[petsc-dev] Deflated Krylov solvers for PETSc

[Jed Brown]

On Fri, Mar 1, 2013 at 10:40 PM, Jie Chen <jiechen at mcs.anl.gov> wrote:

> I think the number of deflation vectors should not be large. So the K_c
> here is a small matrix, and whether Y is dense or sparse does not make a
> big difference. In this regard, deflation is not exactly the same as one
> V-cycle. For multigrid, you coarsen a grid of size 1,000,000 to 500,000.
> But for deflation, you reduce 1,000,000 to 10 or 50. Make sense?


An alternative description for the method in the paper is "two-level
unsmoothed aggregation applied to the ASM-preconditioned operator".

When there are many processes/subdomains, the dimension of the coarse space
can be huge.

Extreme eigenvectors would be more useful, but you would still need a very
large number to scale to many subdomains.
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