int FormJacobian_Grid(GridCtx *grid,Mat *J)
{
Mat jac = *J;
PetscErrorCode ierr;
PetscInt i,j,row,mx,my,xs,ys,xm,ym,Xs,Ys,Xm,Ym,col[5];
PetscInt nloc,grow;
const PetscInt *ltog;
PetscScalar two = 2.0,one = 1.0,v[5],hx,hy,hxdhy,hydhx,value;
mx = grid->mx; my = grid->my;
hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
hxdhy = hx/hy; hydhx = hy/hx;
/* Get ghost points */
ierr = DMDAGetCorners(grid->da,&xs,&ys,0,&xm,&ym,0);CHKERRQ(ierr);
ierr = DMDAGetGhostCorners(grid->da,&Xs,&Ys,0,&Xm,&Ym,0);CHKERRQ(ierr);
ierr = DMDAGetGlobalIndices(grid->da,&nloc,<og);CHKERRQ(ierr);
/* Evaluate Jacobian of function */
for (j=ys; j<ys+ym; j++) {
row = (j - Ys)*Xm + xs - Xs - 1;
for (i=xs; i<xs+xm; i++) {
row++;
grow = ltog[row];
if (i > 0 && i < mx-1 && j > 0 && j < my-1) {
v[0] = -hxdhy; col[0] = ltog[row - Xm];
v[1] = -hydhx; col[1] = ltog[row - 1];
v[2] = two*(hydhx + hxdhy); col[2] = grow;
v[3] = -hydhx; col[3] = ltog[row + 1];
v[4] = -hxdhy; col[4] = ltog[row + Xm];
ierr = MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
} else if ((i > 0 && i < mx-1) || (j > 0 && j < my-1)) {
value = .5*two*(hydhx + hxdhy);
ierr = MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);CHKERRQ(ierr);
} else {
value = .25*two*(hydhx + hxdhy);
ierr = MatSetValues(jac,1,&grow,1,&grow,&value,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
ierr = DMDARestoreGlobalIndices(grid->da,&nloc,<og);CHKERRQ(ierr);
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
return 0;
}
/*
ComputeJacobian - Evaluates Jacobian matrix.
Input Parameters:
. x - input vector
. user - user-defined application context
Output Parameters:
. jac - Jacobian matrix
. flag - flag indicating matrix structure
Notes:
Due to grid point reordering with DMDAs, we must always work
with the local grid points, and then transform them to the new
global numbering with the "ltog" mapping (via DMDAGetGlobalIndices()).
We cannot work directly with the global numbers for the original
uniprocessor grid!
*/
PetscErrorCode ComputeJacobian(AppCtx *user,Vec X,Mat jac)
{
PetscErrorCode ierr;
Vec localX = user->localX; /* local vector */
const PetscInt *ltog; /* local-to-global mapping */
PetscInt i,j,row,mx,my,col[5];
PetscInt nloc,xs,ys,xm,ym,gxs,gys,gxm,gym,grow;
PetscScalar two = 2.0,one = 1.0,lambda,v[5],hx,hy,hxdhy,hydhx,sc,*x;
mx = user->mx; my = user->my; lambda = user->param;
hx = one/(PetscReal)(mx-1); hy = one/(PetscReal)(my-1);
sc = hx*hy; 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 pointer to vector data
*/
ierr = VecGetArray(localX,&x);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);
/*
Get the global node numbers for all local nodes, including ghost points
*/
ierr = DMDAGetGlobalIndices(user->da,&nloc,<og);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. The "grow"
parameter computed below specifies the global row number
corresponding to each local grid point.
- 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).
- Always specify global row and columns of matrix entries.
- Here, we set all entries for a particular row at once.
*/
for (j=ys; j<ys+ym; j++) {
row = (j - gys)*gxm + xs - gxs - 1;
for (i=xs; i<xs+xm; i++) {
row++;
grow = ltog[row];
/* boundary points */
if (i == 0 || j == 0 || i == mx-1 || j == my-1) {
ierr = MatSetValues(jac,1,&grow,1,&grow,&one,INSERT_VALUES);CHKERRQ(ierr);
continue;
}
/* interior grid points */
v[0] = -hxdhy; col[0] = ltog[row - gxm];
v[1] = -hydhx; col[1] = ltog[row - 1];
v[2] = two*(hydhx + hxdhy) - sc*lambda*PetscExpScalar(x[row]); col[2] = grow;
v[3] = -hydhx; col[3] = ltog[row + 1];
v[4] = -hxdhy; col[4] = ltog[row + gxm];
ierr = MatSetValues(jac,1,&grow,5,col,v,INSERT_VALUES);CHKERRQ(ierr);
}
}
ierr = DMDARestoreGlobalIndices(user->da,&nloc,<og);CHKERRQ(ierr);
/*
Assemble matrix, using the 2-step process:
MatAssemblyBegin(), MatAssemblyEnd().
