By the way, thanks for the help with dG preconditioned with h-multigrid
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.
---------- Forwarded message ----------
From: lorenzo alessio botti <lorenzoalessiobotti@...>
Date: Fri, Apr 19, 2013 at 10:56 AM
Subject: Re: [Libmesh-users] iterative solver behavior with h-refinement
To: Jed Brown <jed@...>, libmesh-devel <
>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
On Fri, Apr 19, 2013 at 1:29 AM, Jed Brown <jed@...> wrote:
> "Kirk, Benjamin (JSC-EG311)" <benjamin.kirk-1@...> 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.