Efficient and stable time integration of Cahn-Hilliard equations: explicit, implicit and explicit iterative schemes

TL;DR

The paper introduces a novel explicit time integration method for the Cahn-Hilliard equation that combines Eyre splitting with a local iteration scheme, achieving stability and efficiency with large time steps.

Contribution

It presents a new explicit, gradient-stable time integration algorithm for the Cahn-Hilliard equation that improves stability and computational efficiency over existing methods.

Findings

Method is gradient-stable allowing large time steps

Numerical tests demonstrate improved stability and efficiency

Comparison shows advantages over other time integration schemes

Abstract

To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the implicit system arising each time integration step. The proposed method is gradient-stable and allows to use large time steps, whereas, regarding its computational structure, it is an explicit time integration scheme. Numerical tests are presented to demonstrate abilities of the new method and to compare it with other time integration methods for Cahn-Hilliard equation.