[petsc-users] High-dimensional DMDA

[Tobin Isaac]

On Tue, Oct 17, 2017 at 03:40:10PM -0400, Mark Adams wrote:
> 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.

Which is something so rote that creating DTFD to convert the pointwise
residuals/jacobians into stencils would go along way towards unifying
DMDA and DMPlex in a single useful interface.

</sidebar>

Cheers,
  Toby

> 
> 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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