In this paper, we propose, analyze and implement efficient time parallel methods for the Cahn-Hilliard (CH) equation. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of the CH equation has. The CH equation generally needs to be simulated for a very long time to get the solution of phase coarsening stage. Therefore it is desirable to accelerate the computation using parallel method in time. We present linear and nonlinear Parareal methods for the CH equation depending on the choice of fine approximation. We illustrate our results by numerical experiments.

翻译：本文针对Cahn-Hilliard (CH)方程提出、分析并实现了高效的时间并行方法。鉴于CH方程的广泛应用范围，开发其高效数值方法具有重要意义。CH方程通常需要极长时间的模拟才能获得相粗化阶段的解，因此采用时间并行方法加速计算具有重要价值。我们根据精细逼近的选择，为CH方程分别提出了线性和非线性Parareal方法，并通过数值实验验证了所得结果。