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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