int main(int argc,char **args)
{
Mat C;
PetscErrorCode ierr;
PetscInt i,m = 2,N,M,idx[4],Nsub1,Nsub2,ol=1,x1,x2;
PetscScalar Ke[16];
PetscReal x,y,h;
IS *is1,*is2;
PetscBool flg;
PetscInitialize(&argc,&args,(char *)0,help);
ierr = PetscOptionsGetInt(PETSC_NULL,"-m",&m,PETSC_NULL);
CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
x1= (m+1)/2;
x2= x1;
ierr = PetscOptionsGetInt(PETSC_NULL,"-x1",&x1,PETSC_NULL);
CHKERRQ(ierr);
ierr = PetscOptionsGetInt(PETSC_NULL,"-x2",&x2,PETSC_NULL);
CHKERRQ(ierr);
/* create stiffness matrix */
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,PETSC_NULL,&C);
CHKERRQ(ierr);
/* forms the element stiffness for the Laplacian */
ierr = FormElementStiffness(h*h,Ke);
CHKERRQ(ierr);
for (i=0; i<M; i++) {
/* location of lower left corner of element */
x = h*(i % m);
y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1;
idx[2] = idx[1] + m + 1;
idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);
CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
CHKERRQ(ierr);
for (ol=0; ol<m+2; ++ol) {
ierr = PCASMCreateSubdomains2D(m+1,m+1,x1,x2,1,0,&Nsub1,&is1);
CHKERRQ(ierr);
ierr = MatIncreaseOverlap(C,Nsub1,is1,ol);
CHKERRQ(ierr);
ierr = PCASMCreateSubdomains2D(m+1,m+1,x1,x2,1,ol,&Nsub2,&is2);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"flg == 1 => both index sets are same\n");
CHKERRQ(ierr);
if(Nsub1 != Nsub2) {
ierr = PetscPrintf(PETSC_COMM_SELF,"Error: No of indes sets don't match\n");
CHKERRQ(ierr);
}
for (i=0; i<Nsub1; ++i) {
ierr = ISEqual(is1[i],is2[i],&flg);
CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_SELF,"i = %D,flg = %d \n",i,(int)flg);
CHKERRQ(ierr);
}
for (i=0; i<Nsub1; ++i) {
ierr = ISDestroy(&&is1[i]);
CHKERRQ(ierr);
}
for (i=0; i<Nsub2; ++i) {
ierr = ISDestroy(&&is2[i]);
CHKERRQ(ierr);
}
ierr = PetscFree(is1);
CHKERRQ(ierr);
ierr = PetscFree(is2);
CHKERRQ(ierr);
}
ierr = MatDestroy(&C);
CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C;
PetscErrorCode ierr;
PetscInt i,m = 2,N,M,its,idx[4],count,*rows;
PetscScalar val,Ke[16],r[4];
PetscReal x,y,h,norm,tol=1.e-14;
Vec u,ustar,b;
KSP ksp;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
/* create stiffness matrix */
ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,N,N,9,NULL,&C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
/* forms the element stiffness for the Laplacian */
ierr = FormElementStiffness(h*h,Ke);CHKERRQ(ierr);
for (i=0; i<M; i++) {
/* location of lower left corner of element */
x = h*(i % m); y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* create right hand side and solution */
ierr = VecCreateSeq(PETSC_COMM_SELF,N,&u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecDuplicate(b,&ustar);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
ierr = VecSet(b,0.0);CHKERRQ(ierr);
for (i=0; i<M; i++) {
/* location of lower left corner of element */
x = h*(i % m); y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = FormElementRhs(x,y,h*h,r);CHKERRQ(ierr);
ierr = VecSetValues(b,4,idx,r,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* modify matrix and rhs for Dirichlet boundary conditions */
ierr = PetscMalloc1((4*m+1),&rows);CHKERRQ(ierr);
for (i=0; i<m+1; i++) {
rows[i] = i; /* bottom */
rows[3*m - 1 +i] = m*(m+1) + i; /* top */
}
count = m+1; /* left side */
for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
count = 2*m; /* left side */
for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
for (i=0; i<4*m; i++) {
x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
val = y;
