PetscErrorCode SetCoordinates2d(DM da)
{
PetscErrorCode ierr;
PetscInt i,j,mstart,m,nstart,n;
Vec local,global;
DMDACoor2d **coors,**coorslocal;
DM cda;
PetscFunctionBeginUser;
ierr = DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&global);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(da,&local);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&mstart,&nstart,0,&m,&n,0);CHKERRQ(ierr);
for (i=mstart; i<mstart+m; i++) {
for (j=nstart; j<nstart+n; j++) {
if (i % 2) {
coors[j][i].x = coorslocal[j][i-1].x + .1*(coorslocal[j][i+1].x - coorslocal[j][i-1].x);
}
if (j % 2) {
coors[j][i].y = coorslocal[j-1][i].y + .3*(coorslocal[j+1][i].y - coorslocal[j-1][i].y);
}
}
}
ierr = DMDAVecRestoreArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode MatMult_HYPREStruct(Mat A,Vec x,Vec y)
{
PetscErrorCode ierr;
PetscScalar *xx,*yy;
PetscInt ilower[3],iupper[3];
Mat_HYPREStruct *mx = (Mat_HYPREStruct*)(A->data);
PetscFunctionBegin;
ierr = DMDAGetCorners(mx->da,&ilower[0],&ilower[1],&ilower[2],&iupper[0],&iupper[1],&iupper[2]);CHKERRQ(ierr);
iupper[0] += ilower[0] - 1;
iupper[1] += ilower[1] - 1;
iupper[2] += ilower[2] - 1;
/* copy x values over to hypre */
PetscStackCallStandard(HYPRE_StructVectorSetConstantValues,(mx->hb,0.0));
ierr = VecGetArray(x,&xx);CHKERRQ(ierr);
PetscStackCallStandard(HYPRE_StructVectorSetBoxValues,(mx->hb,(HYPRE_Int *)ilower,(HYPRE_Int *)iupper,xx));
ierr = VecRestoreArray(x,&xx);CHKERRQ(ierr);
PetscStackCallStandard(HYPRE_StructVectorAssemble,(mx->hb));
PetscStackCallStandard(HYPRE_StructMatrixMatvec,(1.0,mx->hmat,mx->hb,0.0,mx->hx));
/* copy solution values back to PETSc */
ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
PetscStackCallStandard(HYPRE_StructVectorGetBoxValues,(mx->hx,(HYPRE_Int *)ilower,(HYPRE_Int *)iupper,yy));
ierr = VecRestoreArray(y,&yy);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode DADefineXLinearField2D(DM da,Vec field)
{
PetscErrorCode ierr;
PetscInt i,j;
PetscInt sx,nx,sy,ny;
Vec Gcoords;
DMDACoor2d **XX;
PetscScalar **FF;
DM cda;
PetscFunctionBeginUser;
ierr = DMGetCoordinateDM(da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&Gcoords);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,Gcoords,&XX);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,field,&FF);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&sx,&sy,0,&nx,&ny,0);CHKERRQ(ierr);
for (i=sx; i<sx+nx; i++) {
for (j=sy; j<sy+ny; j++ ) {
FF[j][i] = 10.0 + 3.0 * XX[j][i].x + 5.5 * XX[j][i].y + 8.003 * XX[j][i].x * XX[j][i].y;
}
}
ierr = DMDAVecRestoreArray(da,field,&FF);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(cda,Gcoords,&XX);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ReactingFlowPostCheck(SNESLineSearch linesearch, Vec X, Vec Y, Vec W, PetscBool *changed_y, PetscBool *changed_w, void *vctx)
{
PetscInt i,j,l,Mx,My,xs,ys,xm,ym;
PetscErrorCode ierr;
Field **x;
SNES snes;
DM da;
PetscScalar min;
PetscFunctionBeginUser;
*changed_w = PETSC_FALSE;
ierr = VecMin(X,NULL,&min);CHKERRQ(ierr);
if (min >= 0.) PetscFunctionReturn(0);
*changed_w = PETSC_TRUE;
ierr = SNESLineSearchGetSNES(linesearch, &snes);CHKERRQ(ierr);
ierr = SNESGetDM(snes,&da);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);
ierr = DMDAVecGetArray(da,W,&x);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
for (l = 0; l < N_SPECIES; l++) {
if (x[j][i].sp[l] < 0.) x[j][i].sp[l] = 0.;
}
}
}
ierr = DMDAVecRestoreArray(da,W,&x);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);
}
PetscErrorCode ComputeB(AppCtx *user)
{
PetscErrorCode ierr;
PetscInt i,j;
PetscInt nx,ny,xs,xm,ys,ym;
PetscReal two=2.0, pi=4.0*atan(1.0);
PetscReal hx,hy,ehxhy;
PetscReal temp;
PetscReal ecc=user->ecc;
PetscReal **b;
PetscFunctionBeginUser;
nx = user->nx;
ny = user->ny;
hx = two*pi/(nx+1.0);
hy = two*user->b/(ny+1.0);
ehxhy = ecc*hx*hy;
/* Get pointer to local vector data */
ierr = DMDAVecGetArray(user->da,user->B, &b);CHKERRQ(ierr);
ierr = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
/* Compute the linear term in the objective function */
for (i=xs; i<xs+xm; i++) {
temp=PetscSinReal((i+1)*hx);
for (j=ys; j<ys+ym; j++) b[j][i] = -ehxhy*temp;
}
/* Restore vectors */
ierr = DMDAVecRestoreArray(user->da,user->B,&b);CHKERRQ(ierr);
ierr = PetscLogFlops(5*xm*ym+3*xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode ComputeMatrix(KSP ksp,Mat J,Mat jac,MatStructure *str,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 ComputeRHS(KSP ksp,Vec b,void *ctx)
{
PetscErrorCode ierr;
PetscInt i,j,k,mx,my,mz,xm,ym,zm,xs,ys,zs;
DM dm;
PetscScalar Hx,Hy,Hz,HxHydHz,HyHzdHx,HxHzdHy;
PetscScalar ***barray;
PetscFunctionBeginUser;
ierr = KSPGetDM(ksp,&dm);CHKERRQ(ierr);
ierr = DMDAGetInfo(dm,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(dm,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
ierr = DMDAVecGetArray(dm,b,&barray);CHKERRQ(ierr);
for (k=zs; k<zs+zm; k++) {
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
if (i==0 || j==0 || k==0 || i==mx-1 || j==my-1 || k==mz-1) {
barray[k][j][i] = 2.0*(HxHydHz + HxHzdHy + HyHzdHx);
} else {
barray[k][j][i] = Hx*Hy*Hz;
}
}
}
}
ierr = DMDAVecRestoreArray(dm,b,&barray);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode SetCoordinates1d(DM da)
{
PetscErrorCode ierr;
PetscInt i,start,m;
Vec local,global;
PetscScalar *coors,*coorslocal;
DM cda;
PetscFunctionBeginUser;
ierr = DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);CHKERRQ(ierr);
ierr = DMGetCoordinateDM(da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&global);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(da,&local);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&start,0,0,&m,0,0);CHKERRQ(ierr);
for (i=start; i<start+m; i++) {
if (i % 2) {
coors[i] = coorslocal[i-1] + .1*(coorslocal[i+1] - coorslocal[i-1]);
}
}
ierr = DMDAVecRestoreArray(cda,global,&coors);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(cda,local,&coorslocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(cda,global,INSERT_VALUES,local);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode FormInitialGuess(DM da,AppCtx *ctx,Vec X)
{
PetscInt i,j,l,Mx,My,xs,ys,xm,ym;
PetscErrorCode ierr;
Field **x;
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 = DMDAVecGetArray(da,X,&x);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
for (l = 0; l < N_SPECIES; l++) {
if (i == 0) {
if (l == 0) x[j][i].sp[l] = (ctx->x_inflow.sp[l]*((PetscScalar)j) / (My - 1));
else if (l == 1) x[j][i].sp[l] = (ctx->x_inflow.sp[l]*(1. - ((PetscScalar)j) / (My - 1)));
else x[j][i].sp[l] = ctx->x_0.sp[l];
}
}
}
}
ierr = DMDAVecRestoreArray(da,X,&x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormInitialGuess - Forms initial approximation.
