oxx; col[1].j = j; col[1].i = i - 1;
v[2] = 2.0 * (oxx + oyy); col[2].j = j; col[2].i = i;
v[3] = -oxx; col[3].j = j; col[3].i = i + 1;
v[4] = -oyy; col[4].j = j + 1; col[4].i = i;
ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
/* Assemble matrix, using the 2-step process: */
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (A != jac) {
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
ierr = PetscLogFlops(2.0*info->ym*info->xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ComputeMatrix(KSP ksp,Mat jac,Mat B,MatStructure *stflg,void *ctx)
{
DM da;
PetscErrorCode ierr;
PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
PetscScalar v[7],Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
MatStencil row,col[7];
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
Hx = 1.0 / (PetscReal)(mx-1); Hy = 1.0 / (PetscReal)(my-1); Hz = 1.0 / (PetscReal)(mz-1);
HxHydHz = Hx*Hy/Hz; HxHzdHy = Hx*Hz/Hy; HyHzdHx = Hy*Hz/Hx;
ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
for (k=zs; k<zs+zm; k++) {
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
row.i = i; row.j = j; row.k = k;
if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
v[0] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
ierr = MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
v[0] = -HxHydHz;col[0].i = i; col[0].j = j; col[0].k = k-1;
v[1] = -HxHzdHy;col[1].i = i; col[1].j = j-1; col[1].k = k;
v[2] = -HyHzdHx;col[2].i = i-1; col[2].j = j; col[2].k = k;
v[3] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);col[3].i = row.i; col[3].j = row.j; col[3].k = row.k;
v[4] = -HyHzdHx;col[4].i = i+1; col[4].j = j; col[4].k = k;
v[5] = -HxHzdHy;col[5].i = i; col[5].j = j+1; col[5].k = k;
v[6] = -HxHydHz;col[6].i = i; col[6].j = j; col[6].k = k+1;
ierr = MatSetValuesStencil(B,1,&row,7,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
}
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
*stflg = SAME_NONZERO_PATTERN;
PetscFunctionReturn(0);
}
PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *flg,void *ctx)
{
PetscErrorCode ierr;
AppCtx *user=(AppCtx*)ctx;
DM cda;
DMDACoor2d **coors;
PetscInt i,j;
PetscInt xs,ys,xm,ym,M,N;
Vec gc;
PetscScalar val[5],xi,yi;
MatStencil row,col[5];
PetscScalar c1,c3,c5,c1pos,c1neg,c3pos,c3neg;
PetscFunctionBeginUser;
*flg = SAME_NONZERO_PATTERN;
ierr = DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
ierr = DMGetCoordinateDM(user->da,&cda);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(user->da,&gc);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,gc,&coors);CHKERRQ(ierr);
for (i=xs; i < xs+xm; i++) {
for (j=ys; j < ys+ym; j++) {
PetscInt nc = 0;
xi = coors[j][i].x; yi = coors[j][i].y;
row.i = i; row.j = j;
c1 = (yi-user->ws)/user->dx;
c1pos = PetscMax(c1,0);
c1neg = PetscMin(c1,0);
c3 = (user->ws/(2.0*user->H))*(user->PM_min - user->Pmax*sin(xi))/user->dy;
c3pos = PetscMax(c3,0);
c3neg = PetscMin(c3,0);
c5 = (PetscPowScalar((user->lambda*user->ws)/(2*user->H),2)*user->q*(1.0-PetscExpScalar(-t/user->lambda)))/(user->dy*user->dy);
col[nc].i = i-1; col[nc].j = j; val[nc++] = c1pos;
col[nc].i = i+1; col[nc].j = j; val[nc++] = -c1neg;
col[nc].i = i; col[nc].j = j-1; val[nc++] = c3pos + c5;
col[nc].i = i; col[nc].j = j+1; val[nc++] = -c3neg + c5;
col[nc].i = i; col[nc].j = j; val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a;
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = DMDAVecRestoreArray(cda,gc,&coors);CHKERRQ(ierr);
ierr = MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (*J != *Jpre) {
ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,rstart,rend,Mx;
PetscReal hx,sx;
AppCtx *user = (AppCtx*)ctx;
DM da;
MatStencil col[3],row;
PetscInt nc;
PetscScalar vals[3];
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(*Jpre,&rstart,&rend);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
for (i=rstart; i<rend; i++) {
nc = 0;
row.i = i;
if (user->boundary == 0 && (i == 0 || i == Mx-1)) {
col[nc].i = i; vals[nc++] = 1.0;
} else if (user->boundary > 0 && i == 0) { /* Left Neumann */
col[nc].i = i; vals[nc++] = 1.0;
col[nc].i = i+1; vals[nc++] = -1.0;
} else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */
col[nc].i = i-1; vals[nc++] = -1.0;
col[nc].i = i; vals[nc++] = 1.0;
} else { /* Interior */
col[nc].i = i-1; vals[nc++] = -1.0*sx;
col[nc].i = i; vals[nc++] = 2.0*sx + a;
col[nc].i = i+1; vals[nc++] = -1.0*sx;
}
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (*J != *Jpre) {
ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
if (user->viewJacobian){
ierr = PetscPrintf(((PetscObject)*Jpre)->comm,"Jpre:\n");CHKERRQ(ierr);
ierr = MatView(*Jpre,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
// in system form F(t,Y,dot Y) = G(t,Y), compute combined/shifted
// Jacobian of F():
// J = (shift) dF/d(dot Y) + dF/dY
//IJACOBIAN
PetscErrorCode FormIJacobianLocal(DMDALocalInfo *info, double t, Field **aY,
Field **aYdot, double shift, Mat J, Mat P,
PatternCtx *user) {
PetscErrorCode ierr;
int i, j, s, c;
const double h = user->L / (double)(info->mx),
Cu = user->Du / (6.0 * h * h),
Cv = user->Dv / (6.0 * h * h);
double val[9], CC;
MatStencil col[9], row;
for (j = info->ys; j < info->ys + info->ym; j++) {
row.j = j;
for (i = info->xs; i < info->xs + info->xm; i++) {
row.i = i;
for (c = 0; c < 2; c++) { // u,v equations are c=0,1
row.c = c;
CC = (c == 0) ? Cu : Cv;
for (s = 0; s < 9; s++)
col[s].c = c;
col[0].i = i; col[0].j = j; val[0] = shift + 20.0 * CC;
col[1].i = i-1; col[1].j = j; val[1] = - 4.0 * CC;
col[2].i = i+1; col[2].j = j; val[2] = - 4.0 * CC;
col[3].i = i; col[3].j = j-1; val[3] = - 4.0 * CC;
col[4].i = i; col[4].j = j+1; val[4] = - 4.0 * CC;
col[5].i = i-1; col[5].j = j-1; val[5] = - CC;
col[6].i = i-1; col[6].j = j+1; val[6] = - CC;
col[7].i = i+1; col[7].j = j-1; val[7] = - CC;
col[8].i = i+1; col[8].j = j+1; val[8] = - CC;
ierr = MatSetValuesStencil(P,1,&row,9,col,val,INSERT_VALUES); CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(P,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = MatAssemblyEnd(P,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
if (J != P) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
}
return 0;
}
/*
RHSJacobian - User-provided routine to compute the Jacobian of
the nonlinear right-hand-side function of the ODE.
Input Parameters:
ts - the TS context
t - current time
U - global input vector
dummy - optional user-defined context, as set by TSetRHSJacobian()
Output Parameters:
J - Jacobian matrix
Jpre - optionally different preconditioning matrix
str - flag indicating matrix structure
*/
PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
{
PetscErrorCode ierr;
DM da;
DMDALocalInfo info;
PetscInt i,j;
PetscReal hx,hy,sx,sy;
PetscFunctionBeginUser;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(info.mx-1); sx = 1.0/(hx*hx);
hy = 1.0/(PetscReal)(info.my-1); sy = 1.0/(hy*hy);
for (j=info.ys; j<info.ys+info.ym; j++) {
for (i=info.xs; i<info.xs+info.xm; i++) {
PetscInt nc = 0;
MatStencil row,col[5];
PetscScalar val[5];
row.i = i; row.j = j;
if (i == 0 || j == 0 || i == info.mx-1 || j == info.my-1) {
col[nc].i = i; col[nc].j = j; val[nc++] = 1.0;
} else {
col[nc].i = i-1; col[nc].j = j; val[nc++] = sx;
col[nc].i = i+1; col[nc].j = j; val[nc++] = sx;
col[nc].i = i; col[nc].j = j-1; val[nc++] = sy;
col[nc].i = i; col[nc].j = j+1; val[nc++] = sy;
col[nc].i = i; col[nc].j = j; val[nc++] = -2*sx - 2*sy;
}
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,val,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (*J != *Jpre) {
ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*
FormJacobian - Evaluates Jacobian matrix.
