> On Nov 3, 2022, at 2:33 PM, Mike Welland <m...@mikewelland.com> wrote:
>
> I am coupling a linear diffusion equation with Allen-Cahn in a time dependent
> problem. I'd like to take advantage of the linear block to speed things up.
> I'm trying two approaches:
>
> 1. Allen-Cahn with double well potential: phi^2*(1-phi^2), which makes it
> nonlinear. The best performance I have is with geometric multigrid on the
> full system. I tried using a schur complement with the linear diffusion block
> on A00 (both inside mg levels, and just mg on S) but didn't get good
> performance.
With geometric multigrid there is not much setup cost (so reusing it is not
important).
>
> 2. Allen-Cahn with the 'obstacle' potential: phi*(1-phi) which is linear but
> needs the vi solver to keep 0<=phi<=1. My whole system becomes linear
> (great!) but needs the nonlinear steps for the vi solver, and I'm not sure if
> it is reusing the factorization since the DOFs are being changed with the
> active step.
You are correct. Since the problem (size) changes for each solve not much of
anything can be directly reused in the solver. But with geometric multigrid
there is not much setup cost (so reusing it is not important).
>
> Any suggestion / guidance would be appreciated!
> Thanks!
