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 <[email protected]> wrote: > On Fri, Sep 5, 2014 at 10:55 PM, Justin Chang <[email protected]> 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 >
