[petsc-users] Finite difference approximation of Jacobian

[Patrick Sanan]

Working on doing this incrementally, in progress here:
https://gitlab.com/petsc/petsc/-/merge_requests/4712

This works in 1D for AIJ matrices, assembling a matrix with a maximal
number of zero entries as dictated by the stencil width (which is intended
to be very very close to what DMDA would do if you
associated all the unknowns with a particular grid point, which is the way
DMStag largely works under the hood).

Dave, before I get into it, am I correct in my understanding that
MATPREALLOCATOR would be better here because you would avoid superfluous
zeros in the sparsity pattern,
because this routine wouldn't have to assemble the Mat returned by
DMCreateMatrix()?

If this seems like a sane way to go, I will continue to add some more tests
(in particular periodic BCs not tested yet) and add the code for 2D and 3D.



Am Mo., 13. Dez. 2021 um 20:17 Uhr schrieb Dave May <dave.mayhem23 at gmail.com
>:

>
>
> On Mon, 13 Dec 2021 at 20:13, Matthew Knepley <knepley at gmail.com> wrote:
>
>> On Mon, Dec 13, 2021 at 1:52 PM Dave May <dave.mayhem23 at gmail.com> wrote:
>>
>>> 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.
>>>
>>
>> Yes, and would not handle higher order stencils.I think the
>> overallocating is livable for the first imeplementation.
>>
>>
> Sure, but neither does DMDA.
>
> The user always has to know what they are doing and set the stencil width
> accordingly.
> I actually had this point listed in my initial email (and the stencil
> growth issue when using FD for nonlinear problems),
> however I deleted it as all the same issue exist in DMDA and no one
> complains (at least not loudly) :D
>
>
>
>
>
>>   Thanks,
>>
>>      Matt
>>
>>
>>> 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/>
>>>>
>>>
>>
>> --
>> 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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