Optimized Ventcel-Schwarz methods for the Cahn-Hilliard equation discretized by the stabilized linear Crank-Nicolson scheme
type: Item
instance of: scholarly article
title: Optimized Ventcel-Schwarz methods for the Cahn-Hilliard equation discretized by the stabilized linear Crank-Nicolson scheme
zbMATH Open document ID: 1501.65017
author: Yafei Sun
author: Yingxiang Xu
author: Shuangbin Wang
author: Shan Gao
published in: Advances in Computational Mathematics
publication date: 2022-10-27T00:00:00Z
review text: One of the most important methods for the time discretization of the Cahn-Hilliard (CH) equation is the stabilized linear Crank-Nicolson (SL-CN) scheme. While this method is an unconditionally energy stable method of second order (allowing to use time steps as large as possible to reduce the total calculation), it is well known that it requires a very large amount of calculations for simulating the CH equation. To accelerate the simulation process, it is proposed to solve the differential system resulting from the time discretization, by an optimized Schwarz method using a newly proposed Ventcel transmission condition. For a setting of two-subdomain domain decomposition with or without overlap, the authors obtain the convergence factor. This is derived using Fourier analysis and takes on two different forms according to the size of the time steps. The convergence factors are optimized for each case, optimized transmission parameters are obtained and so are the estimates for the convergence rates. This is achieved by solving the min-max problem of convergence factors using an asymptotic analysis. Numerical examples are included to illustrate the theoretical findings.
reviewed by: Kanakadurga Sivakumar
Mathematics Subject Classification ID: 65F10
Mathematics Subject Classification ID: 65M22
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N22
zbMATH DE Number: 7608425
zbMATH Keywords: Cahn-Hilliard equation
zbMATH Keywords: optimized Schwarz method
zbMATH Keywords: Ventcel transmission condition
zbMATH Keywords: domain decomposition
zbMATH Keywords: energy stable
zbMATH Keywords: stabilized linear Crank-Nicolson scheme
MaRDI profile type: Publication
full work available at URL: s10444-022-09982-y
OpenAlex ID: W4303199483
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DOI: 10.1007/S10444-022-09982-Y
description: scientific article; zbMATH DE number 7608425