Input Parameters:
user - user-defined application context
X - vector
Output Parameter:
X - vector
*/
PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
{
PetscInt i,j,row,mx,my,xs,ys,xm,ym,gxm,gym,gxs,gys;
PetscErrorCode ierr;
PetscReal one = 1.0,lambda,temp1,temp,hx,hy,hxdhy,hydhx,sc;
PetscScalar *x;
Vec localX = user->localX;
mx = user->mx; my = user->my; lambda = user->param;
hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
temp1 = lambda/(lambda + one);
/*
Get a pointer to vector data.
- For default PETSc vectors,VecGetArray() returns a pointer to
the data array. Otherwise, the routine is implementation dependent.
- You MUST call VecRestoreArray() when you no longer need access to
the array.
*/
ierr = VecGetArray(localX,&x);CHKERRQ(ierr);
/*
Get local grid boundaries (for 2-dimensional DMDA):
xs, ys - starting grid indices (no ghost points)
xm, ym - widths of local grid (no ghost points)
gxs, gys - starting grid indices (including ghost points)
gxm, gym - widths of local grid (including ghost points)
*/
ierr = DMDAGetCorners(user->da,&xs,&ys,PETSC_NULL,&xm,&ym,PETSC_NULL);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(user->da,&gxs,&gys,PETSC_NULL,&gxm,&gym,PETSC_NULL);CHKERRQ(ierr);
/*
Compute initial guess over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
temp = (PetscReal)(PetscMin(j,my-j-1))*hy;
for (i=xs; i<xs+xm; i++) {
row = i - gxs + (j - gys)*gxm;
if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
x[row] = 0.0;
continue;
}
x[row] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,mx-i-1))*hx,temp));
}
}
/*
Restore vector
*/
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
/*
Insert values into global vector
*/
ierr = DMLocalToGlobalBegin(user->da,localX,INSERT_VALUES,X);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(user->da,localX,INSERT_VALUES,X);CHKERRQ(ierr);
return 0;
}
/*
ComputeFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. X - input vector
. user - user-defined application context
Output Parameter:
. F - function vector
*/
PetscErrorCode ComputeFunction(AppCtx *user,Vec X,Vec F)
{
PetscErrorCode ierr;
PetscInt i,j,row,mx,my,xs,ys,xm,ym,gxs,gys,gxm,gym;
PetscReal two = 2.0,one = 1.0,lambda,hx,hy,hxdhy,hydhx,sc;
PetscScalar u,uxx,uyy,*x,*f;
Vec localX = user->localX;
mx = user->mx; my = user->my; lambda = user->param;
hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
sc = hx*hy*lambda; hxdhy = hx/hy; hydhx = hy/hx;
/*
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(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
/*
Get pointers to vector data
*/
ierr = VecGetArray(localX,&x);CHKERRQ(ierr);
ierr = VecGetArray(F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(user->da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(user->da,&gxs,&gys,NULL,&gxm,&gym,NULL);CHKERRQ(ierr);
/*
Compute function over the locally owned part of the grid
*/
for (j=ys; j<ys+ym; j++) {
row = (j - gys)*gxm + xs - gxs - 1;
for (i=xs; i<xs+xm; i++) {
row++;
if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
f[row] = x[row];
continue;
}
u = x[row];
uxx = (two*u - x[row-1] - x[row+1])*hydhx;
uyy = (two*u - x[row-gxm] - x[row+gxm])*hxdhy;
f[row] = uxx + uyy - sc*PetscExpScalar(u);
}
}
/*
Restore vectors
*/
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
ierr = VecRestoreArray(F,&f);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*ym*xm);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);
}
/* Compute the right thickness H = H(x). See lecture notes for exact solution. */
PetscErrorCode FillThicknessAndExactSoln(DM da, AppCtx *user)
{
PetscErrorCode ierr;
PetscInt i,Mx,xs,xm;
PetscReal hx, n, r, Cs, xx, flux, qg, p, B, dudx, ustag;
PetscScalar *H, *uex, *visc;
PetscFunctionBegin;
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);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,PETSC_NULL,PETSC_NULL,&xm,PETSC_NULL,PETSC_NULL);CHKERRQ(ierr);
/* constants, independent of x */
hx = user->L / (PetscReal)(Mx-1);
n = user->n;
r = user->rho / user->rhow;
Cs = user->A * PetscPowScalar( ( 0.25 * user->rho * user->g * (1.0 - r) ), n);
qg = user->ug * user->Hg;
p = 1.0 + 1.0 / user->n;
B = PetscPowScalar(user->A,-1.0/user->n);
/* Compute regular grid exact soln and staggered-grid thickness over the
locally-owned part of the grid */
ierr = DMDAVecGetArray(da,user->uexact,&uex);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,user->H,&H);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,user->viscosity,&visc);CHKERRQ(ierr);
