[petsc-users] Multigrid preconditioning

[Jed Brown]

On Mon, Jul 30, 2012 at 4:06 PM, Michele Rosso <mrosso at uci.edu> wrote:

>  Hi,
>
> I am solving a variable coefficients Poisson equation with periodic BCs.
> The equation is discretized by using the standard 5-points stencil finite
> differencing scheme.
> I managed to solve the system successfully with the PCG method and now I
> would like to add
> a preconditioner to speed up the calculation. My idea is to use the
> multigrid preconditioner.
>
> Example ex22f.F implements what I think I need.
> If I understand correctly example ex22f.F, the subroutines "ComputeRHS"
> and "ComputeMatrix" define how the
> matrix and rhs-vector have to be computed at each level.
> In my case tough, both the jacobian and the rhs-vector cannot be computed
> "analytically", that is, they depend on variables
> whose values are available only at the finest grid.
>
> How can I overcome this difficulty?
>

Two possibilities:

1. homogenize on your own and rediscretize

2. use Galerkin coarse operators (possibly with algebraic multigrid)


Option 2 is much more convenient because it never

For geometric multigrid using DMDA, just use -pc_type mg -pc_mg_galerkin

For algebraic multigrid, use -pc_type gamg -pc_gamg_agg_nsmooths 1
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