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

[Mike Welland]

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.

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.

Any suggestion / guidance would be appreciated!
Thanks!
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