[Trilinos-Users] Correction (Two questions on the smoother of a multilevel preconditioner)

[Jonathan Hu]

Hi Ernesto,

Sorry for the late reply. In answer to your questions, yes, you can 
interpret smoothing as a Richardson iteration. The option "smoothing: 
damping factor", however, does not correspond to your \eta; it's ignored 
in the case of Aztec smoothers, and there is no other way presently to 
use a damping factor.

What sort of smoothers are you interested in using? Ifpack, for example, 
provides a variety of DD, incomplete factorizations, and SOR methods. I 
would encourage you to have a look at the other smoother options 
available in ML.

Regards,
Jonathan

Michael A Heroux wrote:
> FYI.
> ------ Forwarded Message
> From: Ernesto Prudencio <prudenci at slac.stanford.edu>
> Date: Tue, 15 Jan 2008 14:12:04 -0800 (PST)
> To: <trilinos-users at software.sandia.gov>
> Subject: [Trilinos-Users] Correction (Two questions on the smoother of a
> multilevel preconditioner)
>
>
> Sorry for the confusion:
>
> Ax* = b; e(k) = x* - x(k); r(k) = b - A x(k) = A e(k); B = precondtioner.
>
> Damped preconditioned Richardson: x(k+1) = x(k) + \eta B r(k)
>
> Rewriting: e(k+1) = e(k) - \eta B r(k) = [I - \eta B A] e(k) = E e(k)
>
> The questions, though, remain the same.
>
> Thanks in advance,
>
> Ernesto.
>
> On Tue, 15 Jan 2008, Ernesto Prudencio wrote:
>
>   
>> Hi.
>>
>> On page 25 of "ML 5.0 Smoothed Aggregation User's Guide" there is the
>> explanation for the option "smoother: Aztec as solver". If this options is
>> set to 'false', then "only the Aztec's preconditioner function will be used
>> as smoother".
>>
>> Question 1: Is it correct to interpret the 'false' option as a preconditioned
>> Richardson smoother which iterates as many times as determined by "smoother:
>> sweeps" option?
>>
>> By a (damped) preconditioned Richardson iteration I mean [notation: Ax = b;
>> r(k) = b - A x(k); B = preconditioner operator; \eta = dumping factor]:
>>
>> r(k+1) = (I - \eta A B) r(k) = E r(k),
>>
>> where E = error propagation matrix.
>>
>> Question 2: Does the "smoother: damping factor" parameter correspond to the
>> "\eta" parameter above?
>>
>> Thanks,
>>
>> Ernesto.
>>
>>
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>>
>>
>>     
>
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-- 
Jonathan J. Hu, mailto:jhu at sandia.gov
Postal address: Sandia National Laboratories
                Mailstop 9159
                PO Box 969, Livermore, CA 94551-0969
Tel / Fax (925) 294-2931 

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