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Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

Published online by Cambridge University Press:  26 April 2007

Xavier Antoine  and
Marion Darbas
Xavier Antoine
Affiliation:
Institut Élie Cartan de Nancy, Université Henri Poincaré Nancy 1, Bureau 307, BP 239, 54506 Vandoeuvre-lès-Nancy, France. Xavier.Antoine@iecn.u-nancy.fr Institut National Polytechnique de Lorraine, École Nationale Supérieure des Mines de Nancy, Département de Génie Industriel, Bureau 495, Parc de Saurupt, CS 14 234, 54042 Nancy Cedex, France. Xavier.Antoine@mines.inpl-nancy.fr
Marion Darbas
Affiliation:
Ceremade, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France. darbas@ceremade.dauphine.fr
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Abstract

This paper addresses the derivation of new second-kind Fredholm combined field integral equations for the Krylov iterative solution of tridimensional acoustic scattering problems by a smooth closed surface. These integral equations need the introduction of suitable tangential square-root operators to regularize the formulations. Existence and uniqueness occur for these formulations. They can be interpreted as generalizations of the well-known Brakhage-Werner [A. Brakhage and P. Werner, Arch. Math.16 (1965) 325–329] and Combined Field Integral Equations (CFIE) [R.F. Harrington and J.R. Mautz, Arch. Elektron. Übertragungstech (AEÜ)32 (1978) 157–164]. Finally, some numerical experiments are performed to test their efficiency.

Keywords

Acoustic scatteringHelmholtz equationsecond-kind Fredholm integral equationKrylov iterative solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 41 , Issue 1 , January 2007 , pp. 147 - 167
Copyright
© EDP Sciences, SMAI, 2007

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