[petsc-users] ksppreonly question

[Jed Brown]

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.
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