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Commun. Comput. Phys., 5 (2009), pp. 391-397. |
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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, 65F10Key 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) |