A parallel multigrid method of the Cahn-Hilliard equation

Abstract

We present a parallel finite difference scheme and its implementation for solving the Cahn-Hilliard equation, which describes the phase separation process. Our numerical algorithm employs an unconditionally gradient stable splitting discretization method. The resulting discrete equations are solved using a parallel multigrid method. This parallel scheme facilitates the solution of large-scale problems. We provide numerical results related to the speed-up, efficiency, and scalability to demonstrate the high performance of our proposed method. We also propose a linearly stabilized splitting scheme for the Cahn-Hilliard equation with logarithmic free energy. (c) 2013 Elsevier B.V. All rights reserved.