[petsc-users] ksppreonly question

[Barry Smith]

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