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Zbl 1089.65126
Ben Belgacem, Faker; Fournié, Michel; Gmati, Nabil; Jelassi, Faten
On the Schwarz algorithms for the elliptic exterior boundary value problems. (English)
[J] ESAIM, Math. Model. Numer. Anal. 39, No. 4, 693-714 (2005). ISSN 0764-583X; ISSN 1290-3841/e

The focus of this paper is a new iterative method for the Poisson model set in open domains, introduced by them in another article. Here they detail a full analysis. The algorithm is an adaptation of the Schwarz procedure to the unboundedness of the domain. During the iterations one of the subproblems is modified, the one where the condition to the infinity is taken in account. So an explicit expression of its solution is obtained. The other subproblem is set in the bounded subdomain, for which a local Dirichlet or Neumann condition results from the previous step solution; it is solved by Lagrangian finite element methods. The iterative process is stopped when a given tolerance is obtained and the computed solution is considered to be a consistent approximation of the exact model.
[Ariadna Lucia Pletea (Iaşi)]

MSC 2000:: *65N38 Boundary element methods (BVP of PDE)
35J05 Laplace equation, etc.
65N30 Finite numerical methods (BVP of PDE)
65N55 Multigrid methods; domain decomposition (BVP of PDE)

Keywords: boundary integral equation; boundary element methods; finite element methods; coupling methods; domain decomposition; Schwarz algorithm; Poisson equation

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