Linear and nonlinear Dirichlet–Neumann methods 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) methods applied to the CH equation and study the convergence behaviour in one and two spatial dimensions in multiple subdomains. We show numerical experiments to illustrate our theoretical findings and effectiveness of the method.

KEYWORDS:

• Dirichlet–Neumann
• Cahn–Hilliard equation
• parallel computing
• domain decomposition
• convergence analysis

AMS SUBJECT CLASSIFICATIONS:

• 65M55
• 65Y05
• 65M15

Acknowledgments

The authors would like to thank the CSIR India (File No: 09/1059(0019)/2018-EMR-I) and DST-SERB (File No: SRG/2019/002164) for the financial assistance and IIT Bhubaneswar for research facility.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Council of Scientific and Industrial Research, India.