[petsc-users] Construct Matrix based on row and column values

[Matthew Knepley]

On Mon, Mar 23, 2020 at 8:31 AM Elias Karabelas <karabelaselias at gmail.com>
wrote:

> Dear Matt,
>
> I've just found this answer from 2014
>
> https://lists.mcs.anl.gov/pipermail/petsc-users/2014-August/022450.html
>
> wondering if this would theoretically work.
>
> In serial certainly, I just don't see how it works in parallel since you
might not own the row you need from the transpose.

> And the thing with this FCT-Schemes is, that they're build on purely
> algebraic considerations (like AMG) so I don't want to break it back down
> to mesh information if possible at all.
>
The FEM-FCT I am familiar with from Lohner was phrased on a mesh.

  Thanks,

    Matt

> Best regards
>
> Elias
> On 23/03/2020 13:02, Matthew Knepley wrote:
>
> On Mon, Mar 23, 2020 at 7:46 AM Elias Karabelas <karabelaselias at gmail.com>
> wrote:
>
>> Dear Users,
>>
>> I want to implement a FCT (flux corrected transport) scheme with PETSc.
>> To this end I have amongst other things create a Matrix whose entries
>> are given by
>>
>> L_ij = -max(0, A_ij, A_ji) for i neq j
>>
>> L_ii = Sum_{j=0,..n, j neq i} L_ij
>>
>> where Mat A is an (non-symmetric) Input Matrix created beforehand.
>>
>> I was wondering how to do this. My first search brought me to
>>
>> https://www.mcs.anl.gov/petsc/petsc-current/src/mat/examples/tutorials/ex16.c.html
>>
>>
>> but this just goes over the rows of one matrix to set new values and now
>> I would need to run over the rows and columns of the matrix. My Idea was
>> to just create a transpose of A and do the same but then the row-layout
>> will be different and I can't use the same for loop for A and AT and
>> thus also won't be able to calculate the max's above.
>>
>> Any help would be appreciated
>>
>
> I think it would likely be much easier to write your algorithm directly on
> the mesh, rather than using matrices, since the locality information is
> explicit with the mesh, but has to be reconstructed with the matrix.
>
> The problem here is that in parallel there would be no easy way to get the
> halo you need using a matrix. You
> really want the ghosted space for assembly, and that is provided by the DM
> objects. Does this make sense?
> Unless anybody in PETSc has a better idea.
>
>   Thanks,
>
>      Matt
>
>
>> Best regards
>>
>> Elias
>>
>>
>
> --
> 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/>
>
>

-- 
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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