[petsc-users] PCBJACOBI behaves weirdly

[Zhuo Chen]

Dear Petsc users,

My name is Zhuo Chen. I am very new to Petsc.

I have encountered a very weird problem. I try to use Petsc to solve a 2D
diffusion problem (https://en.wikipedia.org/wiki/Heat_equation). When I use
PCLU, the solution looks very good. Then, I change to PCJACOBI because I
plan to use MPI in the future. If I treat the whole matrix as a single
block and set the preconditioner of the "sub-matrix" with PCLU, the
solution is exactly the same as the PCLU setting. However, if I increase
the number of blocks, the result becomes worse. I attached the solution of
a 2D diffusion simulation I have done. The red dots are the analytic
solution and the blue circles are the solution from Petsc with 8 blocks.
The size of the computational domain is 300*8. The result with PCLU only is
very close to the analytic solution so I do not include it here.

Then I implemented the same problem with Matlab
with x=gmres(mat,rhs,10,tol,maxit,p), where mat is the same as the one in
my Petsc code, and p is the block Jacobi matrix (8 blocks). The result from
Matlab is very good, though it is slow. I attach the Matlab result to this
email as well.

I would like to paste a part of my Petsc code here as well.

179     call KSPSetOperators(ksp,A,A,ierr);CHKERRQ(ierr)
180     call KSPGetPC(ksp,pc,ierr);CHKERRQ(ierr)
181     tol=1d-6
182     call
KSPSetTolerances(ksp,tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr);CHKERRQ(ierr)
183     call PCSetType(pc,PCBJACOBI,ierr);CHKERRQ(ierr)
184     nblks=8
185     allocate(blks(nblks))
186     blks=Ntot/nblks
187     call PCBJacobiSetTotalBlocks(pc,nblks,blks,ierr);CHKERRQ(ierr)
188     deallocate(blks)
189     call KSPsetup(ksp,ierr)
190     call PCBJacobiGetSubKSP(pc,nlocal,first,PETSC_NULL_KSP,ierr)
191     allocate(subksp(nlocal))
192     call PCBJacobiGetSubKSP(pc,nlocal,first,subksp,ierr)
193     do i=0,nlocal-1
194         call KSPGetPC(subksp(i+1),subpc,ierr)
195         call PCSetType(subpc,PCLU,ierr); CHKERRA(ierr)
196         call KSPSetType(subksp(i+1),KSPGMRES,ierr); CHKERRA(ierr)
197         tol=1d-6
198         call
KSPSetTolerances(subksp(i+1),tol,PETSC_DEFAULT_REAL,PETSC_DEFAULT_REAL,PETSC_DEFAULT_INTEGER,ierr);CHKERRQ(ierr)
199     end do
200     deallocate(subksp)

It would be great if anyone can help me with this issue. Many thanks!

-- 
Zhuo Chen
Department of Physics
University of Alberta
Edmonton Alberta, Canada T6G 2E1
http://www.pas.rochester.edu/~zchen25/
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