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

[Mark F. Adams]

>> 
> 
>   We had this discussion maybe the first time you were here where you explained to me that Chombo multigrid using red-black for their smoother and how it was a very good thing. What am I missing?


Ok, this is complicated and not a matter of black and white, so let me try to list the issues:

1) R/B G-S is at most 2x as expensive as Cheb. per iteration.

2) You get some of that back by better convergence rate.

3) You have a higher setup cost for Cheb, in the eigenvalue calculation, that can not be amortized well in AMR, in general.  When you regrid you need to redo everything, probably.

4) AMR has a lot of complexity vs a single a grid code and G-S is pretty fast because its generated fortran code on a regular stencil.  Future architectures, optimizations like Jed's, could make this cost even lower.  So the G-S is fast and there is a lot of AMR overhead -- upshot you spend less percent of your time in the smoother than in codes that you and I are used to.  So, I think Cheb could make Chomb faster, but by about, to pull a number out of my ass, 5%.  

5) Its nice not having a global damping parameter, I've never been able to quantify this issue or found errors that this allowed to slip in.  But its a question that hangs in the air.

6) I added GMRES to Chombo and people still use BCGStab so there is inertia here to using new stuff.

So when you add all this up I've just not gotten motivated to add Cheb to Chombo.

Mark