for (i=xs; i<xs+xm; i++) {
/* get exact velocity and strain rate on regular grid */
xx = hx * (PetscReal)i; /* = x_i = distance from grounding line */
flux = user->accum * xx + qg; /* flux at x_i */
GetUEx(user->ug, qg, user->accum, n, Cs, flux, &(uex[i]), &dudx);
/* exact viscosity on regular grid */
visc[i] = GetViscosityFromStrainRate(dudx, p, B);
/* exact thickness on staggered grid */
flux += user->accum * hx * 0.5; /* flux at x_{i+1/2} */
GetUEx(user->ug, qg, user->accum, n, Cs, flux, &ustag, &dudx);
H[i] = flux / ustag;
}
ierr = DMDAVecRestoreArray(da,user->uexact,&uex);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,user->H,&H);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,user->viscosity,&visc);CHKERRQ(ierr);
/* separately compute and store calving-front values */
flux = user->accum * user->L + qg;
GetUEx(user->ug, qg, user->accum, n, Cs, flux, &(user->uexactcalv), &dudx);
user->Hcalv = flux / user->uexactcalv;
/* strain rate at calving front */
/* MATLAB: gamma = ( 0.25 * p.A^(1/n) * (1 - r) * p.rho * p.g * H(end) )^n; */
user->gamma = 0.25 * PetscPowScalar(user->A,1.0/user->n) * (1.0 - r)
* user->rho * user->g * user->Hcalv;
user->gamma = PetscPowScalar(user->gamma,user->n);
PetscFunctionReturn(0);
}
/*
RHSMatrixLaplacian - User-provided routine to compute the right-hand-side
matrix for the Laplacian operator
Input Parameters:
ts - the TS context
t - current time (ignored)
X - current solution (ignored)
dummy - optional user-defined context, as set by TSetRHSJacobian()
Output Parameters:
AA - Jacobian matrix
BB - optionally different matrix from which the preconditioner is built
str - flag indicating matrix structure
*/
PetscErrorCode RHSMatrixLaplaciangllDM(TS ts,PetscReal t,Vec X,Mat A,Mat BB,void *ctx)
{
PetscReal **temp;
PetscReal vv;
AppCtx *appctx = (AppCtx*)ctx; /* user-defined application context */
PetscErrorCode ierr;
PetscInt i,xs,xn,l,j;
PetscInt *rowsDM;
PetscBool flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL,"-gll_mf",&flg,NULL);CHKERRQ(ierr);
if (!flg) {
/*
Creates the element stiffness matrix for the given gll
*/
ierr = PetscGLLElementLaplacianCreate(&appctx->SEMop.gll,&temp);CHKERRQ(ierr);
/* workarround for clang analyzer warning: Division by zero */
if (appctx->param.N <= 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_ARG_WRONG,"Spectral element order should be > 1");
/* scale by the size of the element */
for (i=0; i<appctx->param.N; i++) {
vv=-appctx->param.mu*2.0/appctx->param.Le;
for (j=0; j<appctx->param.N; j++) temp[i][j]=temp[i][j]*vv;
}
ierr = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_FALSE);CHKERRQ(ierr);
ierr = DMDAGetCorners(appctx->da,&xs,NULL,NULL,&xn,NULL,NULL);CHKERRQ(ierr);
xs = xs/(appctx->param.N-1);
xn = xn/(appctx->param.N-1);
ierr = PetscMalloc1(appctx->param.N,&rowsDM);CHKERRQ(ierr);
/*
loop over local elements
*/
for (j=xs; j<xs+xn; j++) {
for (l=0; l<appctx->param.N; l++) {
rowsDM[l] = 1+(j-xs)*(appctx->param.N-1)+l;
}
ierr = MatSetValuesLocal(A,appctx->param.N,rowsDM,appctx->param.N,rowsDM,&temp[0][0],ADD_VALUES);CHKERRQ(ierr);
}
ierr = PetscFree(rowsDM);CHKERRQ(ierr);
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecReciprocal(appctx->SEMop.mass);CHKERRQ(ierr);
ierr = MatDiagonalScale(A,appctx->SEMop.mass,0);CHKERRQ(ierr);
ierr = VecReciprocal(appctx->SEMop.mass);CHKERRQ(ierr);
ierr = PetscGLLElementLaplacianDestroy(&appctx->SEMop.gll,&temp);CHKERRQ(ierr);
} else {
ierr = MatSetType(A,MATSHELL);CHKERRQ(ierr);
ierr = MatSetUp(A);CHKERRQ(ierr);
ierr = MatShellSetContext(A,appctx);CHKERRQ(ierr);
ierr = MatShellSetOperation(A,MATOP_MULT,(void (*)(void))MatMult_Laplacian);CHKERRQ(ierr);
}
return 0;
}
/*
FormInitialGuess - Forms initial approximation.
Input Parameters:
user - user-defined application context
X - vector
Output Parameter:
X - vector
*/
PetscErrorCode FormInitialGuess(AppCtx *user,Vec X)
{
PetscInt i,j,k,Mx,My,Mz,xs,ys,zs,xm,ym,zm;
PetscErrorCode ierr;
PetscReal lambda,temp1,hx,hy,hz,tempk,tempj;
PetscScalar ***x;
PetscFunctionBeginUser;
ierr = DMDAGetInfo(user->da,PETSC_IGNORE,&Mx,&My,&Mz,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr);
lambda = user->param;
hx = 1.0/(PetscReal)(Mx-1);
hy = 1.0/(PetscReal)(My-1);
hz = 1.0/(PetscReal)(Mz-1);
temp1 = lambda/(lambda + 1.0);
/*
Get a pointer to vector data.
- For default PETSc vectors, VecGetArray() returns a pointer to
the data array. Otherwise, the routine is implementation dependent.
- You MUST call VecRestoreArray() when you no longer need access to
the array.
