Generalized Combined Field Integral Equations for the iterative solution of the three-dimensional Helmholtz equation
Antoine, Xavier; Darbas, Marion (2007), Generalized Combined Field Integral Equations for the iterative solution of the three-dimensional Helmholtz equation, Modélisation mathématique et analyse numérique, 41, 1, p. 147-167. http://dx.doi.org/10.1051/m2an:2007009
TypeArticle accepté pour publication ou publié
Journal nameModélisation mathématique et analyse numérique
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Abstract (EN)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.
Subjects / KeywordsAcoustic scattering; Helmholtz equation; second-kind Fredholm integral equation; Krylov iterative solution
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