Roy,

First, I assume that you are using GMRES as the main solver with AMG as the
preconditioner.  Second, what type of discretization are you using because from
my understanding that can affect accuracy and also the resulting solver?  Are you
using an upwinding approach that takes into account the direction of convection?

I believe that this is an active area of research and new theses are churning out
at the moment.  One paper that I just found can be downloaded as below

http://www.cs.umd.edu/~elman/papers/mg-amg-paper.pdf

You can use many command line options with AMG to set different parameters but
you'll need to look through petsc code or documentation to find these options.  I'd
also suggest looking at papers (like the one above) for proper AMG parameters. 

Cheers, Travis

----- Original Message ----
From: Roy Stogner <roystgnr@ices.utexas.edu>
To: Travis Austin <austint73@gmail.com>
Cc: libmesh-users@lists.sourceforge.net
Sent: Friday, March 2, 2007 10:57:23 AM
Subject: Re: [Libmesh-users] Algebraic multigrid

On Thu, 1 Mar 2007, Travis Austin wrote:

> The nonlinear Navier-Stokes equation is a difficult problem.  It is
> nonsymmetric and with strong convection can create a mess.

That's what we're finding.  An undergraduate student here has a
weakly-coupled microfluidics problem with Reynolds number 0.01, which
BoomerAMG handles fine, but Peclet number 10, which makes BoomerAMG
explode.  In other words, weak nonlinearities are fine, but even the
linear convection-diffusion equation fails when the convection is
turned up enough.

His diverged result looks somewhat similar to a coarse grid Galerkin
solution, as if that cell Peclet number is too high and the solution
is overwhelmed by coarse node to coarse node oscillations.  We're
going to play around with limiting the number of multigrid levels, on
the theory that we'll be fine so long as the coarsest grid isn't too
coarse to be stable.  But he knows even less about multigrid than I do,
so nobody's getting their hopes up.

I think the best solution may be to use a stabilized formulation
instead of Galerkin, but that's not an option for us at the moment.

> Is it possible to try regular multigrid on this problem and if so
> how does it perform?  Just curious.

Not unless someone's added geometric multigrid capabilities but just
hasn't committed the changes to CVS yet.  ;-)

It's a shame BoomerAMG isn't more tightly integrated into PETSc.  It
would be nice to play around with smoothers and coarse grid solvers
other than weighted Jacobi, SOR, and Gaussian.  I'd like to try
something like ILU4 on the coarse grid combined with ILU0 on finer
grids, and see what that does for some of my problems.
---
Roy

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