[petsc-users] BLOCK INVERSE FOR ILU

[Barry Smith]

> On Jun 4, 2025, at 1:06 PM, Mark Adams <mfadams at lbl.gov> wrote:
> 
> It looks like it pivots in blocks and is a point-wise ILU: https://urldefense.us/v3/__https://petsc.org/release/manualpages/PC/PCILU/__;!!G_uCfscf7eWS!bLJjV_o5EdHrYFCvaAx1cH4gN3bYp79B0t10NWDhrlPZQWdn7KcKBX_pOyjuYD5pyZO4oNCt22EC7u-7hUelMUc$  <https://urldefense.us/v3/__https://petsc.org/release/manualpages/PC/PCILU/__;!!G_uCfscf7eWS!d82xhlyQ6-cWmSO0PBI3pnGPDROVlCOPZn87hYtI4Pi9Kkbf4wgpQjnYsrJVy0pwHGtZYvPKXDxQCoq9BTvE6Ao$>
> 
> Mark
> 
> On Wed, Jun 4, 2025 at 9:36 AM Frank Bramkamp <bramkamp at nsc.liu.se <mailto:bramkamp at nsc.liu.se>> wrote:
>> Dear PETSc team,
>> 
>> I have a general question regarding the implementation of the inverse
>> For the ILU factorization.
>> 
>> I am looking e.g. on the implementation for block size 6 for the BAIJ matrix format in serial:
>> src/mat/impls/baij/seq/dgefa6.c
>> 
>> I wonder:
>> You are using pivoting in the inverse computation.
>> 
>> But if one changes the position of elements or rows, do we not have to apply an inverse permutation at the end
>> to get the inverse of the original matrix to some column ?!  Otherwise it is the inverse of the permutated matrix ?!

     To compute the explicit inverse it does 6 triangular solves with columns of the identity. During the triangular solves it does the needed permutations so the inverse is the inverse of the original matrix, not a permuted version.
>> 
>> I am not quite sure if one has to do this in principle or if my understanding is not quite correct.
>> Maybe I miss something in your code.
>> 
>> 
>> Thanks, Frank
>> 
>> 
>> 

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