[petsc-users] Monotonic convergence in FGMRES.

[Jed Brown]

On Tue, Dec 21, 2010 at 19:53, Vijay S. Mahadevan <vijay.m at gmail.com> wrote:

> I am running a linear problem discretized with FEM on a diffusion
> reaction system, with discontinuous source distribution. When I run
> FGMRes with geometric multigrid as its preconditioner, I notice that
> every time after the restart in fgmres, the new residual is orders of
> magnitude higher than the previous iteration. I might be wrong on this
> but should the restart not preserve monotonicity in convergence ? Or
> am I thinking of a different variant of Gmres here.
>

It is not possible to guarantee monotonicity for nonsymmetric matrices
without storing the full subspace.  There is no variant of GMRES, or any
Krylov method for that matter, that can do what you want.  You are seeing a
particularly large jump, if you actually have a linear preconditioner (if
you don't use Krylov cycles inside your smoothers) then you might try using
bcgs or some variant thereof which would avoid the high cost of restart.  Or
you could stop using restarts, it looks like you were getting close to an
adequate tolerance.  Or find a way to make the preconditioner strong enough
to converge in a reasonable number of iterations.
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