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.
@article{M2AN_2005__39_4_693_0,
author = {Belgacem, Faker Ben and Fourni\'e, Miche and Gmati, Nabil and Jelassi, Faten},
title = {On the Schwarz algorithms for the elliptic exterior boundary value problems},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
volume = {39},
year = {2005},
pages = {693-714},
doi = {10.1051/m2an:2005030},
mrnumber = {2165675},
zbl = {1089.65126},
language = {en},
url = {http://dml.mathdoc.fr/item/M2AN_2005__39_4_693_0}
}
Belgacem, Faker Ben; Fournié, Miche; Gmati, Nabil; Jelassi, Faten. On the Schwarz algorithms for the elliptic exterior boundary value problems. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Tome 39 (2005) pp. 693-714. doi : 10.1051/m2an:2005030. http://gdmltest.u-ga.fr/item/M2AN_2005__39_4_693_0/
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