[petsc-users] BLOCK INVERSE FOR ILU

[Matthew Knepley]

On Thu, Jun 5, 2025 at 2:27 AM Frank Bramkamp <bramkamp at nsc.liu.se> wrote:

> Thanks for the response,
>
>
> I refer to the routine  src/mat/impls/baij/seq/dgefa6.c
>
>
> /*
>       Inverts 6 by 6 matrix using gaussian elimination with partial
> pivoting.
>
>        Used by the sparse factorization routines in
>      src/mat/impls/baij/seq
>
>        This is a combination of the Linpack routines
>     dgefa() and dgedi() specialized for a size of 6.
>
> */
>
>
> which implements the the computation of an inverse for a dense 6x6 block.
> I think this routine is used in the ILU numeric factorization to compute
> the inverse diagonal block
> when we later apply ILU preconditioning where we need the inverse.
>
> And there it looks we use a direct LU solve and not triangular solves ?!
>
> In this context I am not sure if something is missing at the end or not
> regarding the inverse pivoting ?!
>

We do not think so, but there is a simple test for this. You can construct
a small block diagonal matrix with
blocksize 6, and apply it to the vector [1, 2, 3, 4, 5, 6 ...]. Use that
vector as the RHS for a solve with
preonly/ILU. That should get the exact inverse and output the original
vector. If the vector is permuted, then
we indeed have a bug.

  Thanks!

      Matt


> Greetings, Frank
>
>
>
>
>

-- 
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://urldefense.us/v3/__https://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!d8vX5tFZOpXshlbVrdeXXKCaT9OQePsnBaR3YBpe5DEoej9o3r1ZB9Rs-RgRm4xVgXdw-FNm8ShhNQ_vNueb$  <https://urldefense.us/v3/__http://www.cse.buffalo.edu/*knepley/__;fg!!G_uCfscf7eWS!d8vX5tFZOpXshlbVrdeXXKCaT9OQePsnBaR3YBpe5DEoej9o3r1ZB9Rs-RgRm4xVgXdw-FNm8ShhNTEksffZ$ >
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20250605/2aa1c19a/attachment.html>