PetscErrorCode StokesExactSolution(Stokes *s)
{
PetscInt row, start, end, i, j;
PetscScalar val;
Vec y0,y1;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* velocity part */
ierr = VecGetSubVector(s->y, s->isg[0], &y0);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(y0, &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row,&i,&j);CHKERRQ(ierr);
if (row < s->nx*s->ny) {
val = StokesExactVelocityX(j*s->hy+s->hy/2);
} else {
val = 0;
}
ierr = VecSetValue(y0, row, val, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecRestoreSubVector(s->y, s->isg[0], &y0);CHKERRQ(ierr);
/* pressure part */
ierr = VecGetSubVector(s->y, s->isg[1], &y1);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(y1, &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
val = StokesExactPressure(i*s->hx+s->hx/2);
ierr = VecSetValue(y1, row, val, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecRestoreSubVector(s->y, s->isg[1], &y1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesRhs(Stokes *s)
{
PetscInt row, start, end, i, j;
PetscScalar val;
Vec b0,b1;
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* velocity part */
ierr = VecGetSubVector(s->b, s->isg[0], &b0);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(b0, &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
if (row < s->nx*s->ny) {
ierr = StokesRhsMomX(s, i, j, &val);CHKERRQ(ierr);
} else if (row < 2*s->nx*s->ny) {
ierr = StokesRhsMomY(s, i, j, &val);CHKERRQ(ierr);
}
ierr = VecSetValue(b0, row, val, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecRestoreSubVector(s->b, s->isg[0], &b0);CHKERRQ(ierr);
/* pressure part */
ierr = VecGetSubVector(s->b, s->isg[1], &b1);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(b1, &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
ierr = StokesRhsMass(s, i, j, &val);CHKERRQ(ierr);
ierr = VecSetValue(b1, row, val, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecRestoreSubVector(s->b, s->isg[1], &b1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupMatBlock01(Stokes *s)
{
PetscInt row, start, end, size, i, j;
PetscInt cols[5];
PetscScalar vals[5];
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* A[1] is 2N-by-N */
ierr = MatCreate(PETSC_COMM_WORLD, &s->subA[1]);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->subA[1],"a01_");
ierr = MatSetSizes(s->subA[1],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->subA[1],MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->subA[1],5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(s->subA[1],&start,&end);CHKERRQ(ierr);
ierr = MatSetOption(s->subA[1],MAT_IGNORE_ZERO_ENTRIES,PETSC_TRUE);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
/* first part: rows 0 to (nx*ny-1) */
if (row < s->nx*s->ny) {
ierr = StokesStencilGradientX(s, i, j, &size, cols, vals);CHKERRQ(ierr);
}
/* second part: rows (nx*ny) to (2*nx*ny-1) */
else {
ierr = StokesStencilGradientY(s, i, j, &size, cols, vals);CHKERRQ(ierr);
}
ierr = MatSetValues(s->subA[1], 1, &row, size, cols, vals, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(s->subA[1], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->subA[1], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupMatBlock00(Stokes *s)
{
PetscInt row, start, end, size, i, j;
PetscInt cols[5];
PetscScalar vals[5];
PetscErrorCode ierr;
PetscFunctionBeginUser;
/* A[0] is 2N-by-2N */
ierr = MatCreate(PETSC_COMM_WORLD,&s->subA[0]);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->subA[0],"a00_");CHKERRQ(ierr);
ierr = MatSetSizes(s->subA[0],PETSC_DECIDE,PETSC_DECIDE,2*s->nx*s->ny,2*s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->subA[0],MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->subA[0],5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(s->subA[0], &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
/* first part: rows 0 to (nx*ny-1) */
ierr = StokesStencilLaplacian(s, i, j, &size, cols, vals);CHKERRQ(ierr);
/* second part: rows (nx*ny) to (2*nx*ny-1) */
if (row >= s->nx*s->ny) {
for (i = 0; i < 5; i++) cols[i] = cols[i] + s->nx*s->ny;
}
for (i = 0; i < 5; i++) vals[i] = -1.0*vals[i]; /* dynamic viscosity coef mu=-1 */
ierr = MatSetValues(s->subA[0], 1, &row, size, cols, vals, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(s->subA[0], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->subA[0], MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode StokesSetupMatFp(Stokes *s)
{
PetscInt row, start, end, size, i, j;
PetscInt cols[5];
PetscScalar vals[5];
PetscErrorCode ierr;
PetscFunctionBeginUser;
// Fp is N-by-N
ierr = MatCreate(PETSC_COMM_WORLD,&s->Fp);CHKERRQ(ierr);
ierr = MatSetOptionsPrefix(s->Fp,"Fp_");CHKERRQ(ierr);
ierr = MatSetSizes(s->Fp,PETSC_DECIDE,PETSC_DECIDE,s->nx*s->ny,s->nx*s->ny);CHKERRQ(ierr);
ierr = MatSetType(s->Fp,MATMPIAIJ);CHKERRQ(ierr);
ierr = MatMPIAIJSetPreallocation(s->Fp,5,NULL,5,NULL);CHKERRQ(ierr);
ierr = MatGetOwnershipRange(s->Fp, &start, &end);CHKERRQ(ierr);
for (row = start; row < end; row++) {
ierr = StokesGetPosition(s, row, &i, &j);CHKERRQ(ierr);
ierr = StokesStencilLaplacian(s, i, j, &size, cols, vals);CHKERRQ(ierr);
for (i = 0; i < 5; i++) vals[i] = -1.0*vals[i]; //* dynamic viscosity coef mu=-1
ierr = MatSetValues(s->Fp, 1, &row, size, cols, vals, INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(s->Fp, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(s->Fp, MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
PetscFunctionReturn(0);
}