Input Parameters:
. snes - the SNES context
. x - input vector
. dummy - optional user-defined context (not used here)
Output Parameters:
. jac - Jacobian matrix
. B - optionally different preconditioning matrix
. flag - flag indicating matrix structure
*/
PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *ctx)
{
PetscScalar *xx,A[3];
PetscErrorCode ierr;
PetscInt i,M,xs,xm;
DM da = (DM) ctx;
MatStencil row,cols[3];
PetscReal h;
PetscFunctionBeginUser;
/*
Get pointer to vector data
*/
ierr = DMDAVecGetArrayRead(da,x,&xx);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
Get range of locally owned matrix
*/
ierr = DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
ierr = MatZeroEntries(jac);CHKERRQ(ierr);
h = 1.0/M;
/* because of periodic boundary conditions we can simply loop over all local nodes and access to the left and right */
for (i=xs; i<xs+xm; i++) {
row.i = i;
cols[0].i = i - 1;
cols[1].i = i;
cols[2].i = i + 1;
A[0] = A[2] = 1.0/(h*h); A[1] = -2.0/(h*h);
ierr = MatSetValuesStencil(jac,1,&row,3,cols,A,ADD_VALUES);CHKERRQ(ierr);
}
ierr = DMDAVecRestoreArrayRead(da,x,&xx);CHKERRQ(ierr);
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormJacobian - Evaluates Jacobian matrix.
Input Parameters:
. snes - SNES context
. X - input vector
. ptr - optional user-defined context, as set by SNESSetJacobian()
Output Parameters:
. tH - Jacobian matrix
*/
PetscErrorCode FormJacobian(SNES snes, Vec X, Mat *tH, Mat *tHPre, MatStructure *flag, void *ptr)
{
AppCtx *user = (AppCtx*) ptr;
Mat H = *tH;
PetscErrorCode ierr;
PetscInt i,j,k;
PetscInt mx=user->mx, my=user->my;
MatStencil row,col[7];
PetscScalar hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
PetscScalar f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
PetscScalar hl,hr,ht,hb,hc,htl,hbr;
PetscScalar **x, v[7];
PetscBool assembled;
PetscInt xs,xm,ys,ym;
Vec localX;
PetscScalar *top,*bottom,*left,*right;
PetscFunctionBeginUser;
/* Set various matrix options */
ierr = MatAssembled(H,&assembled);CHKERRQ(ierr);
if (assembled) {ierr = MatZeroEntries(H);CHKERRQ(ierr);}
*flag=SAME_NONZERO_PATTERN;
/* Get local vectors */
ierr = DMGetLocalVector(user->da,&localX);CHKERRQ(ierr);
ierr = VecGetArray(user->Top,&top);CHKERRQ(ierr);
ierr = VecGetArray(user->Bottom,&bottom);CHKERRQ(ierr);
ierr = VecGetArray(user->Left,&left);CHKERRQ(ierr);
ierr = VecGetArray(user->Right,&right);CHKERRQ(ierr);
/* Get ghost points */
ierr = DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
/* Get pointers to vector data */
ierr = DMDAVecGetArray(user->da,localX, &x);CHKERRQ(ierr);
ierr = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
/* Compute Jacobian over the locally owned part of the mesh */
for (j=ys; j< ys+ym; j++) {
for (i=xs; i< xs+xm; i++) {
xc = x[j][i];
xlt=xrb=xl=xr=xb=xt=xc;
/* Left */
if (i==0) {
xl = left[j+1];
xlt = left[j+2];
} else xl = x[j][i-1];
/* Bottom */
if (j==0) {
xb = bottom[i+1];
xrb = bottom[i+2];
} else xb = x[j-1][i];
/* Right */
if (i+1 == mx) {
xr = right[j+1];
xrb = right[j];
} else xr = x[j][i+1];
/* Top */
if (j+1==my) {
xt = top[i+1];
xlt = top[i];
} else xt = x[j+1][i];
/* Top left */
if (i>0 && j+1<my) xlt = x[j+1][i-1];
/* Bottom right */
if (j>0 && i+1<mx) xrb = x[j-1][i+1];
d1 = (xc-xl)/hx;
d2 = (xc-xr)/hx;
d3 = (xc-xt)/hy;
d4 = (xc-xb)/hy;
d5 = (xrb-xr)/hy;
d6 = (xrb-xb)/hx;
d7 = (xlt-xl)/hy;
d8 = (xlt-xt)/hx;
f1 = PetscSqrtReal(1.0 + d1*d1 + d7*d7);
f2 = PetscSqrtReal(1.0 + d1*d1 + d4*d4);
f3 = PetscSqrtReal(1.0 + d3*d3 + d8*d8);
f4 = PetscSqrtReal(1.0 + d3*d3 + d2*d2);
f5 = PetscSqrtReal(1.0 + d2*d2 + d5*d5);
f6 = PetscSqrtReal(1.0 + d4*d4 + d6*d6);
hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
(-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
(-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
(-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
(-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
(hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
(hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);
hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0;
k = 0;
row.i = i;row.j = j;
/* Bottom */
if (j>0) {
v[k] = hb;
col[k].i = i; col[k].j=j-1; k++;
}
/* Bottom right */
if (j>0 && i < mx -1) {
v[k] = hbr;
col[k].i = i+1; col[k].j = j-1; k++;
}
/* left */
if (i>0) {
v[k] = hl;
col[k].i = i-1; col[k].j = j; k++;
}
/* Centre */
v[k]= hc; col[k].i= row.i; col[k].j = row.j; k++;
/* Right */
if (i < mx-1) {
v[k] = hr;
col[k].i= i+1; col[k].j = j;k++;
}
/* Top left */
if (i>0 && j < my-1) {
v[k] = htl;
col[k].i = i-1;col[k].j = j+1; k++;
}
/* Top */
if (j < my-1) {
v[k] = ht;
col[k].i = i; col[k].j = j+1; k++;
}
ierr = MatSetValuesStencil(H,1,&row,k,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = VecRestoreArray(user->Left,&left);CHKERRQ(ierr);
ierr = VecRestoreArray(user->Top,&top);CHKERRQ(ierr);
ierr = VecRestoreArray(user->Bottom,&bottom);CHKERRQ(ierr);
ierr = VecRestoreArray(user->Right,&right);CHKERRQ(ierr);
/* Assemble the matrix */
ierr = MatAssemblyBegin(H,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da,localX,&x);CHKERRQ(ierr);
ierr = MatAssemblyEnd(H,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(user->da,&localX);CHKERRQ(ierr);
ierr = PetscLogFlops(199*mx*my);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
QuadraticH - Evaluates Hessian matrix.
