[petsc-users] Advice on coupling linear physics with Allen-Cahn

[Barry Smith]

> On Nov 3, 2022, at 2:33 PM, Mike Welland <mike at 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!