> On Mar 1, 2016, at 9:59 AM, Mark Adams <[email protected]> wrote: > > > > On Mon, Feb 29, 2016 at 5:42 PM, Boyce Griffith <[email protected] > <mailto:[email protected]>> wrote: > >> On Feb 29, 2016, at 5:36 PM, Mark Adams <[email protected] >> <mailto:[email protected]>> wrote: >> >> >> GAMG is use for AMR problems like this a lot in BISICLES. >> >> Thanks for the reference. However, a quick look at their paper suggests they >> are using a finite volume discretization which should be symmetric and avoid >> all the shenanigans I'm going through! >> >> No, they are not symmetric. FV is even worse than vertex centered methods. >> The BCs and the C-F interfaces add non-symmetry. > > > If you use a different discretization, it is possible to make the c-f > interface discretization symmetric --- but symmetry appears to come at a cost > of the reduction in the formal order of accuracy in the flux along the c-f > interface. I can probably dig up some code that would make it easy to compare. > > I don't know. Chombo/Boxlib have a stencil for C-F and do F-C with > refluxing, which I do not linearize. PETSc sums fluxes at faces directly, > perhaps this IS symmetric? Toby might know.
If you are talking about solving Poisson on a composite grid, then refluxing and summing up fluxes are probably the same procedure. Users of these kinds of discretizations usually want to use the conservative divergence at coarse-fine interfaces, and so the main question is how to set up the viscous/diffusive flux stencil at coarse-fine interfaces (or, equivalently, the stencil for evaluating ghost cell values at coarse-fine interfaces). It is possible to make the overall discretization symmetric if you use a particular stencil for the flux computation. I think this paper (http://www.ams.org/journals/mcom/1991-56-194/S0025-5718-1991-1066831-5/S0025-5718-1991-1066831-5.pdf <http://www.ams.org/journals/mcom/1991-56-194/S0025-5718-1991-1066831-5/S0025-5718-1991-1066831-5.pdf>) is one place to look. (This stuff is related to "mimetic finite difference" discretizations of Poisson.) This coarse-fine interface discretization winds up being symmetric (although possibly only w.r.t. a weighted inner product --- I can't remember the details), but the fluxes are only first-order accurate at coarse-fine interfaces. -- Boyce
