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

[Mark Adams]

On Mon, Mar 23, 2020 at 10:18 AM Elias Karabelas <karabelaselias at gmail.com>
wrote:

> Ok I'll try to decipher that. Thought that I would maybe find something in
> the GAMG routines
>

Not much, GAMG symmetrizes the graph  (G) for coarse grid constriction,
where G_ij must equal G_ji in parallel. G is a graph derived from A or
(A+A^T).

but I'll be happy to scroll through the ASM stuff :D
> On 23/03/2020 13:56, Matthew Knepley wrote:
>
> On Mon, Mar 23, 2020 at 8:41 AM Elias Karabelas <karabelaselias at gmail.com>
> wrote:
>
>> Thanks I'll have a look at it. So I understand correctly, that purely
>> algebraic is not the way to go through PETSc here?
>>
> You can make it work. You would have the same difficulty in any linear
> algebra package, namely that you need
> an overlapped decomposition of the matrix, which no package does by
> default. PETSc does it for ASM, so you could
> use those routines to get what you want.
>
>   Thanks,
>
>      Matt
>
>> Cheers
>>
>> Elias
>> On 23/03/2020 13:39, Matthew Knepley wrote:
>>
>> 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/>
>>
>>
>
> --
> 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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