*/
ierr = DMDAVecGetArray(user->da,X,&x);CHKERRQ(ierr);
/*
Get local grid boundaries (for 3-dimensional DMDA):
xs, ys, zs - starting grid indices (no ghost points)
xm, ym, zm - widths of local grid (no ghost points)
*/
ierr = DMDAGetCorners(user->da,&xs,&ys,&zs,&xm,&ym,&zm);CHKERRQ(ierr);
/*
Compute initial guess over the locally owned part of the grid
*/
for (k=zs; k<zs+zm; k++) {
tempk = (PetscReal)(PetscMin(k,Mz-k-1))*hz;
for (j=ys; j<ys+ym; j++) {
tempj = PetscMin((PetscReal)(PetscMin(j,My-j-1))*hy,tempk);
for (i=xs; i<xs+xm; i++) {
if (i == 0 || j == 0 || k == 0 || i == Mx-1 || j == My-1 || k == Mz-1) {
/* boundary conditions are all zero Dirichlet */
x[k][j][i] = 0.0;
} else {
x[k][j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,tempj));
}
}
}
}
/*
Restore vector
*/
ierr = DMDAVecRestoreArray(user->da,X,&x);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode TcSolver::generateBC2()
{
PetscErrorCode ierr;
PetscInt mstart, nstart, m, n, i, j;
PetscReal **qx, **qy;
PetscReal **bc22;
Vec bc2Global;
ierr = VecSet(bc2, 0.0); CHKERRQ(ierr);
ierr = DMCompositeGetAccess(lambdaPack, bc2, &bc2Global, NULL); CHKERRQ(ierr);
ierr = DMDAVecGetArray(uda, qxLocal, &qx); CHKERRQ(ierr);
ierr = DMDAVecGetArray(vda, qyLocal, &qy); CHKERRQ(ierr);
ierr = DMDAVecGetArray(pda, bc2Global, &bc22); CHKERRQ(ierr);
ierr = DMDAGetCorners(pda, &mstart, &nstart, NULL, &m, &n, NULL); CHKERRQ(ierr);
//x-faces
for(j=nstart; j<nstart+n; j++)
{
//-X
if(mstart == 0) //if -X is current process
{
bc22[j][0] -= qx[j][-1];
}
//+X
if(mstart+m-1 == fluid.nx-1)
{
bc22[j][fluid.nx-1] += qx[j][fluid.nx-1];
}
}
//y-faces
for(i=mstart; i<mstart+m; i++)
{
//-Y
if(nstart ==0)
{
bc22[0][i] -= qy[-1][i];
}
//+Y
if(nstart+n-1 == fluid.ny-1)
{
bc22[fluid.ny-1][i] += qy[fluid.ny-1][i];
}
}
ierr = DMDAVecRestoreArray(pda, bc2Global, &bc22); CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(uda, qxLocal, &qx); CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(vda, qyLocal, &qy); CHKERRQ(ierr);
ierr = DMCompositeRestoreAccess(lambdaPack, bc2, &bc2Global, NULL); CHKERRQ(ierr);
return 0;
}
/*
Evaluates FU = Gradiant(L(w,u,lambda))
*/
PetscErrorCode FormFunction(SNES snes,Vec U,Vec FU,void *dummy)
{
UserCtx *user = (UserCtx*)dummy;
PetscErrorCode ierr;
PetscInt xs,xm,i,N;
PetscScalar *u,*lambda,*w,*fu,*fw,*flambda,d,h;
Vec vw,vu,vlambda,vfw,vfu,vflambda;
PetscFunctionBeginUser;
ierr = DMCompositeGetLocalVectors(user->packer,&vw,&vu,&vlambda);CHKERRQ(ierr);
ierr = DMCompositeGetLocalVectors(user->packer,&vfw,&vfu,&vflambda);CHKERRQ(ierr);
ierr = DMCompositeScatter(user->packer,U,vw,vu,vlambda);CHKERRQ(ierr);
ierr = DMDAGetCorners(user->da1,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
ierr = DMDAGetInfo(user->da1,0,&N,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = VecGetArray(vw,&w);CHKERRQ(ierr);
ierr = VecGetArray(vfw,&fw);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da1,vu,&u);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da1,vfu,&fu);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da1,vlambda,&lambda);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da1,vflambda,&flambda);CHKERRQ(ierr);
d = (N-1.0);
h = 1.0/d;
/* derivative of L() w.r.t. w */
if (xs == 0) { /* only first processor computes this */
fw[0] = -2.*d*lambda[0];
}
/* derivative of L() w.r.t. u */
for (i=xs; i<xs+xm; i++) {
if (i == 0) flambda[0] = h*u[0] + 2.*d*lambda[0] - d*lambda[1];
else if (i == 1) flambda[1] = 2.*h*u[1] + 2.*d*lambda[1] - d*lambda[2];
else if (i == N-1) flambda[N-1] = h*u[N-1] + 2.*d*lambda[N-1] - d*lambda[N-2];
else if (i == N-2) flambda[N-2] = 2.*h*u[N-2] + 2.*d*lambda[N-2] - d*lambda[N-3];
else flambda[i] = 2.*h*u[i] - d*(lambda[i+1] - 2.0*lambda[i] + lambda[i-1]);
}
/* derivative of L() w.r.t. lambda */
for (i=xs; i<xs+xm; i++) {
if (i == 0) fu[0] = 2.0*d*(u[0] - w[0]);
else if (i == N-1) fu[N-1] = 2.0*d*u[N-1];
else fu[i] = -(d*(u[i+1] - 2.0*u[i] + u[i-1]) - 2.0*h);
}
ierr = VecRestoreArray(vw,&w);CHKERRQ(ierr);
ierr = VecRestoreArray(vfw,&fw);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da1,vu,&u);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da1,vfu,&fu);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da1,vlambda,&lambda);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da1,vflambda,&flambda);CHKERRQ(ierr);
ierr = DMCompositeGather(user->packer,FU,INSERT_VALUES,vfw,vfu,vflambda);CHKERRQ(ierr);
ierr = DMCompositeRestoreLocalVectors(user->packer,&vw,&vu,&vlambda);CHKERRQ(ierr);
ierr = DMCompositeRestoreLocalVectors(user->packer,&vfw,&vfu,&vflambda);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
int main(int argc,char **argv)
{
PetscErrorCode ierr;
DM da2D;
PetscInt i,j,ixs, ixm, iys, iym;;
PetscViewer H5viewer;
PetscScalar xm=-1.0, xp=1.0;
PetscScalar ym=-1.0, yp=1.0;
