[petsc-users] High-dimensional DMDA

[Mark Adams]

Let me just add that we (me and Toby (p4est)) think of tensor grids for
kinetic problems. A (phase space) grid at every spatial grid point. THis
allows us to compose our existing 3D grids to get 6D, for instance. This
work well/easily for Valsov-Maxwell because there are only grad_x and
grad_v terms.

I have explored this with a Vlasov code and worked some of it out. We have
a pretty good idea of what to do but it needs work.

So we are moving with the new Plex abstraction and DMDA not in our plans. I
like Plex, it abstracts the grid from the numerics nicely. The only bad
thing about it is that stencil methods are not natural (at all). So you,
for instance, compute fluxes and then divergences, instead of composing
them on paper to create a stencil.

Mark

On Tue, Oct 17, 2017 at 2:54 PM, Matthew Knepley <knepley at gmail.com> wrote:

> On Tue, Oct 17, 2017 at 2:51 PM, Hittinger, Jeffrey A. F. <
> hittinger1 at llnl.gov> wrote:
>
>> Bummer.
>>
>>
>>
>> Matt - Never is a very strong word.  Don’t underestimate the power of
>> mappings and/or AMR. Also, sparse grid techniques haven’t (yet) proven to
>> be particularly useful for kinetic problems.
>>
>
> None of the above is wrong, but I really meant "regular grids in high
> dimension". DMDA will never do AMR or sparse grids since its designed
> to be the simplest thing possible. For AMR we are using p4est, and that
> could definitely work in higher dimensions. I have read the Irene Gamba
> stuff on Boltzmann Transport using higher-D regular grids, but its just
> tremendously expensive, and they really play up spectral convergence,
> which relies on regularity which is often not there in practical problems.
>
>   Thanks,
>
>      Matt
>
>
>>
>>
>> Thanks for the quick response.
>>
>>
>>
>> j-
>>
>> -.-- -.-- --..
>>
>> Jeffrey A. F. Hittinger
>>
>> Center for Applied Scientific Computing
>>
>> Lawrence Livermore National Laboratory
>>
>> Office:  (925) 422-0993
>>
>> FAX:     (925) 423-2993
>>
>>
>>
>> *From: *Matthew Knepley <knepley at gmail.com>
>> *Date: *Tuesday, October 17, 2017 at 11:42 AM
>> *To: *Barry Smith <bsmith at mcs.anl.gov>
>> *Cc: *Undisclosed recipients <hittinger1 at llnl.gov>, "
>> petsc-users at mcs.anl.gov" <petsc-users at mcs.anl.gov>
>> *Subject: *Re: [petsc-users] High-dimensional DMDA
>>
>>
>>
>> On Tue, Oct 17, 2017 at 2:32 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>
>>
>>   No and it is highly unlikely to appear (the 3d code is already too
>> complicated and we tried to write a dimension independent version but that
>> failed)
>>
>>   But note that by using a dof argument > 1 one can handle some "4d"
>> problems so long as one does no parallelize in the 4th dimension.
>>
>>
>>
>> History: We did have a version for arbitrary dimension called ADDA
>> written by a student of David Keyes, that exists
>>
>> in the bowels of Git. We are unlikely to replicate it because regular
>> grids in high dimension never seem like the right
>>
>> thing to do.
>>
>>
>>
>>   Thanks,
>>
>>
>>
>>      Matt
>>
>>
>>
>>
>>    Barry
>>
>>
>> > On Oct 17, 2017, at 1:15 PM, Hittinger, Jeffrey A. F. <
>> hittinger1 at llnl.gov> wrote:
>> >
>> > Quick question: is there a version of the DMDA structured grid
>> interface that supports dimensions higher than 3?
>> >
>> > j-
>> > -.-- -.-- --..
>> > Jeffrey A. F. Hittinger
>> > Center for Applied Scientific Computing
>> > Lawrence Livermore National Laboratory
>> > Office:  (925) 422-0993
>> > FAX:     (925) 423-2993
>>
>>
>>
>>
>>
>> --
>>
>> 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.caam.rice.edu/~mk51/>
>>
>
>
>
> --
> 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.caam.rice.edu/~mk51/>
>
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