[petsc-users] PCBJACOBI behaves weirdly

[Matthew Knepley]

On Sun, May 3, 2020 at 12:34 AM Zhuo Chen <chenzhuotj at gmail.com> wrote:

> 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.
>

The default tolerance for KSP is 1e-5. If you make it lower, you will get
what you want,

  -ksp_rtol 1e-10

However, BJACOBI is a terrible way to solve the diffusion equation. You
should use multigrid, for example

  -pc_type gamg

or Hypre/BoomerAMG or ML.

  Thanks,

    Matt


> 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/
>


-- 
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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