On the convergence of overlapping and non-overlapping Schwarz methods for the Cahn–Hilliard equation

In this study, we develop and investigate the Schwarz method with or without overlap for the Cahn–Hilliard (CH) problem. The CH equation has a wide range of applications, hence it is crucial to develop effective numerical techniques. In this article, we provide the formulation of the classical Schwarz methods (CSM) and optimized Schwarz methods (OSM) for the CH equation and present the convergence behaviour for two as well as multiple subdomain settings. We also formulate the nonlinear variant of the Schwarz and quasi-optimized Schwarz techniques for the same. We provide numerical results to support our conclusions. •Formulation of linear and non-linear Schwarz method.•Formulation of linear and non-linear optimize Schwarz method.•Solution of Min–max problem to predict Robin parameters.•Convergence analysis for proposed methods.•Possibility of parallel computing.