By the way, thanks for the help with dG preconditioned with h-multigrid using PETSc. Alessandro told me that your contribution has been significant. I'm going to send you the paper as soon as possible, the results for the Laplace equation are encouraging.
Lorenzo ---------- Forwarded message ---------- From: lorenzo alessio botti <[email protected]> Date: Fri, Apr 19, 2013 at 10:56 AM Subject: Re: [Libmesh-users] iterative solver behavior with h-refinement To: Jed Brown <[email protected]>, libmesh-devel < [email protected]> >Viscous fluxes are messier with DG: they have tunable parameters and the >tradeoffs are never satisfying. I almost never tune those parameters. Interior penalty can be problematic in case of very stretched elements but BR2 works great in 2D and 3D with stability parameter \eta= 3, 4 or number of element faces (as the theory suggests). I think that the major difference is the convergence rates of iterative solvers, with cG you need far less iterations. That's the reason why I use cG for the pressure solvers in operator splitting algorithms for incompressible flows. Lorenzo On Fri, Apr 19, 2013 at 1:29 AM, Jed Brown <[email protected]> wrote: > "Kirk, Benjamin (JSC-EG311)" <[email protected]> writes: > > > well you probably should clarify that - you are certainly "unwinding" > > at the cell interfaces to get an upwind bias in the scheme, right? So > > that could be alternatively looked at as a central + diffusive > > discretrization… So I would contend the artificial viscosity is (i) > > less direct and (ii) physically based, but could be thought of as > > viscosity nonetheless. > > 1. "upwinding" here means the solution of a Riemann problem. If you use > a Godunov flux, then the "upwinding" is introducing no numerical > viscosity. I think of Riemann problems as being very fundamental when > solving problems that do not have continuous solutions. > > 2. Numerical dissipation introduced by an approximate Riemann solver is > decoupled from the convergence rate of the method. The Riemann solve > has no tunable parameters, does not depend on the grid, and can attain > any order of accuracy purely by raising the order of reconstruction (in > FV) or the basis order (in DG). Compare this to SUPG, for example, > which has an O(h) term. > > Viscous fluxes are messier with DG: they have tunable parameters and the > tradeoffs are never satisfying. > > > Certainly if you computed the interface cell flux as the average of > > the neighbors things would go to hell in a hurry? > > Yes, that's unstable. > ------------------------------------------------------------------------------ Precog is a next-generation analytics platform capable of advanced analytics on semi-structured data. The platform includes APIs for building apps and a phenomenal toolset for data science. Developers can use our toolset for easy data analysis & visualization. Get a free account! http://www2.precog.com/precogplatform/slashdotnewsletter _______________________________________________ Libmesh-users mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/libmesh-users
