Dear Jed,
Thanks for attention!
I recall my previous thread; copy and paste here, and then I try to ask:
Suppose C = P*A_H^{-1}*R is the coarse grid solver. Then with a post-smoother
S, application of the preconditioner
to the vector "b" would be C b + S (b - A C b). If we drop the
post-smoother by setting S = I, We get Prec = C b + b - A C b. Note that there
is no presmoother.
This is the preconditioner I have used before, in PCMG framework, with no
pre-smoothing and Richardson(without any preconditioner) as post smoother.?
I need to apply the updated version of above Prec = C b + (b - A C b), where A
is replaced by M^-1 A , and A_H by M_H^-1 A_H .
Now does it make sense :
1)? incorporating M as only preconditioner in presmoother will replace A by
M^-1 A in Prec = C b + (b - A C b) ?
2) incorporating M as preconditioner to CG-solver will replace A_H by (M_H^-1
A_H ) ? I am kinda of sure about this point 2.
Thanks,
Abdul
From: Jed Brown <[email protected]>
To: Abdul Hanan Sheikh <hanangul12 at yahoo.co.uk>
>Cc: PETSc users list <petsc-users at mcs.anl.gov>
>Sent: Wednesday, 13 June 2012, 18:39
>Subject: Re: [petsc-users] How to implement projection preconditioner?
>
>
>On Wed, Jun 13, 2012 at 10:54 AM, Abdul Hanan Sheikh <hanangul12 at
>yahoo.co.uk> wrote:
>
>Thanks for reply!
>>
>>Well at first look, it looks like that M can be put as precondittioning
>>operator for smoother
>>where keeping ksp as preonly in pre-smoother context.?
>>I am not sure, this leads to the preconditioner desired, coz putting M as
>>preconditioner in
>>
>>pre-smoother alters the residual passed to coarse-grid correction,? i.e.
>>
>>CGC corrects the pre-smoothed solution.
>>
>
>
>That's kind of the point of pre-smoothing. Can you explain more precisely (or
>just try it).
>?
>
>>
>>
>>
>>
>>
>>>________________________________
>>> From: Jed Brown <jedbrown at mcs.anl.gov>
>>>To: Abdul Hanan Sheikh <hanangul12 at yahoo.co.uk>; PETSc users list
>>><petsc-users at mcs.anl.gov>
>>>Cc: Abdul - CITG <A.H.Sheikh at tudelft.nl>
>>>Sent: Friday, 8 June 2012, 19:01
>>>Subject: Re: [petsc-users] How to implement projection preconditioner?
>>>
>>>
>>>
>>>Isn't this just putting M and M_H as the preconditioning operator for the
>>>smoother?
>>>
>>>
>>>On Fri, Jun 8, 2012 at 11:58 AM, Abdul Hanan Sheikh <hanangul12 at
>>>yahoo.co.uk> wrote:
>>>
>>>Dear all,
>>>>
>>>>Summer greetings,
>>>>
>>>>I am back with an other query.
>>>>Before I successfully implement the projection preconditioner which was
>>>>simply
>>>>
>>>>the coarse grid correction operator P = I - A*(P*A_H*R);
>>>>
>>>>I implemented this simply keeping both pre and post smoothing dummy in PCMG
>>>>setup.
>>>>
>>>>Now I need to revise this and re-implement this where I replace A and
>>>>coarse operator A_H with
>>>>
>>>>preconditioned one i.e. M^-1 A and M^-1 A_H respectively. Thus new
>>>>projection reads as
>>>>
>>>>
>>>>
>>>>
>>>>P_new = I - (M^-1 A) {P*(M_H^-1 A_H)*R}
>>>>
>>>>
>>>>Any suggestion to implement this in Petsc would be appreciated.
>>>>
>>>>
>>>>
>>>>Thanking in anticipation.
>>>>
>>>>with regards, Abdul
>>>>
>>>
>>>
>>>
>
>
>
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