Convergence of substructuring Methods for the Cahn-Hilliard Equation

Autor:	Garai, Gobinda, Mandal, Bankim C.
Rok vydání:	2021
Předmět:	Mathematics - Numerical Analysis 65M55 65Y05 65M15
Druh dokumentu:	Working Paper
Popis:	In this paper, we formulate and study substructuring type algorithm for the Cahn-Hilliard (CH) equation, which was originally proposed to describe the phase separation phenomenon for binary melted alloy below the critical temperature and since then it has appeared in many fields ranging from tumour growth simulation, image processing, thin liquid films, population dynamics etc. Being a non-linear equation, it is important to develop robust numerical techniques to solve the CH equation. Here we present the formulation of Dirichlet-Neumann (DN) and Neumann-Neumann (NN) methods applied to CH equation and study their convergence behaviour. We consider the domain-decomposition based DN and NN methods in one and two space dimension for two subdomains and extend the study for multi-subdomain setting for NN method. We verify our findings with numerical results. Comment: 26 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2112.01699 Zobrazit plný text záznamu View this record from Arxiv