A parallel multigrid method of the Cahn–Hilliard equation

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.