Commun. Comput. Phys., 5 (2009), pp. 391-397.


An Iterative Domain Decomposition Algorithm for the Grad(div) Operator

E. Ahusborde 1, M. Azaiez 1, M. O. Deville 2, E. H. Mund 3*

1 TREFLE, (UMR CNRS 8505), Ecole Nationale Superieure de Chimie et de Physique de Bordeaux, Pessac, France.
2 Laboratory of Computational Engineering, Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland.
3 Unite de Thermodynamique, UCL, 1348 Louvain-La-Neuve, Belgium.

Received 16 July 2007; Accepted (in revised version) 8 January 2008
Available online 1 August 2008

Abstract

This paper describes an iterative solution technique for partial differential equations involving the grad(div) operator, based on a domain decomposition. Iterations are performed to solve the solution on the interface. We identify the transmission relationships through the interface. We relate the approach to a Steklov-Poincare operator, and we illustrate the performance of technique through some numerical experiments.

AMS subject classifications: 65N55, 65F10

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Key words: Domain decomposition, grad(div) operator, stable approximation, iterative substructuring method, Steklov-Poincare operator.

*Corresponding author.
Email: ahusborde@enscpb.fr (E. Ahusborde), azaiez@enscpb.fr (M. Azaiez), Michel.Deville@epfl.ch (M. O. Deville), emund@ulb.ac.be (E. H. Mund)
 

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