| Issue |
ESAIM: M2AN
Volume 39, Number 4, July-August 2005
|
|
|---|---|---|
| Page(s) | 693 - 714 | |
| DOI | https://doi.org/10.1051/m2an:2005030 | |
| Published online | 15 August 2005 | |
On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems
1
MIP (UMR CNRS 5640),
UPS, 118 route de Narbonne,
31062 Toulouse, France.
belgacem@mip.ups-tlse.fr; fournie@mip.ups-tlse.fr
2
LAMSIN,
IPEIN, Campus Universitaire, Route Mrazka,
8000 Nabeul, Tunisia.
nabil.gmati@ipein.rnu.tn
3
LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia.
faten.jelassi@lamsin.rnu.tn
Received:
15
April
2004
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
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