# [petsc-users] Block Jacobi for Matrix-free

Barry Smith bsmith at mcs.anl.gov
Thu Jan 7 11:38:58 CST 2016

```  Timothee,

You are mixing up block Jacobi PCBJACOBI (which in PETSc generally uses "big" blocks) and point block Jacobi PCPBJACOBI (which generally means all the degrees of freedom associated with a single grid point -- in your case 3).

If you are doing matrix free with a shell matrix then you need to provide your own MatInvertBlockDiagonal() which in your case would invert each of your little 3 by 3 blocks and store the result in a 1d array; each little block in column major order followed by the next one. See for example MatInvertBlockDiagonal_SeqAIJ(). You also need you matrix to return a block size of 3.

Barry

> On Jan 7, 2016, at 8:08 AM, Timothée Nicolas <timothee.nicolas at gmail.com> wrote:
>
> Ok, so it should be sufficient. Great, I think I can do it.
>
> Best
>
> Timothée
>
> 2016-01-07 23:06 GMT+09:00 Matthew Knepley <knepley at gmail.com>:
> On Thu, Jan 7, 2016 at 7:49 AM, Timothée Nicolas <timothee.nicolas at gmail.com> wrote:
> Hello everyone,
>
> I have discovered that I need to use Block Jacobi, rather than Jacobi, as a preconditioner/smoother. The linear problem I am solving at this stage lives in a subspace with 3 degrees of freedom, which represent the 3 components of a 3D vector. In particular for multigrid, using BJACOBI instead of JACOBI as a smoother changes everything in terms of efficiency. I know it because I have tested with the actual matrix in matrix format for my problem. However, eventually, I want to be matrix free.
>
> My question is, what are the operations I need to provide for the matrix-free approach to accept BJACOBI ? I am confused because when I try to apply BJACOBI to my matrix-free operator; the code asks for MatGetDiagonalBlock (see error below). But MatGetDiagonalBlock, in my understanding, returns a uniprocessor matrix representing the diagonal part of the matrix on this processor (as defined in the manual). Instead, I would expect that what is needed is a routine which returns a 3x3 matrix at the grid point (that is, the block associated with this grid point, coupling the 3 components of the vector together). How does this work ? Do I simply need to code MatGetDiagonalBlock ?
>
> Just like Jacobi does not request one diagonal element at a time, Block-Jacobi does not request one diagonal block at a time. You
> would need to implement that function, or write a custom block Jacobi for this matrix.
>
>   Thanks,
>
>     Matt
>
>
> Thx
> Best
>
> Timothée
>
> [0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
> [0]PETSC ERROR: No support for this operation for this object type
> [0]PETSC ERROR: Matrix type shell does not support getting diagonal block
> [0]PETSC ERROR: See http://www.mcs.anl.gov/petsc/documentation/faq.html for trouble shooting.
> [0]PETSC ERROR: Petsc Release Version 3.6.1, Jul, 22, 2015
> [0]PETSC ERROR: ./miips on a arch-linux2-c-debug named Carl-9000 by timothee Thu Jan  7 22:41:13 2016
> [0]PETSC ERROR: Configure options --with-cc=gcc --with-cxx=g++ --with-fc=gfortran --download-fblaslapack --download-mpich
> [0]PETSC ERROR: #1 MatGetDiagonalBlock() line 166 in /home/timothee/Documents/petsc-3.6.1/src/mat/interface/matrix.c
> [0]PETSC ERROR: #2 PCSetUp_BJacobi() line 126 in /home/timothee/Documents/petsc-3.6.1/src/ksp/pc/impls/bjacobi/bjacobi.c
> [0]PETSC ERROR: #3 PCSetUp() line 982 in /home/timothee/Documents/petsc-3.6.1/src/ksp/pc/interface/precon.c
> [0]PETSC ERROR: #4 KSPSetUp() line 332 in /home/timothee/Documents/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c
> [0]PETSC ERROR: #5 KSPSolve() line 546 in /home/timothee/Documents/petsc-3.6.1/src/ksp/ksp/interface/itfunc.c
>
>
>
> --
> 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
>

```

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