[petsc-users] Finite difference approximation of Jacobian

[Matthew Knepley]

On Tue, Jan 11, 2022 at 12:09 PM Patrick Sanan <patrick.sanan at gmail.com>
wrote:

> 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()?
>

Yes, here is how it works. You throw in all the nonzeros you come across.
Preallocator is a hash table that can check for duplicates. At the end, it
returns the sparsity pattern.

  Thanks,

     Matt


> 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/>
>>>
>>

-- 
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/>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20220111/650b8c80/attachment.html>