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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. [email protected]; [email protected]
Michel Fournié
Affiliation:
MIP (UMR CNRS 5640), UPS, 118 route de Narbonne, 31062 Toulouse, France. [email protected]; [email protected]
Nabil Gmati
Affiliation:
LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia. [email protected]
Faten Jelassi
Affiliation:
LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia. [email protected] 

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Abstract

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

Keywords

Boundary integral equationsboundary element methodsfinite element methodscoupling methodsdomain decomposition techniquesSchwarz algorithm.
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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