On the Schwarz algorithms for the elliptic exterior boundary value problems

Faker Ben Belgacem; Miche Fournié; Nabil Gmati[1]; Faten Jelassi[2]

  • [1] LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia.
  • [2] LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2005)

  • Volume: 39, Issue: 4, page 693-714
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Belgacem, Faker Ben, et al. "On the Schwarz algorithms for the elliptic exterior boundary value problems." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 39.4 (2005): 693-714. <http://eudml.org/doc/244817>.

@article{Belgacem2005,
abstract = {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.},
affiliation = {LAMSIN, IPEIN, Campus Universitaire, Route Mrazka, 8000 Nabeul, Tunisia.; LAMSIN, FSB, Jarzouna, 7021 Bizerte, Tunisia},
author = {Belgacem, Faker Ben, Fournié, Miche, Gmati, Nabil, Jelassi, Faten},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {boundary integral equations; boundary element methods; finite element methods; coupling methods; domain decomposition techniques; Schwarz algorithm; boundary integral equation; domain decomposition; Poisson equation},
language = {eng},
number = {4},
pages = {693-714},
publisher = {EDP-Sciences},
title = {On the Schwarz algorithms for the elliptic exterior boundary value problems},
url = {http://eudml.org/doc/244817},
volume = {39},
year = {2005},
}

TY - JOUR
AU - Belgacem, Faker Ben
AU - Fournié, Miche
AU - Gmati, Nabil
AU - Jelassi, Faten
TI - On the Schwarz algorithms for the elliptic exterior boundary value problems
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2005
PB - EDP-Sciences
VL - 39
IS - 4
SP - 693
EP - 714
AB - 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.
LA - eng
KW - boundary integral equations; boundary element methods; finite element methods; coupling methods; domain decomposition techniques; Schwarz algorithm; boundary integral equation; domain decomposition; Poisson equation
UR - http://eudml.org/doc/244817
ER -

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