Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 1, p. 147-167

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.

DOI : https://doi.org/10.1051/m2an:2007009
Classification:  76Q05,  78A45,  47G30,  35C15,  65F10
Keywords: acoustic scattering, Helmholtz equation, second-kind Fredholm integral equation, Krylov iterative solution
@article{M2AN_2007__41_1_147_0,
     author = {Antoine, Xavier and Darbas, Marion},
     title = {Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     pages = {147-167},
     doi = {10.1051/m2an:2007009},
     zbl = {1123.65117},
     mrnumber = {2323695},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_2007__41_1_147_0}
}
Antoine, Xavier; Darbas, Marion. Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 41 (2007) no. 1, pp. 147-167. doi : 10.1051/m2an:2007009. http://www.numdam.org/item/M2AN_2007__41_1_147_0/

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