This paper introduces, analyses, and implements efficient time parallel methods for solving the Cahn–Hilliard (CH) equation. Efficient numerical methods for the CH equation are crucial due to its wide range of applications. In particular, simulating the CH equation often requires long computational times to obtain the solution during the phase coarsening stage. Therefore, there is a need to accelerate the computations using parallel methods in the time dimension. We propose linear and nonlinear Parareal methods for the CH equation, depending on the choice of the fine approximation. The effectiveness of our approach is demonstrated through numerical experiments.

中文翻译：

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Cahn-Hilliard 方程线性和非线性 Parareal 方法的收敛性

本文介绍、分析并实现了求解 Cahn-Hilliard (CH) 方程的高效时间并行方法。由于 CH 方程的广泛应用，有效的数值方法至关重要。特别是，模拟CH方程通常需要很长的计算时间才能在相位粗化阶段获得解。因此，需要在时间维度上使用并行方法来加速计算。我们针对 CH 方程提出了线性和非线性拟实数方法，具体取决于精细近似的选择。我们的方法的有效性通过数值实验得到了证明。