[petsc-users] Projection preconditioner as PCMG

[Jed Brown]

On Thu, Mar 8, 2012 at 12:57, Abdul Hanan Sheikh <hanangul12 at yahoo.co.uk>wrote:

> I dont want to try snes, since my problem is linear,
>

Note that you can still use SNES for linear problems. (I prefer the
interface, you can choose -snes_type ksponly so there is no extra overhead,
but use whatever you like.)


> but I successfully applied the KSP
> preconditioned with PCMG (not kaskade, but multiplicative; for some
> reasons) .
> I make pre-smoother dummy by setting KSP_PRE context as  PREONLY alongwith
> PCNONE.
>

You can just set the number of pre-smoothing steps to 0.


> CGC and post-smoother serves my purpose to apply preconditioner
> Prec = I - A*P*(A_H)^-1 * R   with KSP_POST as RICHARDSON alongwith
> PCNONE.
>

Read my last message again. You either want the additive

Prec = I + C

(where C = P*A_H^{-1}*R is the coarse solve) or the multiplicative

Prec = C + S (I - A C)

perhaps with S = I (or some scaling factor). I don't think your definition
of Prec makes sense or is the operation that you intend to be applying.


> I hope PCNONE make smoother S = I in the framework you suggested earlier
> i.e.
> C b + S (b - A C b)~~~~~~ where C is read as CGC.
> It seems working well with levels 2, but when I force RICHARDSON_max_it 0.
> To my understanding, it should work with RICHARDSON_max_it = 1;
>

Read through my last message again. I explained that this does not work and
that it is caused by the destabilizing effect of the extra multiply without
a smoother. You can fix it for easy problems with
-mg_levels_ksp_richardson_self_scale.


> What if I want to approximate my all coarse matrices with any Krylov
> iteration ?
>

The methods on each level are independent, you can set them with
-mg_coarse_ksp_type gmres -mg_levels_1_ksp_type cg -mg_levels_1_ksp_max_it
100 -mg_levels_2_ksp_type minres ...
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