Input Parameters:
. user - user-defined context, as set by TaoSetHessian()
. X - input vector
Output Parameter:
. H - Hessian matrix
*/
int QuadraticH(AppCtx *user, Vec X, Mat Hessian)
{
int info;
PetscInt i,j,k;
PetscInt mx=user->mx, my=user->my;
PetscInt xs,xm,gxs,gxm,ys,ym,gys,gym;
double hx=1.0/(mx+1), hy=1.0/(my+1), hydhx=hy/hx, hxdhy=hx/hy;
double f1,f2,f3,f4,f5,f6,d1,d2,d3,d4,d5,d6,d7,d8,xc,xl,xr,xt,xb,xlt,xrb;
double hl,hr,ht,hb,hc,htl,hbr;
PetscScalar **x, v[7];
MatStencil col[7],row;
Vec localX;
PetscTruth assembled;
/* Get local mesh boundaries */
info = DAGetLocalVector(user->da,&localX);CHKERRQ(info);
info = DAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL); CHKERRQ(info);
info = DAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL); CHKERRQ(info);
/* Scatter ghost points to local vector */
info = DAGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
info = DAGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX); CHKERRQ(info);
/* Get pointers to vector data */
info = DAVecGetArray(user->da,localX,(void**)&x);
/* Initialize matrix entries to zero */
info = MatAssembled(Hessian,&assembled); CHKERRQ(info);
if (assembled){info = MatZeroEntries(Hessian); CHKERRQ(info);}
/* Set various matrix options */
info = MatSetOption(Hessian,MAT_IGNORE_OFF_PROC_ENTRIES,PETSC_TRUE); CHKERRQ(info);
/* Compute Hessian over the locally owned part of the mesh */
for (j=ys; j<ys+ym; j++){
for (i=xs; i< xs+xm; i++){
xc = x[j][i];
xlt=xrb=xl=xr=xb=xt=xc;
/* Left side */
if (i==0){
xl = user->left[j-ys+1];
xlt = user->left[j-ys+2];
} else {
xl = x[j][i-1];
}
if (j==0){
xb = user->bottom[i-xs+1];
xrb = user->bottom[i-xs+2];
} else {
xb = x[j-1][i];
}
if (i+1 == mx){
xr = user->right[j-ys+1];
xrb = user->right[j-ys];
} else {
xr = x[j][i+1];
}
if (j+1==my){
xt = user->top[i-xs+1];
xlt = user->top[i-xs];
}else {
xt = x[j+1][i];
}
if (i>0 && j+1<my){
xlt = x[j+1][i-1];
}
if (j>0 && i+1<mx){
xrb = x[j-1][i+1];
}
d1 = (xc-xl)/hx;
d2 = (xc-xr)/hx;
d3 = (xc-xt)/hy;
d4 = (xc-xb)/hy;
d5 = (xrb-xr)/hy;
d6 = (xrb-xb)/hx;
d7 = (xlt-xl)/hy;
d8 = (xlt-xt)/hx;
f1 = sqrt( 1.0 + d1*d1 + d7*d7);
f2 = sqrt( 1.0 + d1*d1 + d4*d4);
f3 = sqrt( 1.0 + d3*d3 + d8*d8);
f4 = sqrt( 1.0 + d3*d3 + d2*d2);
f5 = sqrt( 1.0 + d2*d2 + d5*d5);
f6 = sqrt( 1.0 + d4*d4 + d6*d6);
hl = (-hydhx*(1.0+d7*d7)+d1*d7)/(f1*f1*f1)+
(-hydhx*(1.0+d4*d4)+d1*d4)/(f2*f2*f2);
hr = (-hydhx*(1.0+d5*d5)+d2*d5)/(f5*f5*f5)+
(-hydhx*(1.0+d3*d3)+d2*d3)/(f4*f4*f4);
ht = (-hxdhy*(1.0+d8*d8)+d3*d8)/(f3*f3*f3)+
(-hxdhy*(1.0+d2*d2)+d2*d3)/(f4*f4*f4);
hb = (-hxdhy*(1.0+d6*d6)+d4*d6)/(f6*f6*f6)+
(-hxdhy*(1.0+d1*d1)+d1*d4)/(f2*f2*f2);
hbr = -d2*d5/(f5*f5*f5) - d4*d6/(f6*f6*f6);
htl = -d1*d7/(f1*f1*f1) - d3*d8/(f3*f3*f3);
hc = hydhx*(1.0+d7*d7)/(f1*f1*f1) + hxdhy*(1.0+d8*d8)/(f3*f3*f3) +
hydhx*(1.0+d5*d5)/(f5*f5*f5) + hxdhy*(1.0+d6*d6)/(f6*f6*f6) +
(hxdhy*(1.0+d1*d1)+hydhx*(1.0+d4*d4)-2*d1*d4)/(f2*f2*f2) +
(hxdhy*(1.0+d2*d2)+hydhx*(1.0+d3*d3)-2*d2*d3)/(f4*f4*f4);
hl/=2.0; hr/=2.0; ht/=2.0; hb/=2.0; hbr/=2.0; htl/=2.0; hc/=2.0;
row.j = j; row.i = i;
k=0;
if (j>0){
v[k]=hb;
col[k].j = j - 1; col[k].i = i;
k++;
}
if (j>0 && i < mx -1){
v[k]=hbr;
col[k].j = j - 1; col[k].i = i+1;
k++;
}
if (i>0){
v[k]= hl;
col[k].j = j; col[k].i = i-1;
k++;
}
v[k]= hc;
col[k].j = j; col[k].i = i;
k++;
if (i < mx-1 ){
v[k]= hr;
col[k].j = j; col[k].i = i+1;
k++;
}
if (i>0 && j < my-1 ){
v[k]= htl;
col[k].j = j+1; col[k].i = i-1;
k++;
}
if (j < my-1 ){
v[k]= ht;
col[k].j = j+1; col[k].i = i;
k++;
}
/*
Set matrix values using local numbering, which was defined
earlier, in the main routine.
*/
info = MatSetValuesStencil(Hessian,1,&row,k,col,v,INSERT_VALUES);
CHKERRQ(info);
}
}
/* Restore vectors */
info = DAVecRestoreArray(user->da,localX,(void**)&x);
info = DARestoreLocalVector(user->da,&localX); CHKERRQ(info);
/* Assemble the matrix */
info = MatAssemblyBegin(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = MatAssemblyEnd(Hessian,MAT_FINAL_ASSEMBLY); CHKERRQ(info);
info = PetscLogFlops(199*xm*ym); CHKERRQ(info);
return 0;
}
int main(int argc,char **argv)
{
DM da; /* distributed array */
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A; /* linear system matrix */
KSP ksp; /* linear solver context */
PetscRandom rctx; /* random number generator context */
PetscReal norm; /* norm of solution error */
PetscInt i,j,its;
PetscErrorCode ierr;
PetscBool flg = PETSC_FALSE;
PetscLogStage stage;
DMDALocalInfo info;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
/*
Create distributed array to handle parallel distribution.
The problem size will default to 8 by 7, but this can be
changed using -da_grid_x M -da_grid_y N
*/
ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,-8,-7,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create parallel matrix preallocated according to the DMDA, format AIJ by default.
To use symmetric storage, run with -dm_mat_type sbaij -mat_ignore_lower_triangular
*/
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da,&A);CHKERRQ(ierr);
/*
Set matrix elements for the 2-D, five-point stencil in parallel.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Rows and columns are specified by the stencil
- Entries are normalized for a domain [0,1]x[0,1]
*/
ierr = PetscLogStageRegister("Assembly", &stage);CHKERRQ(ierr);
ierr = PetscLogStagePush(stage);CHKERRQ(ierr);
ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
for (j=info.ys; j<info.ys+info.ym; j++) {
for (i=info.xs; i<info.xs+info.xm; i++) {
PetscReal hx = 1./info.mx,hy = 1./info.my;
MatStencil row = {0},col[5] = {{0}};
PetscScalar v[5];
PetscInt ncols = 0;
row.j = j; row.i = i;
col[ncols].j = j; col[ncols].i = i; v[ncols++] = 2*(hx/hy + hy/hx);
/* boundaries */
if (i>0) {col[ncols].j = j; col[ncols].i = i-1; v[ncols++] = -hy/hx;}
if (i<info.mx-1) {col[ncols].j = j; col[ncols].i = i+1; v[ncols++] = -hy/hx;}
if (j>0) {col[ncols].j = j-1; col[ncols].i = i; v[ncols++] = -hx/hy;}
if (j<info.my-1) {col[ncols].j = j+1; col[ncols].i = i; v[ncols++] = -hx/hy;}
ierr = MatSetValuesStencil(A,1,&row,ncols,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd()
Computations can be done while messages are in transition
by placing code between these two statements.
*/
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = PetscLogStagePop();CHKERRQ(ierr);
/*
Create parallel vectors compatible with the DMDA.
*/
ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(u,&x);CHKERRQ(ierr);
/*
Set exact solution; then compute right-hand-side vector.
By default we use an exact solution of a vector with all
elements of 1.0; Alternatively, using the runtime option
-random_sol forms a solution vector with random components.
*/
ierr = PetscOptionsGetBool(NULL,"-random_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
ierr = VecSetRandom(u,rctx);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
} else {
ierr = VecSet(u,1.);CHKERRQ(ierr);
}
ierr = MatMult(A,u,b);CHKERRQ(ierr);
/*
View the exact solution vector if desired
*/
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-view_exact_sol",&flg,NULL);CHKERRQ(ierr);
if (flg) {ierr = VecView(u,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);}
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Create the linear solver and set various options
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Create linear solver context
*/
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,A,A);CHKERRQ(ierr);
/*
Set runtime options, e.g.,
-ksp_type <type> -pc_type <type> -ksp_monitor -ksp_rtol <rtol>
These options will override those specified above as long as
KSPSetFromOptions() is called _after_ any other customization
routines.
