Parallel domain decomposition methods for the 3D Cahn-Hilliard equation

Domain decomposition methods are studied in a scalable parallel solver for the Cahn-Hilliard equation in 3D. The discretization is based on a stabilized implicit cell-centered finite difference scheme together with an adaptive time-stepping strategy. A Newton-KrylovSchwarz algorithm is applied to solve the nonlinear system of equations arising at each time step. In the Schwarz preconditioner, we find that low-order homogeneous Neumann boundary conditions on the overlapping subdomains lead to better convergence than do the standard conditions for this fourth-order equation. Numerical tests show that the implicit approach scales well on an IBM Blue Gene/L machine with thousands of processor cores.