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On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems

Published online by Cambridge University Press:  15 August 2005

Faker Ben Belgacem ,
Michel Fournié ,
Nabil Gmati  and
Faten Jelassi
Faker Ben Belgacem
Affiliation:
MIP (UMR CNRS 5640), UPS, 118 route de Narbonne, 31062 Toulouse, France. belgacem@mip.ups-tlse.fr; fournie@mip.ups-tlse.fr
Michel Fournié
Affiliation:
MIP (UMR CNRS 5640), UPS, 118 route de Narbonne, 31062 Toulouse, France. belgacem@mip.ups-tlse.fr; fournie@mip.ups-tlse.fr
Nabil Gmati
Affiliation:
LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia. nabil.gmati@ipein.rnu.tn
Faten Jelassi
Affiliation:
LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia. faten.jelassi@lamsin.rnu.tn 

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Abstract

Tuning the alternating Schwarz method to theexterior problems is the subject of this paper.We present the original algorithmand we propose a modification of it, so that the solution of the subproblem involving the condition at infinityhas an explicit integral representation formulas while the solutionof the other subproblem, set in a bounded domain,is approximated by classical variational methods. We investigate many of the advantages of the newSchwarz approach: a geometrical convergence rate,an easy implementation, a substantial economyin computational costs anda satisfactory accuracy in the numerical resultsas well as their agreement with the theoretical statements.

Keywords

Boundary integral equationsboundary element methodsfinite elementmethodscoupling methodsdomain decomposition techniquesSchwarz algorithm.

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 39 , Issue 4 , July 2005 , pp. 693 - 714
Copyright
© EDP Sciences, SMAI, 2005

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