*/
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(ksp,b,x);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Check solution and clean up
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
/*
Check the error
*/
ierr = VecAXPY(x,-1.,u);CHKERRQ(ierr);
ierr = VecNorm(x,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
/*
Print convergence information. PetscPrintf() produces a single
print statement from all processes that share a communicator.
An alternative is PetscFPrintf(), which prints to a file.
*/
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g iterations %D\n",(double)norm,its);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&x);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
/*
Always call PetscFinalize() before exiting a program. This routine
- finalizes the PETSc libraries as well as MPI
- provides summary and diagnostic information if certain runtime
options are chosen (e.g., -log_summary).
*/
ierr = PetscFinalize();
return 0;
}
int main(int Argc,char **Args)
{
PetscBool flg;
PetscInt n = -6;
PetscScalar rho = 1.0;
PetscReal h;
PetscReal beta = 1.0;
DM da;
PetscRandom rctx;
PetscMPIInt comm_size;
Mat H,HtH;
PetscInt x, y, xs, ys, xm, ym;
PetscReal r1, r2;
PetscScalar uxy1, uxy2;
MatStencil sxy, sxy_m;
PetscScalar val, valconj;
Vec b, Htb,xvec;
KSP kspmg;
PC pcmg;
PetscErrorCode ierr;
PetscInt ix[1] = {0};
PetscScalar vals[1] = {1.0};
PetscInitialize(&Argc,&Args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-size",&n,&flg);CHKERRQ(ierr);
ierr = PetscOptionsGetReal(NULL,"-beta",&beta,&flg);CHKERRQ(ierr);
ierr = PetscOptionsGetScalar(NULL,"-rho",&rho,&flg);CHKERRQ(ierr);
/* Set the fudge parameters, we scale the whole thing by 1/(2*h) later */
h = 1.;
rho *= 1./(2.*h);
/* Geometry info */
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC, DMDA_STENCIL_STAR, n, n,
PETSC_DECIDE, PETSC_DECIDE, 2 /* this is the # of dof's */,
1, NULL, NULL, &da);CHKERRQ(ierr);
/* Random numbers */
ierr = PetscRandomCreate(PETSC_COMM_WORLD,&rctx);CHKERRQ(ierr);
ierr = PetscRandomSetFromOptions(rctx);CHKERRQ(ierr);
/* Single or multi processor ? */
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&comm_size);CHKERRQ(ierr);
/* construct matrix */
ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr);
ierr = DMCreateMatrix(da, &H);CHKERRQ(ierr);
/* get local corners for this processor */
ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
/* Assemble the matrix */
for (x=xs; x<xs+xm; x++) {
for (y=ys; y<ys+ym; y++) {
/* each lattice point sets only the *forward* pointing parameters (right, down),
i.e. Nabla_1^+ and Nabla_2^+.
In this way we can use only local random number creation. That means
we also have to set the corresponding backward pointing entries. */
/* Compute some normally distributed random numbers via Box-Muller */
ierr = PetscRandomGetValueReal(rctx, &r1);CHKERRQ(ierr);
r1 = 1.-r1; /* to change from [0,1) to (0,1], which we need for the log */
ierr = PetscRandomGetValueReal(rctx, &r2);CHKERRQ(ierr);
PetscReal R = PetscSqrtReal(-2.*PetscLogReal(r1));
PetscReal c = PetscCosReal(2.*PETSC_PI*r2);
PetscReal s = PetscSinReal(2.*PETSC_PI*r2);
/* use those to set the field */
uxy1 = PetscExpScalar(((PetscScalar) (R*c/beta))*PETSC_i);
uxy2 = PetscExpScalar(((PetscScalar) (R*s/beta))*PETSC_i);
sxy.i = x; sxy.j = y; /* the point where we are */
/* center action */
sxy.c = 0; /* spin 0, 0 */
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy, &rho, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; /* spin 1, 1 */
val = -rho;
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
sxy_m.i = x+1; sxy_m.j = y; /* right action */
sxy.c = 0; sxy_m.c = 0; /* spin 0, 0 */
val = -uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 0; sxy_m.c = 1; /* spin 0, 1 */
val = -uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 0; /* spin 1, 0 */
val = uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 1; /* spin 1, 1 */
val = uxy1; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy_m.i = x; sxy_m.j = y+1; /* down action */
sxy.c = 0; sxy_m.c = 0; /* spin 0, 0 */
val = -uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 0; sxy_m.c = 1; /* spin 0, 1 */
val = -PETSC_i*uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 0; /* spin 1, 0 */
val = -PETSC_i*uxy2; valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
sxy.c = 1; sxy_m.c = 1; /* spin 1, 1 */
val = PetscConj(uxy2); valconj = PetscConj(val);
ierr = MatSetValuesStencil(H, 1, &sxy_m, 1, &sxy, &val, ADD_VALUES);CHKERRQ(ierr);
ierr = MatSetValuesStencil(H, 1, &sxy, 1, &sxy_m, &valconj, ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(H, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(H, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* scale H */
ierr = MatScale(H, 1./(2.*h));CHKERRQ(ierr);
/* it looks like H is Hermetian */
/* construct normal equations */
ierr = MatMatMult(H, H, MAT_INITIAL_MATRIX, 1., &HtH);CHKERRQ(ierr);
/* permutation matrix to check whether H and HtH are identical to the ones in the paper */
/* Mat perm; */
/* ierr = DMCreateMatrix(da, &perm);CHKERRQ(ierr); */
/* PetscInt row, col; */
/* PetscScalar one = 1.0; */
/* for (PetscInt i=0; i<n; i++) { */
/* for (PetscInt j=0; j<n; j++) { */
/* row = (i*n+j)*2; col = i*n+j; */
/* ierr = MatSetValues(perm, 1, &row, 1, &col, &one, INSERT_VALUES);CHKERRQ(ierr); */
/* row = (i*n+j)*2+1; col = i*n+j + n*n; */
/* ierr = MatSetValues(perm, 1, &row, 1, &col, &one, INSERT_VALUES);CHKERRQ(ierr); */
/* } */
/* } */
/* ierr = MatAssemblyBegin(perm, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); */
/* ierr = MatAssemblyEnd(perm, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); */
/* Mat Hperm; */
/* ierr = MatPtAP(H, perm, MAT_INITIAL_MATRIX, 1.0, &Hperm);CHKERRQ(ierr); */
/* ierr = PetscPrintf(PETSC_COMM_WORLD, "Matrix H after construction\n");CHKERRQ(ierr); */
/* ierr = MatView(Hperm, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
/* Mat HtHperm; */
/* ierr = MatPtAP(HtH, perm, MAT_INITIAL_MATRIX, 1.0, &HtHperm);CHKERRQ(ierr); */
/* ierr = PetscPrintf(PETSC_COMM_WORLD, "Matrix HtH:\n");CHKERRQ(ierr); */
/* ierr = MatView(HtHperm, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
/* right hand side */
ierr = DMCreateGlobalVector(da, &b);CHKERRQ(ierr);
ierr = VecSet(b,0.0);CHKERRQ(ierr);
ierr = VecSetValues(b, 1, ix, vals, INSERT_VALUES);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* ierr = VecSetRandom(b, rctx);CHKERRQ(ierr); */
ierr = VecDuplicate(b, &Htb);CHKERRQ(ierr);
ierr = MatMultTranspose(H, b, Htb);CHKERRQ(ierr);
/* construct solver */
ierr = KSPCreate(PETSC_COMM_WORLD,&kspmg);CHKERRQ(ierr);
ierr = KSPSetType(kspmg, KSPCG);CHKERRQ(ierr);
ierr = KSPGetPC(kspmg,&pcmg);CHKERRQ(ierr);
ierr = PCSetType(pcmg,PCASA);CHKERRQ(ierr);
/* maybe user wants to override some of the choices */
