On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems
MIP (UMR CNRS 5640),
UPS, 118 route de Narbonne,
31062 Toulouse, France.
2 LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia. firstname.lastname@example.org
3 LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia. email@example.com
Revised: 29 March 2005
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.
Mathematics Subject Classification: 35J20 / 65N38 / 65N55
Key words: Boundary integral equations / boundary element methods / finite element methods / coupling methods / domain decomposition techniques / Schwarz algorithm.
© EDP Sciences, SMAI, 2005