PetscScalar value=1.0,dx,dy;
PetscInt Nx=40, Ny=40;
Vec gauss;
PetscScalar **gauss_ptr;
dx=(xp-xm)/(Nx-1);
dy=(yp-ym)/(Ny-1);
// Initialize the Petsc context
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
// Build of the DMDA
ierr = DMDACreate2d(PETSC_COMM_WORLD, DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_NONE,DMDA_STENCIL_STAR,Nx,Ny,PETSC_DECIDE,PETSC_DECIDE,1,1,PETSC_NULL,PETSC_NULL,&da2D);CHKERRQ(ierr);
// Set the coordinates
DMDASetUniformCoordinates(da2D, 0.0, 1.0, 0.0, 1.0, 0.0, 0.0);
// Declare gauss as a DMDA component
ierr = DMCreateGlobalVector(da2D,&gauss);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject) gauss, "pressure");CHKERRQ(ierr);
// Initialize vector gauss with a constant value (=1)
ierr = VecSet(gauss,value);CHKERRQ(ierr);
// Get the coordinates of the corners for each process
ierr = DMDAGetCorners(da2D, &ixs, &iys, 0, &ixm, &iym, 0);CHKERRQ(ierr);
/* Build the gaussian profile (exp(-x^2-y^2)) */
ierr = DMDAVecGetArray(da2D,gauss,&gauss_ptr);CHKERRQ(ierr);
for (j=iys; j<iys+iym; j++){
for (i=ixs; i<ixs+ixm; i++){
gauss_ptr[j][i]=exp(-(xm+i*dx)*(xm+i*dx)-(ym+j*dy)*(ym+j*dy));
}
}
ierr = DMDAVecRestoreArray(da2D,gauss,&gauss_ptr);CHKERRQ(ierr);
// Create the HDF5 viewer
ierr = PetscViewerHDF5Open(PETSC_COMM_WORLD,"gauss.h5",FILE_MODE_WRITE,&H5viewer);CHKERRQ(ierr);
// Write the H5 file
ierr = VecView(gauss,H5viewer);CHKERRQ(ierr);
// Cleaning stage
ierr = PetscViewerDestroy(&H5viewer);CHKERRQ(ierr);
ierr = VecDestroy(&gauss);CHKERRQ(ierr);
ierr = DMDestroy(&da2D);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
PetscErrorCode efs_set_sol(efs *slv, double sol[])
{
PetscErrorCode ierr;
ierr = DMCreateGlobalVector(slv->dm, &slv->sol);
slv->state.sol = sol;
if (slv->grid.nd == 2) {
PetscScalar **svec;
double **sol_state;
PetscInt i, j;
PetscInt xs, ys, xm, ym;
ierr = DMDAGetCorners(slv->dm, &xs, &ys, 0, &xm, &ym, 0);CHKERRQ(ierr);
ierr = ef_dmap_get(slv->dmap, slv->state.sol, &sol_state);CHKERRQ(ierr);
ierr = DMDAVecGetArray(slv->dm, slv->sol, &svec);CHKERRQ(ierr);
for (j = ys; j < ys + ym; j++) {
for (i = xs; i < xs + xm; i++) {
svec[j][i] = sol_state[j][i];
}
}
ierr = ef_dmap_restore(slv->dmap, &sol_state);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(slv->dm, slv->sol, &svec);CHKERRQ(ierr);
} else if (slv->grid.nd == 3) {
PetscScalar ***svec;
double ***sol_state;
PetscInt i, j, k;
PetscInt xs, ys, zs, xm, ym, zm;
ierr = DMDAGetCorners(slv->dm, &xs, &ys, &zs, &xm, &ym, &zm);CHKERRQ(ierr);
ierr = ef_dmap_get(slv->dmap, slv->state.sol, &sol_state);CHKERRQ(ierr);
ierr = DMDAVecGetArray(slv->dm, slv->sol, &svec);CHKERRQ(ierr);
for (k = zs; k < zs + zm; k++) {
for (j = ys; j < ys + ym; j++) {
for (i = xs; i < xs + xm; i++) {
svec[k][j][i] = sol_state[k][j][i];
}
}
}
ierr = ef_dmap_restore(slv->dmap, &sol_state);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(slv->dm, slv->sol, &svec);CHKERRQ(ierr);
}
return 0;
}
/*
This solves the equation Δu = qρ with Laplacian defined by 7-point
stencil and periodic boundary conditions. Thus with q = 1 it is
exactly the pseudo-inverse of the Laplacian operator implemented by
7-point stencil. Given the periodicity the pseudo-inverse may
differ by at most a constant.
To get the potential in kcal/mol as used in the rest of the code you
need to supply q = -4π/ε₀ that is -4 * M_PI * EPSILON0INV.
*/
void bgy3d_poisson (const State *BHD, Vec uc_fft, Vec rho, real q)
{
const real *h = BHD->PD->h; /* h[3] */
const int *N = BHD->PD->N; /* N[3] */
const real h3 = h[0] * h[1] * h[3];
/* Get FFT of rho: rho(i, j, k) -> fft_rho(kx, ky, kz) placed into
complex uc_fft: */
MatMult (BHD->fft_mat, rho, uc_fft);
/* With q = -4π/ε₀ you would get the potential: */
/* scale by h3 in forward FFT */
const real scale = - q * h3 / 4;
/* Loop over local portion of the k-grid */
{
int i0, j0, k0, ni, nj, nk;
DMDAGetCorners (BHD->dc, &i0, &j0, &k0, &ni, &nj, &nk);
complex ***uc_fft_;
DMDAVecGetArray (BHD->dc, uc_fft, &uc_fft_);
for (int k = k0; k < k0 + nk; k++)
for (int j = j0; j < j0 + nj; j++)
for (int i = i0; i < i0 + ni; i++)
{
/*
For small i, j, and k and uniform box of size L this
expression approximates to (π/L)² (i² + j² + k²).
FIXME: SQR() macro evaluates the argument twice!
*/
const real k2 = \
SQR (sin (M_PI * i / N[0]) / h[0]) +
SQR (sin (M_PI * j / N[1]) / h[1]) +
SQR (sin (M_PI * k / N[2]) / h[2]);
real fac;
if (likely (k2 != 0.0))
fac = scale / k2;
else
fac = 0.0; /* gamma-point */
/* Here we compute in place: u(kx, ky, kz) := scale *
rho(kx, ky, kz) / k^2 */
uc_fft_[k][j][i] *= fac; /* complex */
}
DMDAVecRestoreArray (BHD->dc, uc_fft, &uc_fft_);
}
/*
* Leave IFFT to the caller when necessary, here we only pass out
* FFT coulomb potential
*/
}
/*
RHSFunction - Evaluates nonlinear function, F(u).
