Two-level parallel Schwarz methods for singularly perturbed semilinear elliptic problems
type: Item
instance of: scholarly article
title: Two-level parallel Schwarz methods for singularly perturbed semilinear elliptic problems
zbMATH Open document ID: 0957.65110
DOI: 10.1016/S0898-1221(00)00185-1
author: R. Smith
publication date: 2000-11-13T00:00:00Z
review text: Two-level domain decomposition methods based on the Schwarz alternating procedure are proposed for the numerical solution of singularly perturbed semilinear elliptic problems. The convergence rate estimates are established on differential level (independently of specific numerical realizations of the methods) and for regular rectangular domain decomposition. The author also describes a modified two-level Schwarz method with Newton's linearization. Numerical experiments for a test problem illustrate the behaviour of the methods with respect to the critical parameters, such as the perturbation parameter, the amount of overlapping and sizes of subdomains.. Application of one of the two-level Schwarz methods to a semiconductor model problem is also discussed.
reviewed by: Karel Najzar
Mathematics Subject Classification ID: 65N55
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 35J65
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 65Y05
zbMATH DE Number: 1528525
zbMATH Keywords: singularly perturbation
zbMATH Keywords: Schwarz alternating procedure
zbMATH Keywords: domain decomposition
zbMATH Keywords: parallel computing
zbMATH Keywords: numerical examples
zbMATH Keywords: semilinear elliptic problems
zbMATH Keywords: convergence
zbMATH Keywords: semiconductor
MaRDI profile type: Publication
cites work: Linear and quasilinear elliptic equations
cites work: Q3788994
cites work: Q4279368
cites work: Q4716273
cites work: Multiplicative Schwarz Methods for Parabolic Problems
cites work: Q4694042
cites work: Domain decomposition and parallel processing for the numerical solution of partial differential equations
cites work: Q3742651
cites work: Q4310146
cites work: A Schwarz Alternating Procedure for Singular Perturbation Problems
cites work: Q3830744
cites work: Physically Motivated Domain Decomposition for Singularly Perturbed Equations
cites work: Q3806726
cites work: Q4036644
cites work: Computational method for a singular perturbation problem via domain decomposition and its parallel implementation
cites work: The solution of singularly perturbed semilinear elliptic problems by iterative domain decomposition algorithms
cites work: Overlapping Schwarz Methods for a Singularly Perturbed Semilinear Elliptic Problem and Their Parallel Implementation
cites work: Parallel two-level Schwarz methods for singularly perturbed elliptic problems
cites work: Q3751948
cites work: Q5652137
cites work: Iterative domain decomposition algorithms for the solution of singularly perturbed parabolic problems
cites work: Q5610080
cites work: An Iterative Solution Method for Linear Systems of Which the Coefficient Matrix is a Symmetric M-Matrix
cites work: The solution of singularly perturbed huge problems via domain decomposition
full work available at URL: s0898-1221(00)00185-1
OpenAlex ID: W2018559092
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1528525