[petsc-users] Finite difference approximation of Jacobian

[Dave May]

On Mon, 13 Dec 2021 at 19:29, Matthew Knepley <knepley at gmail.com> wrote:

> On Mon, Dec 13, 2021 at 1:16 PM Dave May <dave.mayhem23 at gmail.com> wrote:
>
>>
>>
>> On Sat 11. Dec 2021 at 22:28, Matthew Knepley <knepley at gmail.com> wrote:
>>
>>> On Sat, Dec 11, 2021 at 1:58 PM Tang, Qi <tangqi at msu.edu> wrote:
>>>
>>>> Hi,
>>>> Does anyone have comment on finite difference coloring with DMStag? We
>>>> are using DMStag and TS to evolve some nonlinear equations implicitly. It
>>>> would be helpful to have the coloring Jacobian option with that.
>>>>
>>>
>>> Since DMStag produces the Jacobian connectivity,
>>>
>>
>> This is incorrect.
>> The DMCreateMatrix implementation for DMSTAG only sets the number of
>> nonzeros (very inaccurately). It does not insert any zero values and thus
>> the nonzero structure is actually not defined.
>> That is why coloring doesn’t work.
>>
>
> Ah, thanks Dave.
>
> Okay, we should fix that.It is perfectly possible to compute the nonzero
> pattern from the DMStag information.
>

Agreed. The API for DMSTAG is complete enough to enable one to
loop over the cells, and for all quantities defined on the cell (centre,
face, vertex),
insert values into the appropriate slot in the matrix.
Combined with MATPREALLOCATOR, I believe a compact and readable
code should be possible to write for the preallocation (cf DMDA).

I think the only caveat with the approach of using all quantities defined
on the cell is
It may slightly over allocate depending on how the user wishes to impose
the boundary condition,
or slightly over allocate for says Stokes where there is no
pressure-pressure coupling term.

Thanks,
Dave


> Paging Patrick :)
>
>   Thanks,
>
>     Matt
>
>
>> Thanks,
>> Dave
>>
>>
>> you can use -snes_fd_color_use_mat. It has many options. Here is an
>>> example of us using that:
>>>
>>>
>>> https://gitlab.com/petsc/petsc/-/blob/main/src/snes/tutorials/ex19.c#L898
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Thanks,
>>>> Qi
>>>>
>>>>
>>>> On Oct 15, 2021, at 3:07 PM, Jorti, Zakariae via petsc-users <
>>>> petsc-users at mcs.anl.gov> wrote:
>>>>
>>>> Hello,
>>>>
>>>> Does the Jacobian approximation using coloring and finite differencing
>>>> of the function evaluation work in DMStag?
>>>> Thank you.
>>>> Best regards,
>>>>
>>>> Zakariae
>>>>
>>>>
>>>>
>>>
>>> --
>>> 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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