Linear and Nonlinear Parareal Methods for the Cahn-Hilliard Equation

2023/04/27 by Gobinda Garai, Garai, Gobinda, Bankim C. Mandal +1
Materials Science · #65M12 #65M15 #65Y05 #65Y20 #FOS: Mathematics #Numerical Analysis (math.NA) #Solidification and crystal growth phenomena

paper · pdf · doi:10.48550/arxiv.2304.14074

openalex publication_date 2023/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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