[petsc-users] ksppreonly question

[Jed Brown]

On Fri, Sep 21, 2012 at 6:15 PM, Shao-Ching Huang <huangsc at gmail.com> wrote:

> I am reading this page,
>
> http://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/KSP/KSPRICHARDSON.html
> It says:
>
> "This method often (usually) will not converge unless scale is very
> small.


That statement applies if you use a general preconditioner that does not
bound the preconditioned spectrum. With LU, you are fine with a scale of 1
(or close).


> It is described in "
>
> and seems to miss a reference there.
>

The reference is further down the page. Thanks for pointing out the anomaly.


>
>
> On Fri, Sep 21, 2012 at 4:07 PM, Shao-Ching Huang <huangsc at gmail.com>
> wrote:
> > I will try the Richardson procedure Jed suggested. Thank you!
> >
> >
> > On Fri, Sep 21, 2012 at 3:50 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >>
> >>   Ok, so it is using a FULL LU factorization of A1.  Hence with what I
> outlined below you would use -ksp_type preonly -pc_type lu
> >>
> >>    If you reorganize the iteration then in exact arithmetic it is what
> we in PETSc call Richardson's method with preconditioner defined from M
> (the LU of M) so I was wrong; you can do as Jed suggested
> >> KSPSetOperations(ksp, A,A1,….) and run with -ksp_type richardson to
> mimic the old algorithm. Simply switch to -ksp_type gmres and you have the
> late 80's version of the algorithm
> >>
> >>
> >>
> >>    Barry
> >>
> >>
> >> On Sep 21, 2012, at 5:30 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:
> >>
> >>>
> >>> On Sep 21, 2012, at 5:26 PM, Jed Brown <jedbrown at mcs.anl.gov> wrote:
> >>>
> >>>> On Fri, Sep 21, 2012 at 5:21 PM, Shao-Ching Huang <huangsc at gmail.com>
> wrote:
> >>>> In this particular finite volume discretization, the flux normal to a
> >>>> face involves the cell-center values on each side of the face (1),
> >>>> plus values from neighboring nodes (2) [due to non-orthogonal mesh
> >>>> cell shape]. The A1 part include coefficients from (1). A2 includes
> >>>> those in (2).
> >>>>
> >>>> 1. Call KSPSetOperators(ksp,A,A1,flag)
> >>>>
> >>>> You can make A in the above a MATSHELL that applies A1 + A2
> matrix-free (or just the A2 part).
> >>>>
> >>>> 2. Use any Krylov method. The specific method -ksp_type richardson
> will do the defect-correction version of what you have written, but a real
> Krylov method will almost certainly perform much better. Note that A1^{-1}
> will be applied using whatever method you choose (via -pc_type). A V-cycle
> of algebraic multigrid should work very well.
> >>>
> >>>   To mimic the exact old algorithm for comparison purposes
> >>>  I don't think you can get this directly with KSP you'll need to
> manage the "outer" iteration yourself, something like
> >>>
> >>>     for (n=0; n<Nmax ….
> >>>          MatMultAdd(A2,x,b,c) where A2 is the opposite sign of your A2
> above
> >>>          KSPSolve(ksp,c,x);
> >>>    }
> >>> Your KSP solve could use any solver you like (what does the old code
> use?, you should use the same thing for comparison purposes)
> >>>
> >>> Of course, this is only for comparison purposes, no one in 2012 except
> in a legacy code would use such a primitive nested solver.
> >>>
> >>>  Barry
> >>>
> >>
>
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