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 equations, boundary element methods, finite element methods, coupling methods, domain decomposition techniques, Schwarz algorithm
Ben Belgacem, Faker 1 ; Fournié, Miche ; Gmati, Nabil 2 ; Jelassi, Faten 3
@article{M2AN_2005__39_4_693_0,
author = {Ben Belgacem, Faker 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 },
pages = {693--714},
year = {2005},
publisher = {EDP-Sciences},
volume = {39},
number = {4},
doi = {10.1051/m2an:2005030},
mrnumber = {2165675},
zbl = {1089.65126},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005030/}
}
TY - JOUR AU - Ben Belgacem, Faker AU - Fournié, Miche AU - Gmati, Nabil AU - Jelassi, Faten TI - On the Schwarz algorithms for the elliptic exterior boundary value problems JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2005 SP - 693 EP - 714 VL - 39 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005030/ DO - 10.1051/m2an:2005030 LA - en ID - M2AN_2005__39_4_693_0 ER -
%0 Journal Article %A Ben Belgacem, Faker %A Fournié, Miche %A Gmati, Nabil %A Jelassi, Faten %T On the Schwarz algorithms for the elliptic exterior boundary value problems %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2005 %P 693-714 %V 39 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005030/ %R 10.1051/m2an:2005030 %G en %F M2AN_2005__39_4_693_0
Ben Belgacem, Faker; Fournié, Miche; Gmati, Nabil; Jelassi, Faten. On the Schwarz algorithms for the elliptic exterior boundary value problems. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 4, pp. 693-714. doi: 10.1051/m2an:2005030
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