Optimized Schwarz methods with elliptical domain decompositions
type: Item
instance of: scholarly article
title: Optimized Schwarz methods with elliptical domain decompositions
zbMATH Open document ID: 1479.65036
author: Yanyan Li
published in: Journal of Scientific Computing
publication date: 2021-05-28T00:00:00Z
review text: The authors consider the domain decomposition method for solving second-order elliptic equations posed on elliptical geometries. To be more specific, an optimized Schwarz method is proposed with elliptical domain decomposition, i.e., decompositions into an ellipse and elliptical rings. First, using the technique of separation of variables, the spatial variables are decoupled and the subdomain problems are reduced to radial Mathieu-like equations defined on finite intervales. Second, the convergence of the classical Schwarz method is provided. Third, optimized Schwarz methods for both overlapping and nonoverlapping cases are considered, where a series of transmission conditions are introduced and optimized. Lastly, other related topics including the extensions to different geometric domains and the model problem with variable coefficient, and the implementation issues, are discussed.
reviewed by: W. Gong
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65N22
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B30
Mathematics Subject Classification ID: 33E10
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 7352172
zbMATH Keywords: optimized Schwarz method
zbMATH Keywords: elliptical domain decomposition
zbMATH Keywords: optimized transmission condition
zbMATH Keywords: curved interfaces
describes a project that uses: FreeFem++
MaRDI profile type: Publication
full work available at URL: s10915-020-01394-8
OpenAlex ID: W3121007210
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DOI: 10.1007/S10915-020-01394-8
description: scientific article; zbMATH DE number 7352172