-pc_gasm_print_subdomains\n \n";
/*
Note: This example focuses on setting the subdomains for the GASM
preconditioner for a problem on a 2D rectangular grid. See ex1.c
and ex2.c for more detailed comments on the basic usage of KSP
(including working with matrices and vectors).
The GASM preconditioner is fully parallel. The user-space routine
CreateSubdomains2D that computes the domain decomposition is also parallel
and attempts to generate both subdomains straddling processors and multiple
domains per processor.
This matrix in this linear system arises from the discretized Laplacian,
and thus is not very interesting in terms of experimenting with variants
of the GASM preconditioner.
*/
/*T
Concepts: KSP^Additive Schwarz Method (GASM) with user-defined subdomains
Processors: n
T*/
/*
Include "petscksp.h" so that we can use KSP solvers. Note that this file
automatically includes:
petscsys.h - base PETSc routines petscvec.h - vectors
petscmat.h - matrices
petscis.h - index sets petscksp.h - Krylov subspace methods
petscviewer.h - viewers petscpc.h - preconditioners
*/
#include <petscksp.h>
#include <petscmat.h>
int main(int argc,char **args)
{
Vec x,b,u; /* approx solution, RHS, exact solution */
Mat A,perA; /* linear system matrix */
KSP ksp; /* linear solver context */
PC pc; /* PC context */
PetscInt overlap; /* width of subdomain overlap */
PetscInt m,n; /* mesh dimensions in x- and y- directions */
PetscInt M,N; /* number of subdomains in x- and y- directions */
PetscInt i,j,Ii,J,Istart,Iend;
PetscErrorCode ierr;
PetscMPIInt size;
PetscBool flg;
PetscBool user_set_subdomains;
PetscScalar v, one = 1.0;
MatPartitioning part;
IS coarseparts,fineparts;
IS is,isn,isrows;
MPI_Comm comm;
PetscReal e;
ierr = PetscInitialize(&argc,&args,(char*)0,help);
if (ierr) return ierr;
comm = PETSC_COMM_WORLD;
ierr = MPI_Comm_size(comm,&size);
CHKERRQ(ierr);
ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"ex62","PC");
CHKERRQ(ierr);
m = 15;
ierr = PetscOptionsInt("-M", "Number of mesh points in the x-direction","PCGASMCreateSubdomains2D",m,&m,NULL);
CHKERRQ(ierr);
n = 17;
ierr = PetscOptionsInt("-N","Number of mesh points in the y-direction","PCGASMCreateSubdomains2D",n,&n,NULL);
CHKERRQ(ierr);
user_set_subdomains = PETSC_FALSE;
ierr = PetscOptionsBool("-user_set_subdomains","Use the user-specified 2D tiling of mesh by subdomains","PCGASMCreateSubdomains2D",user_set_subdomains,&user_set_subdomains,NULL);
CHKERRQ(ierr);
M = 2;
ierr = PetscOptionsInt("-Mdomains","Number of subdomain tiles in the x-direction","PCGASMSetSubdomains2D",M,&M,NULL);
CHKERRQ(ierr);
N = 1;
ierr = PetscOptionsInt("-Ndomains","Number of subdomain tiles in the y-direction","PCGASMSetSubdomains2D",N,&N,NULL);
CHKERRQ(ierr);
overlap = 1;
ierr = PetscOptionsInt("-overlap","Size of tile overlap.","PCGASMSetSubdomains2D",overlap,&overlap,NULL);
CHKERRQ(ierr);
ierr = PetscOptionsEnd();
CHKERRQ(ierr);
/* -------------------------------------------------------------------
Compute the matrix and right-hand-side vector that define
the linear system, Ax = b.