By placing code between these two statements, computations can be
done while messages are in transition.
*/
ierr = MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = VecRestoreArray(localX,&x);CHKERRQ(ierr);
ierr = MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
return 0;
}
int main(int argc,char **argv)
{
PetscMPIInt rank;
PetscInt M = 3,N = 5,P=3,s=1,w=2,nloc,l,i,j,k,kk,m = PETSC_DECIDE,n = PETSC_DECIDE,p = PETSC_DECIDE;
PetscErrorCode ierr;
PetscInt Xs,Xm,Ys,Ym,Zs,Zm,iloc,*iglobal;
const PetscInt *ltog;
PetscInt *lx = NULL,*ly = NULL,*lz = NULL;
PetscBool test_order = PETSC_FALSE;
DM da;
PetscViewer viewer;
Vec local,global;
PetscScalar value;
DMBoundaryType bx = DM_BOUNDARY_NONE,by = DM_BOUNDARY_NONE,bz = DM_BOUNDARY_NONE;
DMDAStencilType stencil_type = DMDA_STENCIL_BOX;
AO ao;
PetscBool flg = PETSC_FALSE;
ierr = PetscInitialize(&argc,&argv,(char*)0,help);CHKERRQ(ierr);
ierr = PetscViewerDrawOpen(PETSC_COMM_WORLD,0,"",300,0,400,300,&viewer);CHKERRQ(ierr);
/* Read options */
ierr = PetscOptionsGetInt(NULL,"-NX",&M,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-NY",&N,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-NZ",&P,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-n",&n,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-p",&p,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-s",&s,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetInt(NULL,"-w",&w,NULL);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-star",&flg,NULL);CHKERRQ(ierr);
if (flg) stencil_type = DMDA_STENCIL_STAR;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-box",&flg,NULL);CHKERRQ(ierr);
if (flg) stencil_type = DMDA_STENCIL_BOX;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-xperiodic",&flg,NULL);CHKERRQ(ierr);
if (flg) bx = DM_BOUNDARY_PERIODIC;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-xghosted",&flg,NULL);CHKERRQ(ierr);
if (flg) bx = DM_BOUNDARY_GHOSTED;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-xnonghosted",&flg,NULL);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-yperiodic",&flg,NULL);CHKERRQ(ierr);
if (flg) by = DM_BOUNDARY_PERIODIC;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-yghosted",&flg,NULL);CHKERRQ(ierr);
if (flg) by = DM_BOUNDARY_GHOSTED;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-ynonghosted",&flg,NULL);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-zperiodic",&flg,NULL);CHKERRQ(ierr);
if (flg) bz = DM_BOUNDARY_PERIODIC;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-zghosted",&flg,NULL);CHKERRQ(ierr);
if (flg) bz = DM_BOUNDARY_GHOSTED;
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-znonghosted",&flg,NULL);CHKERRQ(ierr);
ierr = PetscOptionsGetBool(NULL,"-testorder",&test_order,NULL);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-distribute",&flg,NULL);CHKERRQ(ierr);
if (flg) {
if (m == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -m option with -distribute option");
ierr = PetscMalloc1(m,&lx);CHKERRQ(ierr);
for (i=0; i<m-1; i++) lx[i] = 4;
lx[m-1] = M - 4*(m-1);
if (n == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -n option with -distribute option");
ierr = PetscMalloc1(n,&ly);CHKERRQ(ierr);
for (i=0; i<n-1; i++) ly[i] = 2;
ly[n-1] = N - 2*(n-1);
if (p == PETSC_DECIDE) SETERRQ(PETSC_COMM_WORLD,1,"Must set -p option with -distribute option");
ierr = PetscMalloc1(p,&lz);CHKERRQ(ierr);
for (i=0; i<p-1; i++) lz[i] = 2;
lz[p-1] = P - 2*(p-1);
}
/* Create distributed array and get vectors */
ierr = DMDACreate3d(PETSC_COMM_WORLD,bx,by,bz,stencil_type,M,N,P,m,n,p,w,s,lx,ly,lz,&da);CHKERRQ(ierr);
