[petsc-users] FE discretization in DMPlex

[Justin Chang]

Hi Matt,

Bringing this thread back from the dead.

1) Have you had the chance to implement things like RT and DG in DMPlex?
2) Are examples/tests that illustrate how to do dualspaces?
3) Or quantities like cell size h, jump, average?

I was originally trying to implement DG and RT0 in FEniCS but I am having
lots of trouble getting the FEniCS code to scale on our university's
clusters, so that's why I want to attempt going back to PETSc's DMPlex to
do strong scaling studies.

Thanks,
Justin

On Sat, Sep 6, 2014 at 3:58 AM, Matthew Knepley <knepley at gmail.com> wrote:

> On Fri, Sep 5, 2014 at 10:55 PM, Justin Chang <jychang48 at gmail.com> wrote:
>
>> Hi all,
>>
>> So I understand how the FEM code works in the DMPlex examples (ex12 and
>> 62). Pardon me if this is a silly question.
>>
>> 1) If I wanted to solve either the poisson or stokes using the
>> discontinuous Galerkin method, is there a way to do this with the built-in
>> DMPlex/FEM functions? Basically each cell/element has its own set of
>> degrees of freedom, and jump/average operations would be needed to
>> "connect" the dofs across element interfaces.
>>
>> 2) Or how about using something like Raviart-Thomas spaces (we'll say
>> lowest order for simplicity). Where the velocity dofs are not nodal
>> quantities, instead they are denoted by edge fluxes (or face fluxes for
>> tetrahedrals). Pressure would be piecewise constant.
>>
>> Intuitively these should be doable if I were to write my own
>> DMPlex/PetscSection code, but I was wondering if the above two
>> discretizations are achievable in the way ex12 and ex62 are.
>>
>
> Lets do RT first since its easier. The primal space is
>
>   P_K = Poly_{q--1}(K) + x Poly_{q-1}(K)
>
> so at lowest order its just Poly_1. The dual space is moments of the
> normal component
> of velocity on the edges. So you would write a dual space where the
> functionals integrated
> the normal component. This is the tricky part:
>
>   http://www.math.chalmers.se/~logg/pub/papers/KirbyLoggEtAl2010a.pdf
>
> DG is just a generalization of this kind of thing where you need to a)
> have some geometric
> quantities available to the pointwise functions (like h), and also some
> field quantities (like
> the jump and average).
>
> I understand exactly how I want to do the RT, BDM, BDMF, and NED elements,
> and those
> will be in soon. I think DG is fairly messy and am not completely sure
> what I want here.
>
>    Matt
>
>
>> Thanks,
>> Justin
>>
>
>
>
> --
> 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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