[petsc-dev] sor smoothers

[Barry Smith]

  Another note for the archive. If one uses SSOR smoothing directly (no Cheby) with the trick of saving the accumulated action of the upper or lower half of the matrix then the matrix-vector product to compute the residual after the pre smoothing can be done using those accumulated values at a cost of .5 work units instead of 1 unit.

   Barry

Each approach has its handful of tricks to shave off work.



On Aug 13, 2013, at 1:19 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:

> "Mark F. Adams" <mfadams at lbl.gov> writes:
> 
>> On Aug 12, 2013, at 7:19 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
>> 
>>> 
>>> Jed,
>>> 
>>>  I don't understand your computations. I run
>>> 
>>> ./ex29 -ksp_type chebyshev -ksp_max_it 2 -ksp_monitor -pc_type eisenstat -log_summary -ksp_view -ksp_chebyshev_eigenvalues 1.0,2.0 -ksp_norm_type none
>>> 
>> 
>> I thought we wanted to use richardson to get PCApplyRichardson_SOR to
>> get invoked and save the MatMults in the KSP, because SOR is a strange
>> PC that can use an existing solution w/o doing residual correction.
>> What am I missing.
> 
> Chebyshev allows us to accelerate it (sometimes) relative to Richardson.
> The cost of Richardson(2)/SOR is remarkably similar to
> Cheby(2)/Eisenstat.