ierr = VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatZeroRows(C,4*m,rows,1.0,0,0);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = VecAssemblyBegin(u);CHKERRQ(ierr);
ierr = VecAssemblyEnd(u);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
/* check error */
for (i=0; i<N; i++) {
x = h*(i % (m+1)); y = h*(i/(m+1));
val = y;
ierr = VecSetValues(ustar,1,&i,&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(ustar);CHKERRQ(ierr);
ierr = VecAssemblyEnd(ustar);CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,ustar);CHKERRQ(ierr);
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G Iterations %D\n",norm*h,its);CHKERRQ(ierr);
}
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&ustar);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C;
PetscMPIInt rank,size;
PetscInt i,m = 5,N,start,end,M,its;
PetscScalar val,Ke[16],r[4];
PetscReal x,y,h,norm,tol=1.e-14;
PetscErrorCode ierr;
PetscInt idx[4],count,*rows;
Vec u,ustar,b;
KSP ksp;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* Create stiffness matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
end = start + M/size + ((M%size) > rank);
/* Assemble matrix */
ierr = FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
for (i=start; i<end; i++) {
/* location of lower left corner of element */
x = h*(i % m); y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Create right-hand-side and solution vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"Approx. Solution");CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)b,"Right hand side");CHKERRQ(ierr);
ierr = VecDuplicate(b,&ustar);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
ierr = VecSet(b,0.0);CHKERRQ(ierr);
/* Assemble right-hand-side vector */
for (i=start; i<end; i++) {
/* location of lower left corner of element */
x = h*(i % m); y = h*(i/m);
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = FormElementRhs(x,y,h*h,r);CHKERRQ(ierr);
ierr = VecSetValues(b,4,idx,r,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
/* Modify matrix and right-hand-side for Dirichlet boundary conditions */
ierr = PetscMalloc1(4*m,&rows);CHKERRQ(ierr);
for (i=0; i<m+1; i++) {
rows[i] = i; /* bottom */
rows[3*m - 1 +i] = m*(m+1) + i; /* top */
}
count = m+1; /* left side */
for (i=m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
count = 2*m; /* left side */
for (i=2*m+1; i<m*(m+1); i+= m+1) rows[count++] = i;
for (i=0; i<4*m; i++) {
x = h*(rows[i] % (m+1)); y = h*(rows[i]/(m+1));
val = y;
ierr = VecSetValues(u,1,&rows[i],&val,INSERT_VALUES);CHKERRQ(ierr);
ierr = VecSetValues(b,1,&rows[i],&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = MatZeroRows(C,4*m,rows,1.0,0,0);CHKERRQ(ierr);
ierr = PetscFree(rows);CHKERRQ(ierr);
ierr = VecAssemblyBegin(u);CHKERRQ(ierr);
ierr = VecAssemblyEnd(u);CHKERRQ(ierr);
ierr = VecAssemblyBegin(b);CHKERRQ(ierr);
ierr = VecAssemblyEnd(b);CHKERRQ(ierr);
{ Mat A;
ierr = MatConvert(C,MATSAME,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&C);CHKERRQ(ierr);
ierr = MatDestroy(&A);CHKERRQ(ierr);
}
/* Solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
/* Check error */
ierr = VecGetOwnershipRange(ustar,&start,&end);CHKERRQ(ierr);
for (i=start; i<end; i++) {
x = h*(i % (m+1)); y = h*(i/(m+1));
val = y;
ierr = VecSetValues(ustar,1,&i,&val,INSERT_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(ustar);CHKERRQ(ierr);
ierr = VecAssemblyEnd(ustar);CHKERRQ(ierr);
ierr = VecAXPY(u,-1.0,ustar);CHKERRQ(ierr);
ierr = VecNorm(u,NORM_2,&norm);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(ksp,&its);CHKERRQ(ierr);
if (norm > tol) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error %G Iterations %D\n",norm*h,its);CHKERRQ(ierr);