------------------------------------------------------------------- */
/*
Assemble the matrix for the five point stencil, YET AGAIN
*/
ierr = MatCreate(comm,&A);
CHKERRQ(ierr);
ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,m*n,m*n);
CHKERRQ(ierr);
ierr = MatSetFromOptions(A);
CHKERRQ(ierr);
ierr = MatSetUp(A);
CHKERRQ(ierr);
ierr = MatGetOwnershipRange(A,&Istart,&Iend);
CHKERRQ(ierr);
for (Ii=Istart; Ii<Iend; Ii++) {
v = -1.0;
i = Ii/n;
j = Ii - i*n;
if (i>0) {
J = Ii - n;
ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
if (i<m-1) {
J = Ii + n;
ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j>0) {
J = Ii - 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
if (j<n-1) {
J = Ii + 1;
ierr = MatSetValues(A,1,&Ii,1,&J,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
v = 4.0;
ierr = MatSetValues(A,1,&Ii,1,&Ii,&v,INSERT_VALUES);
CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
/*
Partition the graph of the matrix
*/
ierr = MatPartitioningCreate(comm,&part);
CHKERRQ(ierr);
ierr = MatPartitioningSetAdjacency(part,A);
CHKERRQ(ierr);
ierr = MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);
CHKERRQ(ierr);
ierr = MatPartitioningHierarchicalSetNcoarseparts(part,2);
CHKERRQ(ierr);
ierr = MatPartitioningHierarchicalSetNfineparts(part,2);
CHKERRQ(ierr);
ierr = MatPartitioningSetFromOptions(part);
CHKERRQ(ierr);
/* get new processor owner number of each vertex */
ierr = MatPartitioningApply(part,&is);
CHKERRQ(ierr);
/* get coarse parts according to which we rearrange the matrix */
ierr = MatPartitioningHierarchicalGetCoarseparts(part,&coarseparts);
CHKERRQ(ierr);
/* fine parts are used with coarse parts */
ierr = MatPartitioningHierarchicalGetFineparts(part,&fineparts);
CHKERRQ(ierr);
/* get new global number of each old global number */
ierr = ISPartitioningToNumbering(is,&isn);
CHKERRQ(ierr);
ierr = ISBuildTwoSided(is,NULL,&isrows);
CHKERRQ(ierr);
ierr = MatGetSubMatrix(A,isrows,isrows,MAT_INITIAL_MATRIX,&perA);
CHKERRQ(ierr);
ierr = MatCreateVecs(perA,&b,NULL);
CHKERRQ(ierr);
ierr = VecSetFromOptions(b);
CHKERRQ(ierr);
ierr = VecDuplicate(b,&u);
CHKERRQ(ierr);
ierr = VecDuplicate(b,&x);
CHKERRQ(ierr);
ierr = VecSet(u,one);
CHKERRQ(ierr);
ierr = MatMult(perA,u,b);
CHKERRQ(ierr);
ierr = KSPCreate(comm,&ksp);
CHKERRQ(ierr);
/*
Set operators. Here the matrix that defines the linear system
also serves as the preconditioning matrix.
*/
ierr = KSPSetOperators(ksp,perA,perA);
CHKERRQ(ierr);
/*
Set the default preconditioner for this program to be GASM
*/
ierr = KSPGetPC(ksp,&pc);
CHKERRQ(ierr);
ierr = PCSetType(pc,PCGASM);
CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);
CHKERRQ(ierr);
/* -------------------------------------------------------------------
Solve the linear system
------------------------------------------------------------------- */
ierr = KSPSolve(ksp,b,x);
CHKERRQ(ierr);
/* -------------------------------------------------------------------
Compare result to the exact solution
------------------------------------------------------------------- */
ierr = VecAXPY(x,-1.0,u);
CHKERRQ(ierr);
ierr = VecNorm(x,NORM_INFINITY, &e);
CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,NULL,"-print_error",&flg,NULL);
CHKERRQ(ierr);
if (flg) {
ierr = PetscPrintf(PETSC_COMM_WORLD, "Infinity norm of the error: %g\n", (double)e);
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 = MatDestroy(&perA);
CHKERRQ(ierr);
ierr = ISDestroy(&is);
