[petsc-users] Are there a set of general rules for picking preconditioners and solvers when solving a 3D Laplace's equation?

[Jed Brown]

"Alletto, John M" <john.m.alletto at lmco.com> 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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