[petsc-users] two-level Schwarz: PCMG or PCComposite

[Hui Zhang]

some corrections:

> I want to implement the two-level Schwarz method.  Let us denote P as the one-level
> Schwarz projection and P_0 as the coarse projection.  If I want the hybrid form of 
> preconditioned system as follows:
> 
>     (I-P_0) P (I-P_0) 

this should be 

      I  -  (I-P_0) (I-P) (I-P_0)

in general case.  Only when P_0 is exact solve, we have the precedent form.
 	 
> which is suitable:  PCMG or PCComposite?  It seems to me that PCComposite is good.
> But PCMG is not suitable because it can only implement the following form:
> 
>     (I-P) P_0 (I-P)

this should be
	
      I - (I-P) (I-P_0) (I-P)

since P is not a projection.