[petsc-dev] Deflated Krylov solvers for PETSc

[Barry Smith]

On Mar 2, 2013, at 11:16 AM, "Mark F. Adams" <mark.adams at columbia.edu> wrote:

>> 
>> An alternative description for the method in the paper is "two-level unsmoothed aggregation applied to the ASM-preconditioned operator".
>> 
> 
> Isn't this paper just doing two level unsmoothed aggregation with a V(0,k) cycle, where k (and the smoother) is K in the paper?
> 
> It looks to me like you are moving the multigrid coarse grid correction (projection) from the PC into the operator, in which case this method is identical to two level MG with the V(0,k) cycle.

  Well, its not "identical" is it? In the deflation approach it introduces a null space into the operator, in the multigrid approach it does not. So identical only in analogy? So what I am interested in EXACTLY how are they related, relationship between eigenvalues or convergence rate.

   Barry

> 
> I'm sure I'm missing something.  Jie's writeup has an orthogonality condition on the restriction operator, which I don't see in the Vuik paper.