ierr = PetscFree(lx);CHKERRQ(ierr);
ierr = PetscFree(ly);CHKERRQ(ierr);
ierr = PetscFree(lz);CHKERRQ(ierr);
ierr = DMView(da,viewer);CHKERRQ(ierr);
ierr = DMCreateGlobalVector(da,&global);CHKERRQ(ierr);
ierr = DMCreateLocalVector(da,&local);CHKERRQ(ierr);
/* Set global vector; send ghost points to local vectors */
value = 1;
ierr = VecSet(global,value);CHKERRQ(ierr);
ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
/* Scale local vectors according to processor rank; pass to global vector */
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
value = rank;
ierr = VecScale(local,value);CHKERRQ(ierr);
ierr = DMLocalToGlobalBegin(da,local,INSERT_VALUES,global);CHKERRQ(ierr);
ierr = DMLocalToGlobalEnd(da,local,INSERT_VALUES,global);CHKERRQ(ierr);
if (!test_order) { /* turn off printing when testing ordering mappings */
if (M*N*P<40) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"\nGlobal Vector:\n");CHKERRQ(ierr);
ierr = VecView(global,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"\n");CHKERRQ(ierr);
}
}
/* Send ghost points to local vectors */
ierr = DMGlobalToLocalBegin(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
ierr = DMGlobalToLocalEnd(da,global,INSERT_VALUES,local);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-local_print",&flg,NULL);CHKERRQ(ierr);
if (flg) {
PetscViewer sviewer;
ierr = PetscViewerASCIISynchronizedAllow(PETSC_VIEWER_STDOUT_WORLD,PETSC_TRUE);CHKERRQ(ierr);
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"\nLocal Vector: processor %d\n",rank);CHKERRQ(ierr);
ierr = PetscViewerGetSingleton(PETSC_VIEWER_STDOUT_WORLD,&sviewer);CHKERRQ(ierr);
ierr = VecView(local,sviewer);CHKERRQ(ierr);
ierr = PetscViewerRestoreSingleton(PETSC_VIEWER_STDOUT_WORLD,&sviewer);CHKERRQ(ierr);
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);CHKERRQ(ierr);
}
/* Tests mappings betweeen application/PETSc orderings */
if (test_order) {
ierr = DMDAGetGhostCorners(da,&Xs,&Ys,&Zs,&Xm,&Ym,&Zm);CHKERRQ(ierr);
ierr = DMDAGetGlobalIndices(da,&nloc,<og);CHKERRQ(ierr);
ierr = DMDAGetAO(da,&ao);CHKERRQ(ierr);
/* ierr = AOView(ao,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); */
ierr = PetscMalloc1(nloc,&iglobal);CHKERRQ(ierr);
/* Set iglobal to be global indices for each processor's local and ghost nodes,
using the DMDA ordering of grid points */
kk = 0;
for (k=Zs; k<Zs+Zm; k++) {
for (j=Ys; j<Ys+Ym; j++) {
for (i=Xs; i<Xs+Xm; i++) {
iloc = w*((k-Zs)*Xm*Ym + (j-Ys)*Xm + i-Xs);
for (l=0; l<w; l++) {
iglobal[kk++] = ltog[iloc+l];
}
}
}
}
/* Map this to the application ordering (which for DMDAs is just the natural ordering
that would be used for 1 processor, numbering most rapidly by x, then y, then z) */
ierr = AOPetscToApplication(ao,nloc,iglobal);CHKERRQ(ierr);
/* Then map the application ordering back to the PETSc DMDA ordering */
ierr = AOApplicationToPetsc(ao,nloc,iglobal);CHKERRQ(ierr);
/* Verify the mappings */
kk=0;
for (k=Zs; k<Zs+Zm; k++) {
for (j=Ys; j<Ys+Ym; j++) {
for (i=Xs; i<Xs+Xm; i++) {
iloc = w*((k-Zs)*Xm*Ym + (j-Ys)*Xm + i-Xs);
for (l=0; l<w; l++) {
if (iglobal[kk] != ltog[iloc+l]) {
ierr = PetscPrintf(MPI_COMM_WORLD,"[%D] Problem with mapping: z=%D, j=%D, i=%D, l=%D, petsc1=%D, petsc2=%D\n",
rank,k,j,i,l,ltog[iloc+l],iglobal[kk]);
}
kk++;
}
}
}
}
ierr = PetscFree(iglobal);CHKERRQ(ierr);
ierr = DMDARestoreGlobalIndices(da,&nloc,<og);CHKERRQ(ierr);
}
/* Free memory */
ierr = PetscViewerDestroy(&viewer);CHKERRQ(ierr);
ierr = VecDestroy(&local);CHKERRQ(ierr);
ierr = VecDestroy(&global);CHKERRQ(ierr);
ierr = DMDestroy(&da);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