Input Parameters:
. ts - the TS context
. U - input vector
. ptr - optional user-defined context, as set by TSSetFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode RHSFunction(TS ts,PetscReal ftime,Vec U,Vec F,void *ptr)
{
/* PETSC_UNUSED AppCtx *user=(AppCtx*)ptr; */
DM da;
PetscErrorCode ierr;
PetscInt i,j,Mx,My,xs,ys,xm,ym;
PetscReal two = 2.0,hx,hy,sx,sy;
PetscScalar u,uxx,uyy,**uarray,**f;
Vec localU;
PetscFunctionBeginUser;
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);
hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx);
hy = 1.0/(PetscReal)(My-1); 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 = DMDAVecGetArray(da,localU,&uarray);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/* Get local grid boundaries */
ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr);
/* Compute function over the locally owned part of the grid */
for (j=ys; j<ys+ym; j++) {
for (i=xs; i<xs+xm; i++) {
if (i == 0 || j == 0 || i == Mx-1 || j == My-1) {
f[j][i] = uarray[j][i];
continue;
}
u = uarray[j][i];
uxx = (-two*u + uarray[j][i-1] + uarray[j][i+1])*sx;
uyy = (-two*u + uarray[j-1][i] + uarray[j+1][i])*sy;
f[j][i] = uxx + uyy;
}
}
/* Restore vectors */
ierr = DMDAVecRestoreArray(da,localU,&uarray);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr);
ierr = PetscLogFlops(11.0*ym*xm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode ini_bou(Vec X,AppCtx* user)
{
PetscErrorCode ierr;
DM cda;
DMDACoor2d **coors;
PetscScalar **p;
Vec gc;
PetscInt i,j;
PetscInt xs,ys,xm,ym,M,N;
PetscScalar xi,yi;
PetscScalar sigmax=user->sigmax,sigmay=user->sigmay;
PetscScalar rho =user->rho;
PetscScalar mux =user->mux,muy=user->muy;
PetscMPIInt rank;
PetscScalar sum;
PetscFunctionBeginUser;
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);
user->dx = (user->xmax - user->xmin)/(M-1); user->dy = (user->ymax - user->ymin)/(N-1);
ierr = DMGetCoordinateDM(user->da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(user->da,&gc);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,gc,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da,X,&p);CHKERRQ(ierr);
ierr = DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
/* mux and muy need to be grid points in the x and y-direction otherwise the solution goes unstable
muy is set by choosing the y domain, no. of grid points along y-direction so that muy is a grid point
in the y-direction. We only modify mux here
*/
mux = user->mux = coors[0][M/2+10].x; /* For -pi < x < pi, this should be some angle between 0 and pi/2 */
if (user->nonoiseinitial) {
for (i=xs; i < xs+xm; i++) {
for (j=ys; j < ys+ym; j++) {
xi = coors[j][i].x; yi = coors[j][i].y;
if ((xi == mux) && (yi == muy)) {
p[j][i] = 1.0;
}
}
}
} else {
/* Change PM_min accordingly */
user->PM_min = user->Pmax*sin(mux);
for (i=xs; i < xs+xm; i++) {
for (j=ys; j < ys+ym; j++) {
xi = coors[j][i].x; yi = coors[j][i].y;
p[j][i] = (0.5/(PETSC_PI*sigmax*sigmay*PetscSqrtScalar(1.0-rho*rho)))*PetscExpScalar(-0.5/(1-rho*rho)*(PetscPowScalar((xi-mux)/sigmax,2) + PetscPowScalar((yi-muy)/sigmay,2) - 2*rho*(xi-mux)*(yi-muy)/(sigmax*sigmay)));
}
}
}
ierr = DMDAVecRestoreArray(cda,gc,&coors);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da,X,&p);CHKERRQ(ierr);
ierr = VecSum(X,&sum);CHKERRQ(ierr);
ierr = VecScale(X,1.0/sum);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode DAApplyTrilinearMapping(DM da)
{
PetscErrorCode ierr;
PetscInt i,j,k;
PetscInt sx,nx,sy,ny,sz,nz;
Vec Gcoords;
DMDACoor3d ***XX;
PetscScalar xx,yy,zz;
DM cda;
PetscFunctionBeginUser;
ierr = DMDASetUniformCoordinates(da, -1.0,1.0, -1.0,1.0, -1.0,1.0 );CHKERRQ(ierr);
ierr = DMGetCoordinateDM(da,&cda);CHKERRQ(ierr);
ierr = DMGetCoordinates(da,&Gcoords);CHKERRQ(ierr);
ierr = DMDAVecGetArray(cda,Gcoords,&XX);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&sx,&sy,&sz,&nx,&ny,&nz);CHKERRQ(ierr);
for (i=sx; i<sx+nx; i++) {
for (j=sy; j<sy+ny; j++ ) {
for (k=sz; k<sz+nz; k++ ) {
PetscScalar Ni[8];
PetscScalar xi = XX[k][j][i].x;
PetscScalar eta = XX[k][j][i].y;
PetscScalar zeta = XX[k][j][i].z;
PetscScalar xn[] = {0.0,2.0,0.2,3.5, 0.0,2.1,0.23,3.125 };
PetscScalar yn[] = {-1.3,0.0,2.0,4.0, -1.45,-0.1,2.24,3.79 };
PetscScalar zn[] = {0.0,0.3,-0.1,0.123, 0.956,1.32,1.12,0.798 };
PetscInt p;
Ni[0] = 0.125*(1.0-xi)*(1.0-eta)*(1.0-zeta);
Ni[1] = 0.125*(1.0+xi)*(1.0-eta)*(1.0-zeta);
Ni[2] = 0.125*(1.0-xi)*(1.0+eta)*(1.0-zeta);
Ni[3] = 0.125*(1.0+xi)*(1.0+eta)*(1.0-zeta);
Ni[4] = 0.125*(1.0-xi)*(1.0-eta)*(1.0+zeta);
Ni[5] = 0.125*(1.0+xi)*(1.0-eta)*(1.0+zeta);
Ni[6] = 0.125*(1.0-xi)*(1.0+eta)*(1.0+zeta);
Ni[7] = 0.125*(1.0+xi)*(1.0+eta)*(1.0+zeta);
xx = yy = zz = 0.0;
for (p=0; p<8; p++ ) {
xx += Ni[p]*xn[p];
yy += Ni[p]*yn[p];
zz += Ni[p]*zn[p];
}
XX[k][j][i].x = xx;
XX[k][j][i].y = yy;
XX[k][j][i].z = zz;
}
}
}
ierr = DMDAVecRestoreArray(cda,Gcoords,&XX);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
Evaluates FU = Gradiant(L(w,u,lambda))
This local function acts on the ghosted version of U (accessed via DMCompositeGetLocalVectors() and
DMCompositeScatter()) BUT the global, nonghosted version of FU (via DMCompositeGetAccess()).
