A parallel multigrid method of the Cahn-Hilliard equation

作者：Shin Jaemin; Kim Sungki; Lee Dongsun; Kim Junseok^*

来源：Computational Materials Science, 2013, 71: 89-96.

DOI：10.1016/j.commatsci.2013.01.008

• Parallel computing
• Cahn-Hilliard equation
• Multigrid
• Phase separation
• Linearly stabilized splitting scheme

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.

• 出版日期2013-4