A Schwarz alternating procedure for singular perturbation problems

Marc Garbey

doi:10.1137/S1064827593258437

A Schwarz alternating procedure for singular perturbation problems

Marc Garbey

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

We show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. We give sharp estimates for the optimal position of the domain boundaries and study the convergence rates of the algorithm for various linear second-order singular perturbation problems. We report on implementation results for a turning-point problem and a combustion problem.

Original language	English (US)
Pages (from-to)	1175-1201
Number of pages	27
Journal	SIAM Journal of Scientific Computing
Volume	17
Issue number	5
DOIs	https://doi.org/10.1137/S1064827593258437
State	Published - Sep 1996

Keywords

Boundary layers
Domain decomposition
Singular perturbations

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1137/S1064827593258437

Cite this

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title = "A Schwarz alternating procedure for singular perturbation problems",

abstract = "We show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. We give sharp estimates for the optimal position of the domain boundaries and study the convergence rates of the algorithm for various linear second-order singular perturbation problems. We report on implementation results for a turning-point problem and a combustion problem.",

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AB - We show that the Schwarz alternating procedure offers a good algorithm for the numerical solution of singular perturbation problems, provided the domain decomposition is properly designed to resolve the boundary and transition layers. We give sharp estimates for the optimal position of the domain boundaries and study the convergence rates of the algorithm for various linear second-order singular perturbation problems. We report on implementation results for a turning-point problem and a combustion problem.

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KW - Singular perturbations

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A Schwarz alternating procedure for singular perturbation problems

Abstract

Keywords

ASJC Scopus subject areas

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