On the Schwarz algorithms for the elliptic exterior boundary value problems
ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 693-714.

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.

DOI : 10.1051/m2an:2005030
Classification : 35J20, 65N38, 65N55
Mots clés : boundary integral equations, boundary element methods, finite element methods, coupling methods, domain decomposition techniques, Schwarz algorithm
Belgacem, Faker Ben  ; Fournié, Miche  ; Gmati, Nabil 1 ; Jelassi, Faten 2

1 LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia.
2 LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia
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     title = {On the {Schwarz} algorithms for the elliptic exterior boundary value problems},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
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Belgacem, Faker Ben; Fournié, Miche; Gmati, Nabil; Jelassi, Faten. On the Schwarz algorithms for the elliptic exterior boundary value problems. ESAIM: Modélisation mathématique et analyse numérique, Tome 39 (2005) no. 4, pp. 693-714. doi : 10.1051/m2an:2005030. http://www.numdam.org/articles/10.1051/m2an:2005030/

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