On the Schwarz algorithms for the elliptic exterior boundary value problems
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 39 (2005) no. 4, p. 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 : https://doi.org/10.1051/m2an:2005030
Classification:  35J20,  65N38,  65N55
Keywords: boundary integral equations, boundary element methods, finite element methods, coupling methods, domain decomposition techniques, Schwarz algorithm
@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},
     publisher = {EDP-Sciences},
     volume = {39},
     number = {4},
     year = {2005},
     pages = {693-714},
     doi = {10.1051/m2an:2005030},
     zbl = {1089.65126},
     mrnumber = {2165675},
     language = {en},
     url = {http://www.numdam.org/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, Volume 39 (2005) no. 4, pp. 693-714. doi : 10.1051/m2an:2005030. http://www.numdam.org/item/M2AN_2005__39_4_693_0/

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