"Alletto, John M" <[email protected]> writes: > 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?
Always use Full Multigrid. If solving up to discretization error takes more than 5 work units, something is wrong. PETSc does not have built-in high-order interpolation operators like would be most suitable for the 13-point stencil (assuming it is higher order accurate). Dealing with boundary conditions for high-order FD and (especially) FV methods are a common source of errors in MG solvers.
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