ierr = KSPSetFromOptions(kspmg);CHKERRQ(ierr);
ierr = KSPSetOperators(kspmg, HtH, HtH, DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = DMDASetRefinementFactor(da, 3, 3, 3);CHKERRQ(ierr);
ierr = PCSetDM(pcmg,da);CHKERRQ(ierr);
ierr = PCASASetTolerances(pcmg, 1.e-6, 1.e-10,PETSC_DEFAULT,PETSC_DEFAULT);CHKERRQ(ierr);
ierr = VecDuplicate(b, &xvec);CHKERRQ(ierr);
ierr = VecSet(xvec, 0.0);CHKERRQ(ierr);
/* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Solve the linear system
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */
ierr = KSPSolve(kspmg, Htb, xvec);CHKERRQ(ierr);
/* ierr = VecView(xvec, PETSC_VIEWER_STDOUT_(PETSC_COMM_WORLD));CHKERRQ(ierr); */
ierr = KSPDestroy(&kspmg);CHKERRQ(ierr);
ierr = VecDestroy(&xvec);CHKERRQ(ierr);
/* seems to be destroyed by KSPDestroy */
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = VecDestroy(&Htb);CHKERRQ(ierr);
ierr = MatDestroy(&HtH);CHKERRQ(ierr);
ierr = MatDestroy(&H);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscRandomDestroy(&rctx);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscErrorCode ComputeMatrix(KSP ksp, Mat J,Mat jac, void *ctx)
{
PetscErrorCode ierr;
PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs,num, numi, numj, numk;
PetscScalar v[7],Hx,Hy,Hz,HyHzdHx,HxHzdHy,HxHydHz;
MatStencil row, col[7];
DM da;
MatNullSpace nullspace;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&mx,&my,&mz,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
Hx = 1.0 / (PetscReal)(mx);
Hy = 1.0 / (PetscReal)(my);
Hz = 1.0 / (PetscReal)(mz);
HyHzdHx = Hy*Hz/Hx;
HxHzdHy = Hx*Hz/Hy;
HxHydHz = Hx*Hy/Hz;
ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
for (k=zs; k<zs+zm; k++) {
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
row.i = i; row.j = j; row.k = k;
if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
num = 0; numi=0; numj=0; numk=0;
if (k!=0) {
v[num] = -HxHydHz;
col[num].i = i;
col[num].j = j;
col[num].k = k-1;
num++; numk++;
}
if (j!=0) {
v[num] = -HxHzdHy;
col[num].i = i;
col[num].j = j-1;
col[num].k = k;
num++; numj++;
}
if (i!=0) {
v[num] = -HyHzdHx;
col[num].i = i-1;
col[num].j = j;
col[num].k = k;
num++; numi++;
}
if (i!=mx-1) {
v[num] = -HyHzdHx;
col[num].i = i+1;
col[num].j = j;
col[num].k = k;
num++; numi++;
}
if (j!=my-1) {
v[num] = -HxHzdHy;
col[num].i = i;
col[num].j = j+1;
col[num].k = k;
num++; numj++;
}
if (k!=mz-1) {
v[num] = -HxHydHz;
col[num].i = i;
col[num].j = j;
col[num].k = k+1;
num++; numk++;
}
v[num] = (PetscReal)(numk)*HxHydHz + (PetscReal)(numj)*HxHzdHy + (PetscReal)(numi)*HyHzdHx;
col[num].i = i; col[num].j = j; col[num].k = k;
num++;
ierr = MatSetValuesStencil(jac,1,&row,num,col,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
v[0] = -HxHydHz; col[0].i = i; col[0].j = j; col[0].k = k-1;
v[1] = -HxHzdHy; col[1].i = i; col[1].j = j-1; col[1].k = k;
v[2] = -HyHzdHx; col[2].i = i-1; col[2].j = j; col[2].k = k;
v[3] = 2.0*(HyHzdHx + HxHzdHy + HxHydHz); col[3].i = i; col[3].j = j; col[3].k = k;
v[4] = -HyHzdHx; col[4].i = i+1; col[4].j = j; col[4].k = k;
v[5] = -HxHzdHy; col[5].i = i; col[5].j = j+1; col[5].k = k;
v[6] = -HxHydHz; col[6].i = i; col[6].j = j; col[6].k = k+1;
ierr = MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
}
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,0,&nullspace);CHKERRQ(ierr);
ierr = MatSetNullSpace(jac,nullspace);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullspace);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormJacobian(SNES snes,Vec X,Mat jac,Mat B,void *ptr)
{
AppCtx *user = (AppCtx*)ptr;
PetscErrorCode ierr;
PetscInt i,j,mx,my,xs,ys,xm,ym;
PetscScalar one = 1.0,hx,hy,hxdhy,hydhx,t0,tn,ts,te,tw;
PetscScalar dn,ds,de,dw,an,as,ae,aw,bn,bs,be,bw,gn,gs,ge,gw;
PetscScalar tleft,tright,beta,bm1,coef;
PetscScalar v[5],**x;
Vec localX;
MatStencil col[5],row;
DM da;
PetscFunctionBeginUser;
ierr = SNESGetDM(snes,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,NULL,&mx,&my,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
hxdhy = hx/hy; hydhx = hy/hx;
tleft = user->tleft; tright = user->tright;
beta = user->beta; bm1 = user->bm1; coef = user->coef;
/* Get ghost points */
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,localX,&x);CHKERRQ(ierr);
/* Evaluate Jacobian of function */
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
t0 = x[j][i];
if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
/* general interior volume */
tw = x[j][i-1];
aw = 0.5*(t0 + tw);
bw = PetscPowScalar(aw,bm1);
/* dw = bw * aw */
dw = PetscPowScalar(aw,beta);
gw = coef*bw*(t0 - tw);
te = x[j][i+1];
ae = 0.5*(t0 + te);
be = PetscPowScalar(ae,bm1);
/* de = be * ae; */
de = PetscPowScalar(ae,beta);
ge = coef*be*(te - t0);
ts = x[j-1][i];
as = 0.5*(t0 + ts);
bs = PetscPowScalar(as,bm1);
/* ds = bs * as; */
ds = PetscPowScalar(as,beta);
gs = coef*bs*(t0 - ts);
tn = x[j+1][i];
an = 0.5*(t0 + tn);
bn = PetscPowScalar(an,bm1);
/* dn = bn * an; */
dn = PetscPowScalar(an,beta);
gn = coef*bn*(tn - t0);
v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i;
v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1;
v[2] = hxdhy*(ds + dn + gs - gn) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i;
v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1;
v[4] = -hxdhy*(dn + gn); col[4].j = j+1; col[4].i = i;
ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
} else if (i == 0) {
/* left-hand boundary */
tw = tleft;
aw = 0.5*(t0 + tw);
bw = PetscPowScalar(aw,bm1);
/* dw = bw * aw */
dw = PetscPowScalar(aw,beta);
gw = coef*bw*(t0 - tw);
te = x[j][i + 1];
ae = 0.5*(t0 + te);
be = PetscPowScalar(ae,bm1);
/* de = be * ae; */
de = PetscPowScalar(ae,beta);
ge = coef*be*(te - t0);
/* left-hand bottom boundary */
if (j == 0) {
tn = x[j+1][i];
an = 0.5*(t0 + tn);
bn = PetscPowScalar(an,bm1);
/* dn = bn * an; */
dn = PetscPowScalar(an,beta);
gn = coef*bn*(tn - t0);
v[0] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[0].j = row.j = j; col[0].i = row.i = i;
v[1] = -hydhx*(de + ge); col[1].j = j; col[1].i = i+1;
v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
/* left-hand interior boundary */
} else if (j < my-1) {
ts = x[j-1][i];
as = 0.5*(t0 + ts);
bs = PetscPowScalar(as,bm1);
/* ds = bs * as; */
ds = PetscPowScalar(as,beta);
gs = coef*bs*(t0 - ts);
tn = x[j+1][i];
an = 0.5*(t0 + tn);
bn = PetscPowScalar(an,bm1);
/* dn = bn * an; */
dn = PetscPowScalar(an,beta);
gn = coef*bn*(tn - t0);
v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i;
v[1] = hxdhy*(ds + dn + gs - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i;
v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1;
v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i;
ierr = MatSetValuesStencil(jac,1,&row,4,col,v,INSERT_VALUES);CHKERRQ(ierr);
/* left-hand top boundary */
} else {
ts = x[j-1][i];
as = 0.5*(t0 + ts);
bs = PetscPowScalar(as,bm1);
