[petsc-users] DM question.

Matthew Knepley knepley at gmail.com
Fri Oct 23 06:14:18 CDT 2015 

On Fri, Oct 23, 2015 at 3:01 AM, Afanasiev Michael <
michael.afanasiev at erdw.ethz.ch> wrote:

> Hi Matthew,
>
> So I’m discretizing via a tensor product of Lagrange polynomials
> co-located at the Gauss-Lobatto-Legendre (GLL) points. The polynomial order
> might range from 4 to 10 or something like that. The current problem is
> solved on 2D hexes.
>
> I had found DMPlexCreateSection, and followed plex/ex1to get things set
> up. You can see my attempt below. Basically I’ve got 4 fields
> (displacement, velocity, acceleration, and strain) over each element. Here
> I’ve tried to setup a tensor product of 4th order (5 GLL points) Lagrange
> polynomials (line 11). This seemed to * somewhat* achieve what I wanted —
> I created a global vector and wrote it to a vtk file with VecView, and the
> numbering seemed to make sense. You can also see my attempt at defining a
> boundary condition (it looked like DMPlexCreateFromExodus labeled side sets
> as “Face Sets”, seems to have worked).
>
> Does this seem to be headed in the right direction?
>

Yes, however I have some questions. Starting out, I think the GLL points
include the endpoints, so
that means for polynomial degree k that numDof[] should really have 4*1
dofs on each vertex,
4*(k-1) dofs on each edge, and 4*(k-1)^2 on each quad. It looks like below
you have numDof[] for
a 1D mesh with DG element.

The "Face Sets" is the right label to use for boundary conditions. This
will eliminate those variables
from the global system, but they will be present in the local spaces.

With elements like these, it is common (I think) to eliminate the cell
unknown explicitly, since the
system is dense and not connected to other cells. For this, you would
retain the vertex and edge
unknowns, but not the cell unknowns. I have not tried to do this myself, so
I do not know if there
are any pitfalls.

You can see an example of a similar implementation specifically for the
kind of spectral elements
you are considering here: https://github.com/jedbrown/dohp. It would
probably be useful to understand
what is done there as you implement.

  Thanks,

     Matt


> Cheers,
> Mike.
>
> DM
> mesh::createSection(const DM &dm)
> {
>
> 01        // displacement, velocity, acceleration, strain
> 02        IS bcPointIs[1];
> 03        PetscInt numBc = 1;
> 04        PetscInt bcField[1];
> 05        PetscInt numFields = 4;
> 06        PetscInt dim; DMGetDimension(dm, &dim);
> 07        PetscInt numComp[numFields];
> 08        for (auto i=0; i<numFields; i++) {numComp[i] = dim;}
> 09        PetscInt numDof[numFields*(dim+1)];
> 10        for (auto i=0; i<numFields*(dim+1); i++) {numDof[i] = 0;}
> 11        for (auto i=0; i<numFields; i++) {numDof[i*(dim+1)+dim] = 5;}
> 12        bcField[0] = 0;
> 13        PetscSection section;
> 14        DMPlexGetStratumIS(dm, "Face Sets", 1, &bcPointIs[0]);
> 15        DMPlexCreateSection(dm, dim, numFields, numComp, numDof, numBc,
> bcField,
> 16                                                NULL, bcPointIs, NULL,
> &section);
> 17        ISDestroy(&bcPointIs[0]);
> 18        PetscSectionSetFieldName(section, 0, "u");
> 19        PetscSectionSetFieldName(section, 1, "v");
> 20        PetscSectionSetFieldName(section, 2, "a");
> 21        PetscSectionSetFieldName(section, 3, "e");
> 22        DMSetDefaultSection(dm, section);
> 23        return dm;
> }
>
> --
> Michael Afanasiev
> Ph.D. Candidate
> Computational Seismology
> Institut für Geophysik
> ETH Zürich
>
> Sonneggstrasse 5, NO H 39.2
> CH 8092 Zürich
> michael.afanasiev at erdw.ethz.ch
>
> On Oct 22, 2015, at 2:32 AM, Matthew Knepley <knepley at gmail.com> wrote:
>
> On Wed, Oct 21, 2015 at 3:07 PM, Dave May <dave.may at erdw.ethz.ch> wrote:
>
>> Hey Mike,
>>
>>
>>
>> On 21 October 2015 at 18:01, Afanasiev Michael <
>> michael.afanasiev at erdw.ethz.ch> wrote:
>>
>>> Hey Dave,
>>>
>>> So I’ve got a couple of days where there’s nothing pressing to work on…
>>> was thinking of ripping out the parallel routines (ugly) in my wave
>>> propagation code and replacing them with Petsc DM routines. I can read in
>>> my exodusii mesh with DMPLEX, and partition it with chaco, which gives me a
>>> nicely partitioned DM. This takes me like 5 lines of code.  That’s amazing.
>>>
>>> But here I’m stuck, and am having a whale of a time with the
>>> documentation. All I *think* I need is a way to modify the
>>> exodus-created DM, and add to it the degrees of freedom that are introduced
>>> by my quadrature rule. This would be really neat. I can just treat each
>>> sub-domain as its own mesh, with its own global numbering. Then whenever
>>> necessary I can scatter stuff the the *real* global degrees of freedom
>>> with something like VecLocToGlob. Most of the things I like about the code
>>> could stay the same (element-wise, matrix-free nature), just these parallel
>>> broadcasts would be infinitely nicer.
>>>
>>>
>> First off - I don't use DMPLEX.
>>
>
> Dave is refreshingly candid about his shortcomings ;)
>
>
>>
>>
> But I just can’t figure out how to set this up. The main problem really
>>> boils down to: what’s the best way to add my quadrature points to an
>>> already-created DM, which was constructed with an exodus file? I guess I
>>> could do this after the file is read, but before the partitioning. In this
>>> case though, what’s stopping the partitioner from cutting an element in
>>> half? It seems like it would be a lot cleaner to do this post-partitioning.
>>>
>>>
>> Presumably what is read from exodus is just the vertices of the hexes,
>> and what you want to do is define the function space (given by your GLL
>> locations) on top of element geometry read in. Is that what you are asking
>> about?
>>
>
> So Dave is right. We read in topology and geometry from ExodusII. Then you
> define a function space on top. How
> exactly are you discretizing? In order to create vectors, do local to
> global, etc. Petsc really only need to know the
> amount of data associated with each mesh piece. You can define this with
> PetscSection. If you give me an idea
> what you want I can help you write the code easily I think.
>
>   Thanks,
>
>      Matt
>
>
>> Any hints here?
>>>
>>
>> Actually I have no experience with this object.
>> I would just send an email to
>>   petsc-users at mcs.anl.gov
>> asking for help.
>>
>> The developer of DMPLEX (Matt Knepley) will definitely answer within in 1
>> day.
>>
>> Cheers,
>>   Dave
>>
>>
>>> Best,
>>> Mike.
>>> --
>>> Michael Afanasiev
>>> Ph.D. Candidate
>>> Computational Seismology
>>> Institut für Geophysik
>>> ETH Zürich
>>>
>>> Sonneggstrasse 5, NO H 39.2
>>> CH 8092 Zürich
>>> michael.afanasiev at erdw.ethz.ch
>>>
>>>
>>
>
>
> --
> 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
>
>
>


-- 
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
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