Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
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. email@example.com
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