}
/* Free work space */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&ustar);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
Mat C;
Vec u,b;
PetscErrorCode ierr;
PetscMPIInt size,rank;
PetscInt i,m = 5,N,start,end,M,idx[4];
PetscInt j,nrsub,ncsub,*rsub,*csub,mystart,myend;
PetscBool flg;
PetscScalar one = 1.0,Ke[16],*vals;
PetscReal h,norm;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* Create stiffness matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
end = start + M/size + ((M%size) > rank);
/* Form the element stiffness for the Laplacian */
ierr = FormElementStiffness(h*h,Ke);CHKERRQ(ierr);
for (i=start; i<end; i++) {
/* location of lower left corner of element */
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Assemble the matrix again */
ierr = MatZeroEntries(C);CHKERRQ(ierr);
for (i=start; i<end; i++) {
/* location of lower left corner of element */
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Create test vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = VecSet(u,one);CHKERRQ(ierr);
/* Check error */
ierr = MatMult(C,u,b);CHKERRQ(ierr);
ierr = VecNorm(b,NORM_2,&norm);CHKERRQ(ierr);
if (norm > PETSC_SQRT_MACHINE_EPSILON) {
ierr = PetscPrintf(PETSC_COMM_WORLD,"Norm of error b %g should be near 0\n",(double)norm);CHKERRQ(ierr);
}
/* Now test MatGetValues() */
ierr = PetscOptionsHasName(NULL,NULL,"-get_values",&flg);CHKERRQ(ierr);
if (flg) {
ierr = MatGetOwnershipRange(C,&mystart,&myend);CHKERRQ(ierr);
nrsub = myend - mystart; ncsub = 4;
ierr = PetscMalloc1(nrsub*ncsub,&vals);CHKERRQ(ierr);
ierr = PetscMalloc1(nrsub,&rsub);CHKERRQ(ierr);
ierr = PetscMalloc1(ncsub,&csub);CHKERRQ(ierr);
for (i=myend-1; i>=mystart; i--) rsub[myend-i-1] = i;
for (i=0; i<ncsub; i++) csub[i] = 2*(ncsub-i) + mystart;
ierr = MatGetValues(C,nrsub,rsub,ncsub,csub,vals);CHKERRQ(ierr);
ierr = MatView(C,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr);
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD,"processor number %d: start=%D, end=%D, mystart=%D, myend=%D\n",rank,start,end,mystart,myend);CHKERRQ(ierr);
for (i=0; i<nrsub; i++) {
for (j=0; j<ncsub; j++) {
if (PetscImaginaryPart(vals[i*ncsub+j]) != 0.0) {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD," C[%D, %D] = %g + %g i\n",rsub[i],csub[j],(double)PetscRealPart(vals[i*ncsub+j]),(double)PetscImaginaryPart(vals[i*ncsub+j]));CHKERRQ(ierr);
} else {
ierr = PetscSynchronizedPrintf(PETSC_COMM_WORLD," C[%D, %D] = %g\n",rsub[i],csub[j],(double)PetscRealPart(vals[i*ncsub+j]));CHKERRQ(ierr);
}
}
}
ierr = PetscSynchronizedFlush(PETSC_COMM_WORLD,PETSC_STDOUT);CHKERRQ(ierr);
ierr = PetscFree(rsub);CHKERRQ(ierr);
ierr = PetscFree(csub);CHKERRQ(ierr);
ierr = PetscFree(vals);CHKERRQ(ierr);
}
/* Free data structures */
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
int main(int argc,char **args)
{
Mat C;
int i,m = 5,rank,size,N,start,end,M;
int ierr,idx[4];
PetscBool flg;
PetscScalar Ke[16];
PetscReal h;
Vec u,b;
KSP ksp;
MatNullSpace nullsp;
PetscInitialize(&argc,&args,(char*)0,help);
ierr = PetscOptionsGetInt(NULL,"-m",&m,NULL);CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* Create stiffness matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
end = start + M/size + ((M%size) > rank);
/* Assemble matrix */
ierr = FormElementStiffness(h*h,Ke); /* element stiffness for Laplacian */
for (i=start; i<end; i++) {
/* location of lower left corner of element */
