[dune-pdelab] Implementing OVLP_AMG_4_DG solver

[Christian Engwer]

Hi Lukas,

as the DG disccretization only requires face neighbors, the ghosts
should be sufficient. The problem is the low order space.

You basically have two options: p0 (aka Finite Volume), which should
also work with ghosts. The other option is p1/q1 which requires all
vertex neighbors present on the local machine, or you have to add an
additional commuication to obtain the full matrix rows (this is what
is implemented in the non-overlaping version).

>From that point of view the p0 version would be better, but in my
experience the convergence rate is significantly lower. In the p1/q1
version you obtain (like in the standard case) a h-independent
convergence rate betweeen 0.1 and 0.2. In the p1/q1 case it is also
h-independent (so it is still optimal), but the constant is worse
(between 0.6 and 0.8).

Ciao
Christian

On Mon, Mar 06, 2017 at 01:11:08PM +0100, Lukas Riedel wrote:
> Dear all,
> 
> I’m trying to ‘go parallel’ with our instationary DG solver by implementing the OVLP_AMG_4_DG linear solver. I use UG and YaspGrid as grid backends. Apparently, UG does not support Overlap, but only Ghosts. Can I still use this linear solver in both cases or do I need different solver implementations for the two grids?
> 
> I use PkLocalFiniteElementMap (UG grid only) or QkDGLocalFiniteElementMap (UG & Yasp) for my solution (DG) GFS. For the solver to work, I understand that I have to assemble another (CG) GFS with the same FEMs, but with polynomial order 0. Which EntitySet and which Constraints should I use for the two GridFunctionSpaces? Does this choice depend on the type of Grid used?
> 
> Thank you in advance!
> Cheers,
> Lukas
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