On the convergence of linear and nonlinear Parareal methods for the Cahn–Hilliard equation

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. •Formulation of linear and non-linear Parallel-in-time methods for the Cahn–Hilliard equation.•Convergence analysis of proposed time parallel methods.•Numerical illustration of convergence behaviour of proposed time parallel methods.•Possibility of parallel computing.