On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems

Faker Ben Belgacem; Michel Fournié; Nabil Gmati; Faten Jelassi

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • 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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Ben Belgacem, Faker, et al. "On the Schwarz algorithms for the Elliptic Exterior Boundary Value Problems." ESAIM: Mathematical Modelling and Numerical Analysis 39.4 (2010): 693-714. <http://eudml.org/doc/194282>.

@article{BenBelgacem2010,
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. },
author = {Ben Belgacem, Faker, Fournié, Michel, Gmati, Nabil, Jelassi, Faten},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Boundary integral equations; boundary element methods; finite element methods; coupling methods; domain decomposition techniques; Schwarz algorithm.; boundary integral equation; boundary element methods; finite element methods; domain decomposition; Schwarz algorithm; Poisson equation},
language = {eng},
month = {3},
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/194282},
volume = {39},
year = {2010},
}

TY - JOUR
AU - Ben Belgacem, Faker
AU - Fournié, Michel
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
DA - 2010/3//
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; boundary element methods; finite element methods; domain decomposition; Schwarz algorithm; Poisson equation
UR - http://eudml.org/doc/194282
ER -

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