Geodesic
On the Schwarz algorithms for the elliptic exterior boundary value problems
Ben Belgacem, Faker1  ; Fournié, Miche ; Gmati, Nabil2 ; Jelassi, Faten3 
1 MIP (UMR CNRS 5640), UPS, 118 route de Narbonne, 31062 Toulouse, France
2 LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia.
3 LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 39 (2005) no. 4, pp. 693-714

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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
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

1 MIP (UMR CNRS 5640), UPS, 118 route de Narbonne, 31062 Toulouse, France
2 LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia.
3 LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia 
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     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},
     publisher = {EDP-Sciences},
     volume = {39},
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     year = {2005},
     doi = {10.1051/m2an:2005030},
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     zbl = {1089.65126},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2005030/}
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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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