[petsc-users] How to implement projection preconditioner?

[Abdul Hanan Sheikh]

Thank you for reply! 
I didnt get , what does it mean by applying the preconditioner to the right hand side, making it look just like a smoother ?

More simply, how can I implement Prec = \bar C b + (b - \bar A \bar C b)
where \bar C =  P (M_H^-1 A_H)^-1 R
and \bar A = M^-1 A. 
Note: we know how to implement Prec = C b + (b - A C b). 

Many thanks, Abdul 



>________________________________
> From: Jed Brown <jedbrown at mcs.anl.gov>
>To: Abdul Hanan Sheikh <hanangul12 at yahoo.co.uk> 
>Cc: PETSc users list <petsc-users at mcs.anl.gov> 
>Sent: Friday, 15 June 2012, 21:36
>Subject: Re: [petsc-users] How to implement projection preconditioner?
> 
>
>On Fri, Jun 15, 2012 at 2:23 PM, Abdul Hanan Sheikh <hanangul12 at yahoo.co.uk> wrote:
>
>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 . 
>>
>
>
>With left preconditioning, you also have to apply the preconditioner to the right hand side, thus making it look just like a smoother.
> 
>
>>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) ?
>>
>
>
>No, it uses the preconditioner the way that preconditioners work, see above.
> 
>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. 
>
>C already contains A_H^{-1}. Replacing that by M_H^{-1} is an approximate coarse level solve (that's okay and seems to be what you want, just not what you have written, which is not a consistent method).
>
>
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20120615/65c63664/attachment.html>