/* ds = bs * as; */
ds = PetscPowScalar(as,beta);
gs = coef*bs*(t0 - ts);
v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i;
v[1] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i;
v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
} else if (i == mx-1) {
/* right-hand boundary */
tw = x[j][i-1];
aw = 0.5*(t0 + tw);
bw = PetscPowScalar(aw,bm1);
/* dw = bw * aw */
dw = PetscPowScalar(aw,beta);
gw = coef*bw*(t0 - tw);
te = tright;
ae = 0.5*(t0 + te);
be = PetscPowScalar(ae,bm1);
/* de = be * ae; */
de = PetscPowScalar(ae,beta);
ge = coef*be*(te - t0);
/* right-hand bottom boundary */
if (j == 0) {
tn = x[j+1][i];
an = 0.5*(t0 + tn);
bn = PetscPowScalar(an,bm1);
/* dn = bn * an; */
dn = PetscPowScalar(an,beta);
gn = coef*bn*(tn - t0);
v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1;
v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i;
v[2] = -hxdhy*(dn + gn); col[2].j = j+1; col[2].i = i;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
/* right-hand interior boundary */
} else if (j < my-1) {
ts = x[j-1][i];
as = 0.5*(t0 + ts);
bs = PetscPowScalar(as,bm1);
/* ds = bs * as; */
ds = PetscPowScalar(as,beta);
gs = coef*bs*(t0 - ts);
tn = x[j+1][i];
an = 0.5*(t0 + tn);
bn = PetscPowScalar(an,bm1);
/* dn = bn * an; */
dn = PetscPowScalar(an,beta);
gn = coef*bn*(tn - t0);
v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i;
v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1;
v[2] = hxdhy*(ds + dn + gs - gn) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i;
v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i;
ierr = MatSetValuesStencil(jac,1,&row,4,col,v,INSERT_VALUES);CHKERRQ(ierr);
/* right-hand top boundary */
} else {
ts = x[j-1][i];
as = 0.5*(t0 + ts);
bs = PetscPowScalar(as,bm1);
/* ds = bs * as; */
ds = PetscPowScalar(as,beta);
gs = coef*bs*(t0 - ts);
v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i;
v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1;
v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i;
ierr = MatSetValuesStencil(jac,1,&row,3,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
/* bottom boundary,and i <> 0 or mx-1 */
} else if (j == 0) {
tw = x[j][i-1];
aw = 0.5*(t0 + tw);
bw = PetscPowScalar(aw,bm1);
/* dw = bw * aw */
dw = PetscPowScalar(aw,beta);
gw = coef*bw*(t0 - tw);
te = x[j][i+1];
ae = 0.5*(t0 + te);
be = PetscPowScalar(ae,bm1);
/* de = be * ae; */
de = PetscPowScalar(ae,beta);
ge = coef*be*(te - t0);
tn = x[j+1][i];
an = 0.5*(t0 + tn);
bn = PetscPowScalar(an,bm1);
/* dn = bn * an; */
dn = PetscPowScalar(an,beta);
gn = coef*bn*(tn - t0);
v[0] = -hydhx*(dw - gw); col[0].j = j; col[0].i = i-1;
v[1] = hxdhy*(dn - gn) + hydhx*(dw + de + gw - ge); col[1].j = row.j = j; col[1].i = row.i = i;
v[2] = -hydhx*(de + ge); col[2].j = j; col[2].i = i+1;
v[3] = -hxdhy*(dn + gn); col[3].j = j+1; col[3].i = i;
ierr = MatSetValuesStencil(jac,1,&row,4,col,v,INSERT_VALUES);CHKERRQ(ierr);
/* top boundary,and i <> 0 or mx-1 */
} else if (j == my-1) {
tw = x[j][i-1];
aw = 0.5*(t0 + tw);
bw = PetscPowScalar(aw,bm1);
/* dw = bw * aw */
dw = PetscPowScalar(aw,beta);
gw = coef*bw*(t0 - tw);
te = x[j][i+1];
ae = 0.5*(t0 + te);
be = PetscPowScalar(ae,bm1);
/* de = be * ae; */
de = PetscPowScalar(ae,beta);
ge = coef*be*(te - t0);
ts = x[j-1][i];
as = 0.5*(t0 + ts);
bs = PetscPowScalar(as,bm1);
/* ds = bs * as; */
ds = PetscPowScalar(as,beta);
gs = coef*bs*(t0 - ts);
v[0] = -hxdhy*(ds - gs); col[0].j = j-1; col[0].i = i;
v[1] = -hydhx*(dw - gw); col[1].j = j; col[1].i = i-1;
v[2] = hxdhy*(ds + gs) + hydhx*(dw + de + gw - ge); col[2].j = row.j = j; col[2].i = row.i = i;
v[3] = -hydhx*(de + ge); col[3].j = j; col[3].i = i+1;
ierr = MatSetValuesStencil(jac,1,&row,4,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,localX,&x);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
ierr = PetscLogFlops((41.0 + 8.0*POWFLOP)*xm*ym);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info, PetscScalar ***au,
Mat J, Mat Jpre, FishCtx *user) {
PetscErrorCode ierr;
const double hx = 1.0/(info->mx-1),
hy = 1.0/(info->my-1),
hz = 1.0/(info->mz-1),
h = pow(hx*hy*hz,1.0/3.0),
cx = h*h / (hx*hx),
cy = h*h / (hy*hy),
cz = h*h / (hz*hz);
int i,j,k,ncols;
double v[7];
MatStencil col[7],row;
if (user->printevals) {
ierr = PetscPrintf(COMM," [Jacobian eval on %d x %d x %d grid]\n",
info->mx,info->my,info->mz); CHKERRQ(ierr);
}
for (k = info->zs; k < info->zs+info->zm; k++) {
row.k = k;
col[0].k = k;
for (j = info->ys; j < info->ys+info->ym; j++) {
row.j = j;
col[0].j = j;
for (i = info->xs; i < info->xs+info->xm; i++) {
row.i = i;
col[0].i = i;
ncols = 1;
if ( i==0 || i==info->mx-1
|| j==0 || j==info->my-1
|| k==0 || k==info->mz-1) {
v[0] = 1.0;
} else {
v[0] = 2.0 * (cx + cy + cz);
if (i-1 > 0) {
col[ncols].k = k; col[ncols].j = j; col[ncols].i = i-1;
v[ncols++] = - cx;
}
if (i+1 < info->mx-1) {
col[ncols].k = k; col[ncols].j = j; col[ncols].i = i+1;
v[ncols++] = - cx;
}
if (j-1 > 0) {
col[ncols].k = k; col[ncols].j = j-1; col[ncols].i = i;
v[ncols++] = - cy;
}
if (j+1 < info->my-1) {
col[ncols].k = k; col[ncols].j = j+1; col[ncols].i = i;
v[ncols++] = - cy;
}
if (k-1 > 0) {
col[ncols].k = k-1; col[ncols].j = j; col[ncols].i = i;
v[ncols++] = - cz;
}
if (k+1 < info->mz-1) {
col[ncols].k = k+1; col[ncols].j = j; col[ncols].i = i;
v[ncols++] = - cz;
}
}
ierr = MatSetValuesStencil(Jpre,1,&row,ncols,col,v,INSERT_VALUES); CHKERRQ(ierr);
}
}
}
ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
if (J != Jpre) {
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY); CHKERRQ(ierr);
}
return 0;
}
/*
FormJacobian - Evaluates Jacobian matrix.
Input Parameters:
. snes - the SNES context
. x - input vector
. ptr - optional user-defined context, as set by SNESSetJacobian()
Output Parameters:
. A - Jacobian matrix
. B - optionally different preconditioning matrix
*/
PetscErrorCode FormJacobian(SNES snes,Vec X,Mat J,Mat jac,void *ptr)
{
AppCtx *user = (AppCtx*)ptr; /* user-defined application context */
Vec localX;
PetscErrorCode ierr;
PetscInt i,j,k,Mx,My,Mz;
MatStencil col[7],row;
PetscInt xs,ys,zs,xm,ym,zm;
PetscScalar lambda,v[7],hx,hy,hz,hxhzdhy,hyhzdhx,hxhydhz,sc,***x;
DM da;
PetscFunctionBeginUser;
ierr = SNESGetDM(snes,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,
PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
lambda = user->param;
hx = 1.0/(PetscReal)(Mx-1);
hy = 1.0/(PetscReal)(My-1);
hz = 1.0/(PetscReal)(Mz-1);
sc = hx*hy*hz*lambda;
hxhzdhy = hx*hz/hy;
hyhzdhx = hy*hz/hx;
hxhydhz = hx*hy/hz;
/*
Scatter ghost points to local vector, using the 2-step process
DMGlobalToLocalBegin(), DMGlobalToLocalEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
/*
Get pointer to vector data
*/
ierr = DMDAVecGetArray(da,localX,&x);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
/*
Compute entries for the locally owned part of the Jacobian.
- Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Here, we set all entries for a particular row at once.
- We can set matrix entries either using either
MatSetValuesLocal() or MatSetValues(), as discussed above.
*/
for (k=zs; k<zs+zm; k++) {
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
row.k = k; row.j = j; row.i = i;
/* boundary points */
if (i == 0 || j == 0 || k == 0|| i == Mx-1 || j == My-1 || k == Mz-1) {
v[0] = 1.0;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
/* interior grid points */
v[0] = -hxhydhz; col[0].k=k-1;col[0].j=j; col[0].i = i;
v[1] = -hxhzdhy; col[1].k=k; col[1].j=j-1;col[1].i = i;
v[2] = -hyhzdhx; col[2].k=k; col[2].j=j; col[2].i = i-1;
v[3] = 2.0*(hyhzdhx+hxhzdhy+hxhydhz)-sc*PetscExpScalar(x[k][j][i]);col[3].k=row.k;col[3].j=row.j;col[3].i = row.i;
v[4] = -hyhzdhx; col[4].k=k; col[4].j=j; col[4].i = i+1;
v[5] = -hxhzdhy; col[5].k=k; col[5].j=j+1;col[5].i = i;
v[6] = -hxhydhz; col[6].k=k+1;col[6].j=j; col[6].i = i;
ierr = MatSetValuesStencil(jac,1,&row,7,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
}
ierr = DMDAVecRestoreArray(da,localX,&x);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd().
*/
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Normally since the matrix has already been assembled above; this
would do nothing. But in the matrix free mode -snes_mf_operator
this tells the "matrix-free" matrix that a new linear system solve
is about to be done.
*/
ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Tell the matrix we will never add a new nonzero location to the
matrix. If we do, it will generate an error.
*/
ierr = MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat *J,Mat *Jpre,MatStructure *str,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,c,Mx,xs,xm,nc;
DM da;
MatStencil col[3],row;
PetscScalar vals[3],hx,sx;
AppCtx *user = (AppCtx*)ctx;
PetscInt N = user->N;
PetscScalar **u;
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
ierr = DMDAVecGetArrayDOF(da,U,&u);CHKERRQ(ierr);
ierr = MatZeroEntries(*Jpre);CHKERRQ(ierr);
for (i=xs; i<xs+xm; i++) {
for (c=0; c<N; c++) {
nc = 0;
row.c = c; row.i = i;
col[nc].c = c; col[nc].i = i-1; vals[nc++] = -sx;
col[nc].c = c; col[nc].i = i; vals[nc++] = 2.0*sx + a;
col[nc].c = c; col[nc].i = i+1; vals[nc++] = -sx;
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,ADD_VALUES);CHKERRQ(ierr);
}
for (c=0; c<N/3; c++) {
nc = 0;
row.c = c; row.i = i;
col[nc].c = c; col[nc].i = i; vals[nc++] = 1000*u[i][c] + 500*u[i][c+1];
col[nc].c = c+1; col[nc].i = i; vals[nc++] = 500*u[i][c];
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,ADD_VALUES);CHKERRQ(ierr);
nc = 0;
row.c = c+1; row.i = i;
col[nc].c = c; col[nc].i = i; vals[nc++] = -1000*u[i][c] + 500*u[i][c+1];
col[nc].c = c+1; col[nc].i = i; vals[nc++] = 500*u[i][c];
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,ADD_VALUES);CHKERRQ(ierr);
nc = 0;
row.c = c+2; row.i = i;
col[nc].c = c; col[nc].i = i; vals[nc++] = -500*u[i][c+1];
col[nc].c = c+1; col[nc].i = i; vals[nc++] = -500*u[i][c];
ierr = MatSetValuesStencil(*Jpre,1,&row,nc,col,vals,ADD_VALUES);CHKERRQ(ierr);
}
}
ierr = MatAssemblyBegin(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
if (*J != *Jpre) {
ierr = MatAssemblyBegin(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(*J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
}
ierr = DMDAVecRestoreArrayDOF(da,U,&u);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormJacobianLocal - Evaluates Jacobian matrix.
*/
PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,AppCtx *user)
{
MatStencil col[5], row;
PetscScalar D, K, A, v[5], hx, hy, hxdhy, hydhx, ux, uy;
PetscReal normGradZ;
PetscInt i, j,k;
PetscErrorCode ierr;
PetscFunctionBegin;
D = user->D;
K = user->K;
hx = 1.0/(PetscReal)(info->mx-1);
hy = 1.0/(PetscReal)(info->my-1);
hxdhy = hx/hy;
hydhx = hy/hx;
/*
Compute entries for the locally owned part of the Jacobian.
- Currently, all PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Here, we set all entries for a particular row at once.
- We can set matrix entries either using either
MatSetValuesLocal() or MatSetValues(), as discussed above.
*/
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
row.j = j; row.i = i;
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
/* boundary points */
v[0] = 1.0;
ierr = MatSetValuesStencil(jac,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
/* interior grid points */
ux = (x[j][i+1] - x[j][i])/hx;
uy = (x[j+1][i] - x[j][i])/hy;
normGradZ = PetscRealPart(sqrt(ux*ux + uy*uy));
//PetscPrintf(PETSC_COMM_SELF, "i: %d j: %d normGradZ: %g\n", i, j, normGradZ);
if (normGradZ < 1.0e-8) {
normGradZ = 1.0e-8;
}
A = funcA(x[j][i], user);
v[0] = -D*hxdhy; col[0].j = j - 1; col[0].i = i;
v[1] = -D*hydhx; col[1].j = j; col[1].i = i-1;
v[2] = D*2.0*(hydhx + hxdhy) + K*(funcADer(x[j][i], user)*normGradZ - A/normGradZ)*hx*hy; col[2].j = row.j; col[2].i = row.i;
v[3] = -D*hydhx + K*A*hx*hy/(2.0*normGradZ); col[3].j = j; col[3].i = i+1;
v[4] = -D*hxdhy + K*A*hx*hy/(2.0*normGradZ); col[4].j = j + 1; col[4].i = i;
for(k = 0; k < 5; ++k) {
if (PetscIsInfOrNanScalar(v[k])) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_FP, "Invalid residual: %g", PetscRealPart(v[k]));
}
ierr = MatSetValuesStencil(jac,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd().
*/
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Tell the matrix we will never add a new nonzero location to the
matrix. If we do, it will generate an error.
*/
ierr = MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormJacobianLocal - Evaluates Jacobian matrix.
*/
static PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat B,AppCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
MatStencil col[9],row;
PetscScalar v[9];
PetscReal hx,hy,hxdhy,hydhx,dhx,dhy,sc;
PetscFunctionBegin;
hx = 1.0/(PetscReal)(info->mx-1);
hy = 1.0/(PetscReal)(info->my-1);
sc = hx*hy*user->lambda;
dhx = 1/hx;
dhy = 1/hy;
hxdhy = hx/hy;
hydhx = hy/hx;
/*
Compute entries for the locally owned part of the Jacobian.
- PETSc parallel matrix formats are partitioned by
contiguous chunks of rows across the processors.
- Each processor needs to insert only elements that it owns
locally (but any non-local elements will be sent to the
appropriate processor during matrix assembly).
- Here, we set all entries for a particular row at once.