*/
PetscErrorCode ComputeFunction(SNES snes,Vec U,Vec FU,void *ctx)
{
PetscErrorCode ierr;
PetscInt xs,xm,i,N;
ULambda *u_lambda,*fu_lambda;
PetscScalar d,h,*w,*fw;
Vec vw,vfw,vu_lambda,vfu_lambda;
DM packer,red,da;
PetscFunctionBeginUser;
ierr = VecGetDM(U, &packer);CHKERRQ(ierr);
ierr = DMCompositeGetEntries(packer,&red,&da);CHKERRQ(ierr);
ierr = DMCompositeGetLocalVectors(packer,&vw,&vu_lambda);CHKERRQ(ierr);
ierr = DMCompositeScatter(packer,U,vw,vu_lambda);CHKERRQ(ierr);
ierr = DMCompositeGetAccess(packer,FU,&vfw,&vfu_lambda);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,0,&N,0,0,0,0,0,0,0,0,0,0,0);CHKERRQ(ierr);
ierr = VecGetArray(vw,&w);CHKERRQ(ierr);
ierr = VecGetArray(vfw,&fw);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,vu_lambda,&u_lambda);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,vfu_lambda,&fu_lambda);CHKERRQ(ierr);
d = N-1.0;
h = 1.0/d;
/* derivative of L() w.r.t. w */
if (xs == 0) { /* only first processor computes this */
fw[0] = -2.0*d*u_lambda[0].lambda;
}
/* derivative of L() w.r.t. u */
for (i=xs; i<xs+xm; i++) {
if (i == 0) fu_lambda[0].lambda = h*u_lambda[0].u + 2.*d*u_lambda[0].lambda - d*u_lambda[1].lambda;
else if (i == 1) fu_lambda[1].lambda = 2.*h*u_lambda[1].u + 2.*d*u_lambda[1].lambda - d*u_lambda[2].lambda;
else if (i == N-1) fu_lambda[N-1].lambda = h*u_lambda[N-1].u + 2.*d*u_lambda[N-1].lambda - d*u_lambda[N-2].lambda;
else if (i == N-2) fu_lambda[N-2].lambda = 2.*h*u_lambda[N-2].u + 2.*d*u_lambda[N-2].lambda - d*u_lambda[N-3].lambda;
else fu_lambda[i].lambda = 2.*h*u_lambda[i].u - d*(u_lambda[i+1].lambda - 2.0*u_lambda[i].lambda + u_lambda[i-1].lambda);
}
/* derivative of L() w.r.t. lambda */
for (i=xs; i<xs+xm; i++) {
if (i == 0) fu_lambda[0].u = 2.0*d*(u_lambda[0].u - w[0]);
else if (i == N-1) fu_lambda[N-1].u = 2.0*d*u_lambda[N-1].u;
else fu_lambda[i].u = -(d*(u_lambda[i+1].u - 2.0*u_lambda[i].u + u_lambda[i-1].u) - 2.0*h);
}
ierr = VecRestoreArray(vw,&w);CHKERRQ(ierr);
ierr = VecRestoreArray(vfw,&fw);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,vu_lambda,&u_lambda);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,vfu_lambda,&fu_lambda);CHKERRQ(ierr);
ierr = DMCompositeRestoreLocalVectors(packer,&vw,&vu_lambda);CHKERRQ(ierr);
ierr = DMCompositeRestoreAccess(packer,FU,&vfw,&vfu_lambda);CHKERRQ(ierr);
ierr = PetscLogFlops(13.0*N);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
{
PetscErrorCode ierr;
AppCtx *user=(AppCtx*)ctx;
DM cda;
DMDACoor2d **coors;
PetscScalar **p,**f,**pdot;
PetscInt i,j;
PetscInt xs,ys,xm,ym,M,N;
Vec localX,gc,localXdot;
PetscScalar p_adv1,p_adv2,p_diff;
PetscFunctionBeginUser;
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 = DMGetLocalVector(user->da,&localX);CHKERRQ(ierr);
ierr = DMGetLocalVector(user->da,&localXdot);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot);CHKERRQ(ierr);
ierr = DMGetCoordinatesLocal(user->da,&gc);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(cda,gc,&coors);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(user->da,localX,&p);CHKERRQ(ierr);
ierr = DMDAVecGetArrayRead(user->da,localXdot,&pdot);CHKERRQ(ierr);
ierr = DMDAVecGetArray(user->da,F,&f);CHKERRQ(ierr);
PetscScalar diffuse1,gamma;
gamma = user->D*user->ws/(2*user->H);
diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda));
user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1;
for (i=xs; i < xs+xm; i++) {
for (j=ys; j < ys+ym; j++) {
ierr = adv1(p,coors[j][i].y,i,j,M,&p_adv1,user);CHKERRQ(ierr);
ierr = adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user);CHKERRQ(ierr);
ierr = diffuse(p,i,j,t,&p_diff,user);CHKERRQ(ierr);
f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i];
}
}
ierr = DMDAVecRestoreArrayRead(user->da,localX,&p);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(user->da,localX,&pdot);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(user->da,&localX);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(user->da,&localXdot);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(user->da,F,&f);CHKERRQ(ierr);
ierr = DMDAVecRestoreArrayRead(cda,gc,&coors);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
PostCheck - Optional user-defined routine that checks the validity of
candidate steps of a line search method. Set by SNESLineSearchSetPostCheck().
Input Parameters:
snes - the SNES context
ctx - optional user-defined context for private data for the
monitor routine, as set by SNESLineSearchSetPostCheck()
xcurrent - current solution
y - search direction and length
x - the new candidate iterate
Output Parameters:
y - proposed step (search direction and length) (possibly changed)
x - current iterate (possibly modified)
*/
PetscErrorCode PostCheck(SNESLineSearch linesearch,Vec xcurrent,Vec y,Vec x,PetscBool *changed_y,PetscBool *changed_x, void * ctx)
{
PetscErrorCode ierr;
PetscInt i,iter,xs,xm;
StepCheckCtx *check;
ApplicationCtx *user;
PetscScalar *xa,*xa_last,tmp;
PetscReal rdiff;
DM da;
SNES snes;
PetscFunctionBeginUser;
*changed_x = PETSC_FALSE;
*changed_y = PETSC_FALSE;
ierr = SNESLineSearchGetSNES(linesearch, &snes);CHKERRQ(ierr);
check = (StepCheckCtx*)ctx;
user = check->user;
ierr = SNESGetIterationNumber(snes,&iter);CHKERRQ(ierr);
ierr = SNESLineSearchGetPreCheck(linesearch, NULL, (void**)&check);CHKERRQ(ierr);
/* iteration 1 indicates we are working on the second iteration */
if (iter > 0) {
da = user->da;
ierr = PetscPrintf(PETSC_COMM_WORLD,"Checking candidate step at iteration %D with tolerance %G\n",iter,check->tolerance);CHKERRQ(ierr);
/* Access local array data */
ierr = DMDAVecGetArray(da,check->last_step,&xa_last);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,x,&xa);CHKERRQ(ierr);
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
If we fail the user-defined check for validity of the candidate iterate,
then modify the iterate as we like. (Note that the particular modification
below is intended simply to demonstrate how to manipulate this data, not
as a meaningful or appropriate choice.)
