[petsc-users] GAMG parameters for ideal coarsening ratio

[Mark Adams]

On Tue, Mar 17, 2020 at 1:42 PM Sajid Ali <sajidsyed2021 at u.northwestern.edu>
wrote:

> Hi Mark/Jed,
>
> The problem I'm solving is scalar helmholtz in 2D, (u_t = A*u_xx + A*u_yy
> + F_t*u, with the familiar 5 point central difference as the derivative
> approximation,
>

I assume this is definite HelmHoltz. The time integrator will also add a
mass term. I'm assuming F_t looks like a mass matrix.


> I'm also attaching the result of -info | grep GAMG if that helps). My goal
> is to get weak and strong scaling results for the FD solver (leading me to
> double check all my parameters). I ran the sweep again as Mark suggested
> and it looks like my base params were close to optimal ( negative threshold
> and 10 levels of squaring
>

For low order discretizations, squaring every level, as you are doing,
sound right. And the mass matrix confuses GAMG's filtering heuristics so no
filter sounds reasonable.

Note, hypre would do better than GAMG on this problem.


> with gmres/jacobi smoothers (chebyshev/sor is slower)).
>

You don't want to use GMRES as a smoother (unless you have
indefinite Helmholtz). SOR will be more expensive but often converges a lot
faster. chebyshev/jacobi would probably be better for you.

And you want CG (-ksp_type cg) if this system is symmetric positive
definite.


>
> [image: image.png]
>
> While I think that the base parameters should work well for strong
> scaling, do I have to modify any of my parameters for a weak scaling run ?
> Does GAMG automatically increase the number of mg-levels as grid size
> increases or is it upon the user to do that ?
>
> @Mark : Is there a GAMG implementation paper I should cite ? I've already
> added a citation for the Comput. Mech. (2007) 39: 497–507 as a reference
> for the general idea of applying agglomeration type multigrid
> preconditioning to helmholtz operators.
>
>
> Thank You,
> Sajid Ali | PhD Candidate
> Applied Physics
> Northwestern University
> s-sajid-ali.github.io
>
>
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