Linear and Nonlinear Dirichlet-Neumann Method in Multiple Subdomains for the Cahn-Hilliard Equation

Abstract

In this paper, we propose and present a non-overlapping substructuring type iterative algorithm for the Cahn-Hilliard (CH) equation, which is a prototype for phase-field models. It is of great importance to develop efficient numerical methods for the CH equation, given the range of applicability of CH equation has. Here we present a formulation for the linear and non-linear Dirichlet-Neumann (DN) method applied to the CH equation and study the convergence behaviour in one and two spatial dimension in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.