John,

   For any non-trivial size problem for the Laplacian you definitely want to 
use multigrid. You can start by trying algebraic multigrid on both cases with 

-pc_type gamg

  Barry

On Sep 22, 2014, at 6:41 PM, Alletto, John M <[email protected]> wrote:

> I am solving one of the PETSc 3D Laplacian examples with a 7 point stencil of 
> width 1 and in a separate baseline with a 13 point stencil of width 2 (a more 
> accurate mesh).
>  
> What worked fast in terms of solvers and pre-conditioner for the less 
> accurate baseline was non-optimal (very slow) for the more accurate baseline.
>  
> Are there a set of general rules for picking preconditioners and solvers when 
> solving a 3D Laplace's equation?
>  
>  
> Thank you for your time
> John Alletto

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