[petsc-users] Finite difference approximation of Jacobian

Tue Jan 11 23:30:22 CST 2022

  I think the MATPREALLOCATOR as a MatType is a cumbersome strange thing and would prefer it was just functionality that Mat provided directly; for example MatSetOption(mat, preallocator_mode,true); matsetvalues,... MatAssemblyBegin/End. Now the matrix has its proper nonzero structure of whatever type the user set initially, aij, baij, sbaij, .... And the user can now use it efficiently.

  Barry

So turning on the option just swaps out temporarily the operations for MatSetValues and AssemblyBegin/End to be essentially those in MATPREALLOCATOR. The refactorization should take almost no time and would be faster than trying to rig dmstag to use MATPREALLOCATOR as is.

> On Jan 11, 2022, at 9:43 PM, Matthew Knepley <knepley at gmail.com> wrote:
> 
> On Tue, Jan 11, 2022 at 12:09 PM Patrick Sanan <patrick.sanan at gmail.com <mailto:patrick.sanan at gmail.com>> wrote:
> Working on doing this incrementally, in progress here: https://gitlab.com/petsc/petsc/-/merge_requests/4712 <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 <mailto:dave.mayhem23 at gmail.com>>:
> 
> 
> On Mon, 13 Dec 2021 at 20:13, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
> On Mon, Dec 13, 2021 at 1:52 PM Dave May <dave.mayhem23 at gmail.com <mailto:dave.mayhem23 at gmail.com>> wrote:
> On Mon, 13 Dec 2021 at 19:29, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
> On Mon, Dec 13, 2021 at 1:16 PM Dave May <dave.mayhem23 at gmail.com <mailto:dave.mayhem23 at gmail.com>> wrote:
> 
> 
> On Sat 11. Dec 2021 at 22:28, Matthew Knepley <knepley at gmail.com <mailto:knepley at gmail.com>> wrote:
> On Sat, Dec 11, 2021 at 1:58 PM Tang, Qi <tangqi at msu.edu <mailto: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 <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 <mailto: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/>

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