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Issue ESAIM: M2AN
Volume 43, Number 3, May-June 2009
Page(s) 487 - 506
DOI 10.1051/m2an/2009010
Published online 08 April 2009

ESAIM: M2AN 43 (2009) 487-506
DOI: 10.1051/m2an/2009010

A multiplicative Schwarz method and its application to nonlinear acoustic-structure interaction

Roland Ernst1, Bernd Flemisch2 and Barbara Wohlmuth1

1  Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany.
2  Institute of Hydraulic Engineering, University of Stuttgart, Germany. bernd@iws.uni-stuttgart.de

Received November 20, 2007. Revised August 14, 2008. Published online April 8, 2009.

Abstract
A new Schwarz method for nonlinear systems is presented, constituting the multiplicative variant of a straightforward additive scheme. Local convergence can be guaranteed under suitable assumptions. The scheme is applied to nonlinear acoustic-structure interaction problems. Numerical examples validate the theoretical results. Further improvements are discussed by means of introducing overlapping subdomains and employing an inexact strategy for the local solvers.


Mathematics Subject Classification. 74F10, 65B99, 65M12.

Key words: Schwarz method, fluid-structure interaction, coupled problems, nonlinear elasticity, nonlinear acoustics, elasto-acoustic.


© EDP Sciences, SMAI 2009


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