| Issue |
ESAIM: M2AN
Volume 41, Number 1, January-February 2007
|
|
|---|---|---|
| Page(s) | 147 - 167 | |
| DOI | https://doi.org/10.1051/m2an:2007009 | |
| Published online | 26 April 2007 | |
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
1
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
2
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
3
Ceremade, Université Paris Dauphine, Place du Maréchal de Lattre
de Tassigny, 75775 Paris Cedex 16, France. darbas@ceremade.dauphine.fr
Received:
9
January
2006
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.
Mathematics Subject Classification: 76Q05 / 78A45 / 47G30 / 35C15 / 65F10
Key words: Acoustic scattering / Helmholtz equation / second-kind Fredholm integral equation / Krylov iterative solution.
© EDP Sciences, SMAI, 2007
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