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

[Elias Karabelas]

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.

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.

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 <mailto: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/>
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