*/
for (j=info->ys; j<info->ys+info->ym; j++) {
for (i=info->xs; i<info->xs+info->xm; i++) {
row.j = j; row.i = i;
/* boundary points */
if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) {
v[0] = 1.0;
ierr = MatSetValuesStencil(B,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr);
} else {
/* interior grid points */
const PetscScalar
ux_E = dhx*(x[j][i+1]-x[j][i]),
uy_E = 0.25*dhy*(x[j+1][i]+x[j+1][i+1]-x[j-1][i]-x[j-1][i+1]),
ux_W = dhx*(x[j][i]-x[j][i-1]),
uy_W = 0.25*dhy*(x[j+1][i-1]+x[j+1][i]-x[j-1][i-1]-x[j-1][i]),
ux_N = 0.25*dhx*(x[j][i+1]+x[j+1][i+1]-x[j][i-1]-x[j+1][i-1]),
uy_N = dhy*(x[j+1][i]-x[j][i]),
ux_S = 0.25*dhx*(x[j-1][i+1]+x[j][i+1]-x[j-1][i-1]-x[j][i-1]),
uy_S = dhy*(x[j][i]-x[j-1][i]),
u = x[j][i],
e_E = eta(user,ux_E,uy_E),
e_W = eta(user,ux_W,uy_W),
e_N = eta(user,ux_N,uy_N),
e_S = eta(user,ux_S,uy_S),
de_E = deta(user,ux_E,uy_E),
de_W = deta(user,ux_W,uy_W),
de_N = deta(user,ux_N,uy_N),
de_S = deta(user,ux_S,uy_S),
skew_E = de_E*ux_E*uy_E,
skew_W = de_W*ux_W*uy_W,
skew_N = de_N*ux_N*uy_N,
skew_S = de_S*ux_S*uy_S,
cross_EW = 0.25*(skew_E - skew_W),
cross_NS = 0.25*(skew_N - skew_S),
newt_E = e_E+de_E*PetscSqr(ux_E),
newt_W = e_W+de_W*PetscSqr(ux_W),
newt_N = e_N+de_N*PetscSqr(uy_N),
newt_S = e_S+de_S*PetscSqr(uy_S);
/* interior grid points */
switch (user->jtype) {
case 1:
/* Jacobian from p=2 */
v[0] = -hxdhy; col[0].j = j-1; col[0].i = i;
v[1] = -hydhx; col[1].j = j; col[1].i = i-1;
v[2] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(u); col[2].j = row.j; col[2].i = row.i;
v[3] = -hydhx; col[3].j = j; col[3].i = i+1;
v[4] = -hxdhy; col[4].j = j+1; col[4].i = i;
ierr = MatSetValuesStencil(B,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
break;
case 2:
/* Jacobian arising from Picard linearization */
v[0] = -hxdhy*e_S; col[0].j = j-1; col[0].i = i;
v[1] = -hydhx*e_W; col[1].j = j; col[1].i = i-1;
v[2] = (e_W+e_E)*hydhx + (e_S+e_N)*hxdhy; col[2].j = row.j; col[2].i = row.i;
v[3] = -hydhx*e_E; col[3].j = j; col[3].i = i+1;
v[4] = -hxdhy*e_N; col[4].j = j+1; col[4].i = i;
ierr = MatSetValuesStencil(B,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
break;
case 3:
/* Full Jacobian, but only a star stencil */
col[0].j = j-1; col[0].i = i;
col[1].j = j; col[1].i = i-1;
col[2].j = j; col[2].i = i;
col[3].j = j; col[3].i = i+1;
col[4].j = j+1; col[4].i = i;
v[0] = -hxdhy*newt_S + cross_EW;
v[1] = -hydhx*newt_W + cross_NS;
v[2] = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*PetscExpScalar(u);
v[3] = -hydhx*newt_E - cross_NS;
v[4] = -hxdhy*newt_N - cross_EW;
ierr = MatSetValuesStencil(B,1,&row,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
break;
case 4:
/** The Jacobian is
*
* -div [ eta (grad u) + deta (grad u0 . grad u) grad u0 ] - (eE u0) u
*
**/
col[0].j = j-1; col[0].i = i-1;
col[1].j = j-1; col[1].i = i;
col[2].j = j-1; col[2].i = i+1;
col[3].j = j; col[3].i = i-1;
col[4].j = j; col[4].i = i;
col[5].j = j; col[5].i = i+1;
col[6].j = j+1; col[6].i = i-1;
col[7].j = j+1; col[7].i = i;
col[8].j = j+1; col[8].i = i+1;
v[0] = -0.25*(skew_S + skew_W);
v[1] = -hxdhy*newt_S + cross_EW;
v[2] = 0.25*(skew_S + skew_E);
v[3] = -hydhx*newt_W + cross_NS;
v[4] = hxdhy*(newt_N + newt_S) + hydhx*(newt_E + newt_W) - sc*PetscExpScalar(u);
v[5] = -hydhx*newt_E - cross_NS;
v[6] = 0.25*(skew_N + skew_W);
v[7] = -hxdhy*newt_N - cross_EW;
v[8] = -0.25*(skew_N + skew_E);
ierr = MatSetValuesStencil(B,1,&row,9,col,v,INSERT_VALUES);CHKERRQ(ierr);
break;
default:
SETERRQ1(((PetscObject)info->da)->comm,PETSC_ERR_SUP,"Jacobian type %d not implemented",user->jtype);
}
}
}
}
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd().
*/
ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/*
Tell the matrix we will never add a new nonzero location to the
matrix. If we do, it will generate an error.
*/
ierr = MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode RHSJacobian(TS ts,PetscReal t,Vec U,Mat A,Mat BB,void *ctx)
{
AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */
DM da;
PetscErrorCode ierr;
PetscInt i,j,Mx,My,xs,ys,xm,ym;
PetscReal hx,hy,sx,sy;
PetscScalar uc,vc;
Field **u;
Vec localU;
MatStencil stencil[6],rowstencil;
PetscScalar entries[6];
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
hx = 2.50/(PetscReal)(Mx); sx = 1.0/(hx*hx);
hy = 2.50/(PetscReal)(My); sy = 1.0/(hy*hy);
/*
Scatter ghost points to local vector,using the 2-step process
DMGlobalToLocalBegin(),DMGlobalToLocalEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localU,&u);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
stencil[0].k = 0;
stencil[1].k = 0;
stencil[2].k = 0;
stencil[3].k = 0;
stencil[4].k = 0;
stencil[5].k = 0;
rowstencil.k = 0;
/*
Compute function over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
stencil[0].j = j-1;
stencil[1].j = j+1;
stencil[2].j = j;
stencil[3].j = j;
stencil[4].j = j;
stencil[5].j = j;
rowstencil.k = 0; rowstencil.j = j;
for (i=xs; i<xs+xm; i++) {
uc = u[j][i].u;
vc = u[j][i].v;
/* uxx = (-2.0*uc + u[j][i-1].u + u[j][i+1].u)*sx;
uyy = (-2.0*uc + u[j-1][i].u + u[j+1][i].u)*sy;
vxx = (-2.0*vc + u[j][i-1].v + u[j][i+1].v)*sx;
vyy = (-2.0*vc + u[j-1][i].v + u[j+1][i].v)*sy;
f[j][i].u = appctx->D1*(uxx + uyy) - uc*vc*vc + appctx->gamma*(1.0 - uc);*/
stencil[0].i = i; stencil[0].c = 0; entries[0] = appctx->D1*sy;
stencil[1].i = i; stencil[1].c = 0; entries[1] = appctx->D1*sy;
stencil[2].i = i-1; stencil[2].c = 0; entries[2] = appctx->D1*sx;
stencil[3].i = i+1; stencil[3].c = 0; entries[3] = appctx->D1*sx;
stencil[4].i = i; stencil[4].c = 0; entries[4] = -2.0*appctx->D1*(sx + sy) - vc*vc - appctx->gamma;
stencil[5].i = i; stencil[5].c = 1; entries[5] = -2.0*uc*vc;
rowstencil.i = i; rowstencil.c = 0;
ierr = MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES);CHKERRQ(ierr);
stencil[0].c = 1; entries[0] = appctx->D2*sy;
stencil[1].c = 1; entries[1] = appctx->D2*sy;
stencil[2].c = 1; entries[2] = appctx->D2*sx;
stencil[3].c = 1; entries[3] = appctx->D2*sx;
stencil[4].c = 1; entries[4] = -2.0*appctx->D2*(sx + sy) + 2.0*uc*vc - appctx->gamma - appctx->kappa;
stencil[5].c = 0; entries[5] = vc*vc;
rowstencil.c = 1;
ierr = MatSetValuesStencil(A,1,&rowstencil,6,stencil,entries,INSERT_VALUES);CHKERRQ(ierr);
/* f[j][i].v = appctx->D2*(vxx + vyy) + uc*vc*vc - (appctx->gamma + appctx->kappa)*vc; */
}
}
/*
Restore vectors
*/
ierr = PetscLogFlops(19*xm*ym);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(da,localU,&u);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatSetOption(A,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
