[petsc-dev] Multigrid is confusing

[Barry Smith]

On May 23, 2012, at 9:23 AM, Mark F. Adams wrote:

> 
> On May 22, 2012, at 11:09 PM, Barry Smith wrote:
> 
>> 
>> On May 22, 2012, at 9:58 PM, Jed Brown wrote:
>> 
>>> On Tue, May 22, 2012 at 9:52 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>>> How about a default nonlinear Krylov accelerator? fgrmes is not much more expensive than gmres under causal circumstances.
>>> 
>>> I could handle that. The extra storage concerns me more than time.
>>> 
>>> I'd eventually like to make PCMG linear by default, especially considering that the convergence with GMRES(1) smoothers tends to be worse in my experience (except when coarse level operators are poorly scaled/unstable) and adds a ton of synchronization points.
>>> 
>>> Oh, FGMRES by default would necessarily switch from left to right preconditioning. I'm not sure that's a good thing since it requires much tighter tolerances for ill-conditioned systems to reach a given error (especially penalty boundaries). There are advantages both ways and I keep waffling. I expect that changing the default will cause some surprises.
>> 
>> 
>>   So does it make sense to use ILU(0) smoothing with Chebyshev(3) acceleration (with eigenvalues precomputed by GMRES?).  
> 
> I don't like ILU(0) because it does not guarantee to keep the operator positive (eg, elasticity), which is annoying if you have SPD matrix.

    There is an option for that:  -pc_factor_shift_type  POSITIVE_DEFINITE     



> And if you use Cheby then its obviously bad.
> 
> Mark
> 
>>  I'm fine with switching now, I just want something reasonably robust so for example ex19 converges well with the defaults.
>> 
>> 
>>  Barry
>> 
>> 
>