Dear members, I had to implement the projection preconditioner (P = I - A*R*(A_H)^1 *P) along with an standard preconditioner (M). And I read in some thread of users list that multilevel preconditioner can better handled by PCMG too, thus I had tried to implement the later (M) as pre smoother, where as the earlier (P) as CGC in PCMG framework. 1. Does it make sense ? or the coarse grid correction of PCMG only does this part: R*(A_H)^1 *P ?? 2. How can I adapt my projection preconditioner (P) as (P1 = I - A*R*(A_H)^1 *P + R*(A_H)^1 *P ) ? I hope made you to get my problem. Even sorry for not a good narration. Thank you in anticipation, Abdul H. TechnischeUniversiteit Delft Faculteit Elektrotechniek, Wiskunde en Informatica Numerical Analysis