*/
for (i=xs; i<xs+xm; i++) {
if (!PetscAbsScalar(xa[i])) rdiff = 2*check->tolerance;
else rdiff = PetscAbsScalar((xa[i] - xa_last[i])/xa[i]);
if (rdiff > check->tolerance) {
tmp = xa[i];
xa[i] = .5*(xa[i] + xa_last[i]);
*changed_x = PETSC_TRUE;
ierr = PetscPrintf(PETSC_COMM_WORLD," Altering entry %D: x=%G, x_last=%G, diff=%G, x_new=%G\n",
i,PetscAbsScalar(tmp),PetscAbsScalar(xa_last[i]),rdiff,PetscAbsScalar(xa[i]));CHKERRQ(ierr);
}
}
ierr = DMDAVecRestoreArray(da,check->last_step,&xa_last);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,x,&xa);CHKERRQ(ierr);
}
ierr = VecCopy(x,check->last_step);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode DMDAGetElements_3D(DM dm,PetscInt *nel,PetscInt *nen,const PetscInt *e[])
{
PetscErrorCode ierr;
DM_DA *da = (DM_DA*)dm->data;
PetscInt i,xs,xe,Xs,Xe;
PetscInt j,ys,ye,Ys,Ye;
PetscInt k,zs,ze,Zs,Ze;
PetscInt cnt=0, cell[8], ns=6, nn=4;
PetscInt c, split[] = {0,1,3,7,
0,1,7,4,
1,2,3,7,
1,2,7,6,
1,4,5,7,
1,5,6,7};
PetscFunctionBegin;
if (!da->e) {
if (!da->s) SETERRQ(PetscObjectComm((PetscObject)dm),PETSC_ERR_SUP,"Cannot get elements for DMDA with zero stencil width");
if (da->elementtype == DMDA_ELEMENT_P1) {ns=6; nn=4;}
if (da->elementtype == DMDA_ELEMENT_Q1) {ns=1; nn=8;}
ierr = DMDAGetCorners(dm,&xs,&ys,&zs,&xe,&ye,&ze);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(dm,&Xs,&Ys,&Zs,&Xe,&Ye,&Ze);CHKERRQ(ierr);
xe += xs; Xe += Xs; if (xs != Xs) xs -= 1;
ye += ys; Ye += Ys; if (ys != Ys) ys -= 1;
ze += zs; Ze += Zs; if (zs != Zs) zs -= 1;
da->ne = ns*(xe - xs - 1)*(ye - ys - 1)*(ze - zs - 1);
ierr = PetscMalloc1(1 + nn*da->ne,&da->e);CHKERRQ(ierr);
for (k=zs; k<ze-1; k++) {
for (j=ys; j<ye-1; j++) {
for (i=xs; i<xe-1; i++) {
cell[0] = (i-Xs ) + (j-Ys )*(Xe-Xs) + (k-Zs )*(Xe-Xs)*(Ye-Ys);
cell[1] = (i-Xs+1) + (j-Ys )*(Xe-Xs) + (k-Zs )*(Xe-Xs)*(Ye-Ys);
cell[2] = (i-Xs+1) + (j-Ys+1)*(Xe-Xs) + (k-Zs )*(Xe-Xs)*(Ye-Ys);
cell[3] = (i-Xs ) + (j-Ys+1)*(Xe-Xs) + (k-Zs )*(Xe-Xs)*(Ye-Ys);
cell[4] = (i-Xs ) + (j-Ys )*(Xe-Xs) + (k-Zs+1)*(Xe-Xs)*(Ye-Ys);
cell[5] = (i-Xs+1) + (j-Ys )*(Xe-Xs) + (k-Zs+1)*(Xe-Xs)*(Ye-Ys);
cell[6] = (i-Xs+1) + (j-Ys+1)*(Xe-Xs) + (k-Zs+1)*(Xe-Xs)*(Ye-Ys);
cell[7] = (i-Xs ) + (j-Ys+1)*(Xe-Xs) + (k-Zs+1)*(Xe-Xs)*(Ye-Ys);
if (da->elementtype == DMDA_ELEMENT_P1) {
for (c=0; c<ns*nn; c++) da->e[cnt++] = cell[split[c]];
}
if (da->elementtype == DMDA_ELEMENT_Q1) {
for (c=0; c<ns*nn; c++) da->e[cnt++] = cell[c];
}
}
}
}
}
*nel = da->ne;
*nen = nn;
*e = da->e;
PetscFunctionReturn(0);
}
/*
FormFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. ts - the TS context
. X - input vector
. ptr - optional user-defined context, as set by SNESSetFunction()
Output Parameter:
. F - function vector
*/
PetscErrorCode FormFunction(TS ts,PetscReal ftime,Vec X,Vec F,void *ptr)
{
DM da;
PetscErrorCode ierr;
PetscInt i,Mx,xs,xm;
PetscReal hx,sx;
PetscScalar *x,*f;
Vec localX;
UserCtx *ctx = (UserCtx*)ptr;
PetscFunctionBegin;
ierr = TSGetDM(ts,&da);CHKERRQ(ierr);
ierr = DMGetLocalVector(da,&localX);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);CHKERRQ(ierr);
hx = 1.0/(PetscReal)Mx; sx = 1.0/(hx*hx);
/*
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 pointers to vector data
*/
ierr = DMDAVecGetArrayRead(da,localX,&x);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr);
/*
Get local grid boundaries
*/
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
/*
Compute function over the locally owned part of the grid
*/
for (i=xs; i<xs+xm; i++) {
f[i] = ctx->kappa*(x[i-1] + x[i+1] - 2.0*x[i])*sx;
if (ctx->allencahn) f[i] += (x[i] - x[i]*x[i]*x[i]);
}
/*
Restore vectors
*/
ierr = DMDAVecRestoreArrayRead(da,localX,&x);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
FormFunction - Evaluates nonlinear function, F(x).
Input Parameters:
. snes - the SNES context
. x - input vector
. ctx - optional user-defined context, as set by SNESSetFunction()
Output Parameter:
. f - function vector
Note:
The user-defined context can contain any application-specific
data needed for the function evaluation.
*/
PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *ctx)
{
DM da = (DM) ctx;
PetscScalar *xx,*ff;
PetscReal h;
PetscErrorCode ierr;
PetscInt i,M,xs,xm;
Vec xlocal;
PetscFunctionBeginUser;
/* Get local work vector */
ierr = DMGetLocalVector(da,&xlocal);CHKERRQ(ierr);
/*
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,xlocal);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,x,INSERT_VALUES,xlocal);CHKERRQ(ierr);
/*
Get pointers to vector data.
- The vector xlocal includes ghost point; the vectors x and f do
NOT include ghost points.
- Using DMDAVecGetArray() allows accessing the values using global ordering
*/
ierr = DMDAVecGetArray(da,xlocal,&xx);CHKERRQ(ierr);
ierr = DMDAVecGetArray(da,f,&ff);CHKERRQ(ierr);
/*
Get local grid boundaries (for 1-dimensional DMDA):
xs, xm - starting grid index, width of local grid (no ghost points)
*/
ierr = DMDAGetCorners(da,&xs,NULL,NULL,&xm,NULL,NULL);CHKERRQ(ierr);
ierr = DMDAGetInfo(da,NULL,&M,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL);CHKERRQ(ierr);
/*
Compute function over locally owned part of the grid
Note the [i-1] and [i+1] will automatically access the ghost points from other processes or the periodic points.
*/
h = 1.0/M;
for (i=xs; i<xs+xm; i++) ff[i] = (xx[i-1] - 2.0*xx[i] + xx[i+1])/(h*h) - PetscSinReal(2.0*PETSC_PI*i*h);
/*
Restore vectors
*/
ierr = DMDAVecRestoreArray(da,xlocal,&xx);CHKERRQ(ierr);
ierr = DMDAVecRestoreArray(da,f,&ff);CHKERRQ(ierr);
ierr = DMRestoreLocalVector(da,&xlocal);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
