The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation, especially on parallel and hybrid supercomputers. In this paper, we propose an exponential time integration method for the Cahn-Hilliard equation and describe its efficient Krylov subspace based implementation. We compare the method to a Chebyshev polynomial local iteration modified (LIM) time stepping scheme. Both methods are explicit (i.e., do not involve linear system solution) and tested with both constant and adaptively chosen time steps.

翻译：Cahn-Hilliard方程已广泛应用于物理学、化学和工程学中的各类数学模型。显式稳定化时间步进方法对于Cahn-Hilliard方程的时间积分具有吸引力，尤其是在并行与混合超级计算机上。本文针对Cahn-Hilliard方程提出一种指数时间积分方法，并描述其基于Krylov子空间的高效实现。我们将该方法与一种Chebyshev多项式局部迭代修正（LIM）时间步进方案进行比较。两种方法均为显式（即不涉及线性方程组求解），并采用固定时间步长与自适应选取时间步长进行测试。