CHKERRQ(ierr);
ierr = ISDestroy(&coarseparts);
CHKERRQ(ierr);
ierr = ISDestroy(&fineparts);
CHKERRQ(ierr);
ierr = ISDestroy(&isrows);
CHKERRQ(ierr);
ierr = ISDestroy(&isn);
CHKERRQ(ierr);
ierr = MatPartitioningDestroy(&part);
CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat A;
PetscErrorCode ierr;
PetscMPIInt rank,size;
PetscInt *ia,*ja;
MatPartitioning part;
IS is,isn,isrows;
IS coarseparts,fineparts;
MPI_Comm comm;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
comm = PETSC_COMM_WORLD;
ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
if (size != 4) SETERRQ(comm,1,"Must run with 4 processors");
ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);
ierr = PetscMalloc1(5,&ia);CHKERRQ(ierr);
ierr = PetscMalloc1(16,&ja);CHKERRQ(ierr);
if (!rank) {
ja[0] = 1; ja[1] = 4; ja[2] = 0; ja[3] = 2; ja[4] = 5; ja[5] = 1; ja[6] = 3; ja[7] = 6;
ja[8] = 2; ja[9] = 7;
ia[0] = 0; ia[1] = 2; ia[2] = 5; ia[3] = 8; ia[4] = 10;
} else if (rank == 1) {
ja[0] = 0; ja[1] = 5; ja[2] = 8; ja[3] = 1; ja[4] = 4; ja[5] = 6; ja[6] = 9; ja[7] = 2;
ja[8] = 5; ja[9] = 7; ja[10] = 10; ja[11] = 3; ja[12] = 6; ja[13] = 11;
ia[0] = 0; ia[1] = 3; ia[2] = 7; ia[3] = 11; ia[4] = 14;
} else if (rank == 2) {
ja[0] = 4; ja[1] = 9; ja[2] = 12; ja[3] = 5; ja[4] = 8; ja[5] = 10; ja[6] = 13; ja[7] = 6;
ja[8] = 9; ja[9] = 11; ja[10] = 14; ja[11] = 7; ja[12] = 10; ja[13] = 15;
ia[0] = 0; ia[1] = 3; ia[2] = 7; ia[3] = 11; ia[4] = 14;
} else {
ja[0] = 8; ja[1] = 13; ja[2] = 9; ja[3] = 12; ja[4] = 14; ja[5] = 10; ja[6] = 13; ja[7] = 15;
ja[8] = 11; ja[9] = 14;
ia[0] = 0; ia[1] = 2; ia[2] = 5; ia[3] = 8; ia[4] = 10;
}
ierr = MatCreateMPIAdj(comm,4,16,ia,ja,NULL,&A);CHKERRQ(ierr);
ierr = MatView(A,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/*
Partition the graph of the matrix
*/
ierr = MatPartitioningCreate(comm,&part);CHKERRQ(ierr);
ierr = MatPartitioningSetAdjacency(part,A);CHKERRQ(ierr);
ierr = MatPartitioningSetType(part,MATPARTITIONINGHIERARCH);CHKERRQ(ierr);
ierr = MatPartitioningHierarchicalSetNcoarseparts(part,2);CHKERRQ(ierr);
ierr = MatPartitioningHierarchicalSetNfineparts(part,2);CHKERRQ(ierr);
ierr = MatPartitioningSetFromOptions(part);CHKERRQ(ierr);
/* get new processor owner number of each vertex */
ierr = MatPartitioningApply(part,&is);CHKERRQ(ierr);
/* coarse parts */
ierr = MatPartitioningHierarchicalGetCoarseparts(part,&coarseparts);CHKERRQ(ierr);
ierr = ISView(coarseparts,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* fine parts */
ierr = MatPartitioningHierarchicalGetFineparts(part,&fineparts);CHKERRQ(ierr);
ierr = ISView(fineparts,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* partitioning */
ierr = ISView(is,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
/* get new global number of each old global number */
ierr = ISPartitioningToNumbering(is,&isn);CHKERRQ(ierr);
ierr = ISView(isn,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = ISBuildTwoSided(is,&isrows);CHKERRQ(ierr);
ierr = ISView(isrows,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = ISDestroy(&is);CHKERRQ(ierr);
ierr = ISDestroy(&coarseparts);CHKERRQ(ierr);
ierr = ISDestroy(&fineparts);CHKERRQ(ierr);
ierr = ISDestroy(&isrows);CHKERRQ(ierr);
ierr = ISDestroy(&isn);CHKERRQ(ierr);
ierr = MatPartitioningDestroy(&part);CHKERRQ(ierr);
/*
Free work space. All PETSc objects should be destroyed when they
are no longer needed.
*/
ierr = MatDestroy(&A);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
