[petsc-dev] Should -pc_type mg be a linear preconditioner by default?

[Mark F. Adams]

Krylov smoother are weird and should be avoided unless you know what you are doing (eg, they can be useful for Helmholtz operators, the "bad" kind).

As Jed says Cheb is great for SPD problem, and his estimator stuff is excellent and should be made the default for smoothers.  One problem is that the lower range should depend on coarsening rate (ie, 3D cubic elements should be lower than 2D quads but the Cheb polynomial is at least smooth at that end).  I might use a lower factor than 0.1 (thats a 2D quad and is at the low end of what anyone would do) but not a big deal.

For very unsymmetric problems, that is problems with hyperbolic terms you want to use Gauss-Seidel, and sometimes you want to damp it.  (I would still use Cheb for unsymmetric elliptic operators like what you can get in FV or other minor perturbations to an SPD matrix.)  Setting a damping parameter is too complex to figure out automatically, and is not always needed, and we do not have a parallel Gauss-Seidel in PETSc.  I actually have a parallel G-S, it is complex but I could move it over to PETSc if there is demand for it.

On Oct 25, 2011, at 6:06 PM, Jed Brown wrote:

> On Tue, Oct 25, 2011 at 16:39, Barry Smith <bsmith at mcs.anl.gov> wrote:
> Chebychev?
> 
> Once I learned how to configure it, I quite like Chebychev for symmetric problems (and it is a natural fit for newer hardware).
> 
> I don't know a good default for non-symmetric. Playing with ex50 (increasing lid velocity and such), Chebychev with -mg_levels_ksp_chebychev_estimate_eigenvalues 0,.1,0,1.1 seems like not a bad default.

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