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Create right-hand-side and solution vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"Approx. Solution");CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)b,"Right hand side");CHKERRQ(ierr);
ierr = VecSet(u,1.0);CHKERRQ(ierr);
ierr = MatMult(C,u,b);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
/* Solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,C,C,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
flg = PETSC_FALSE;
ierr = PetscOptionsGetBool(NULL,"-fixnullspace",&flg,NULL);CHKERRQ(ierr);
if (flg) {
ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
ierr = KSPSetNullSpace(ksp,nullsp);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&&nullsp);CHKERRQ(ierr);
}
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
/* Free work space */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return 0;
}
int main(int argc,char **args)
{
PetscErrorCode ierr;
Mat C;
PetscMPIInt rank,size;
PetscInt i,m = 5,N,start,end,M;
PetscInt idx[4];
PetscScalar Ke[16];
PetscReal h;
Vec u,b;
KSP ksp;
MatNullSpace nullsp;
ierr = PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
ierr = PetscOptionsGetInt(NULL,NULL,"-m",&m,NULL);CHKERRQ(ierr);
N = (m+1)*(m+1); /* dimension of matrix */
M = m*m; /* number of elements */
h = 1.0/m; /* mesh width */
ierr = MPI_Comm_rank(PETSC_COMM_WORLD,&rank);CHKERRQ(ierr);
ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr);
/* Create stiffness matrix */
ierr = MatCreate(PETSC_COMM_WORLD,&C);CHKERRQ(ierr);
ierr = MatSetSizes(C,PETSC_DECIDE,PETSC_DECIDE,N,N);CHKERRQ(ierr);
ierr = MatSetFromOptions(C);CHKERRQ(ierr);
ierr = MatSetUp(C);CHKERRQ(ierr);
start = rank*(M/size) + ((M%size) < rank ? (M%size) : rank);
end = start + M/size + ((M%size) > rank);
/* Assemble matrix */
ierr = FormElementStiffness(h*h,Ke);CHKERRQ(ierr); /* element stiffness for Laplacian */
for (i=start; i<end; i++) {
/* location of lower left corner of element */
/* node numbers for the four corners of element */
idx[0] = (m+1)*(i/m) + (i % m);
idx[1] = idx[0]+1; idx[2] = idx[1] + m + 1; idx[3] = idx[2] - 1;
ierr = MatSetValues(C,4,idx,4,idx,Ke,ADD_VALUES);CHKERRQ(ierr);
}
ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
/* Create right-hand-side and solution vectors */
ierr = VecCreate(PETSC_COMM_WORLD,&u);CHKERRQ(ierr);
ierr = VecSetSizes(u,PETSC_DECIDE,N);CHKERRQ(ierr);
ierr = VecSetFromOptions(u);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)u,"Approx. Solution");CHKERRQ(ierr);
ierr = VecDuplicate(u,&b);CHKERRQ(ierr);
ierr = PetscObjectSetName((PetscObject)b,"Right hand side");CHKERRQ(ierr);
ierr = VecSet(b,1.0);CHKERRQ(ierr);
ierr = VecSetValue(b,0,1.2,ADD_VALUES);CHKERRQ(ierr);
ierr = VecSet(u,0.0);CHKERRQ(ierr);
/* Solve linear system */
ierr = KSPCreate(PETSC_COMM_WORLD,&ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(ksp,C,C);CHKERRQ(ierr);
ierr = KSPSetFromOptions(ksp);CHKERRQ(ierr);
ierr = KSPSetInitialGuessNonzero(ksp,PETSC_TRUE);CHKERRQ(ierr);
ierr = MatNullSpaceCreate(PETSC_COMM_WORLD,PETSC_TRUE,0,NULL,&nullsp);CHKERRQ(ierr);
/*
The KSP solver will remove this nullspace from the solution at each iteration
*/
ierr = MatSetNullSpace(C,nullsp);CHKERRQ(ierr);
/*
The KSP solver will remove from the right hand side any portion in this nullspace, thus making the linear system consistent.
*/
ierr = MatSetTransposeNullSpace(C,nullsp);CHKERRQ(ierr);
ierr = MatNullSpaceDestroy(&nullsp);CHKERRQ(ierr);
ierr = KSPSolve(ksp,b,u);CHKERRQ(ierr);
/* Free work space */
ierr = KSPDestroy(&ksp);CHKERRQ(ierr);
ierr = VecDestroy(&u);CHKERRQ(ierr);
ierr = VecDestroy(&b);CHKERRQ(ierr);
ierr = MatDestroy(&C);CHKERRQ(ierr);
ierr = PetscFinalize();
return ierr;
}
