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

[Matthew Knepley]

On Mon, Mar 23, 2020 at 8:38 AM Elias Karabelas <karabelaselias at gmail.com>
wrote:

>
> On 23/03/2020 13:36, Matthew Knepley wrote:
>
> 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.
>
> Can you give me a reference to that? I based my things on this work
> https://www.sciencedirect.com/science/article/pii/S0045782508003150#!
>
Volker is of course great. I believe I was thinking of
https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.1650071007

  Thanks,

    Matt

> Best regards
>
> Elias
>
>
>
>   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/>
>
>

-- 
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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