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 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: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {147--167},
year = {2007},
publisher = {EDP Sciences},
volume = {41},
number = {1},
doi = {10.1051/m2an:2007009},
mrnumber = {2323695},
zbl = {1123.65117},
language = {en},
url = {https://www.numdam.org/articles/10.1051/m2an:2007009/}
}
TY - JOUR AU - Antoine, Xavier AU - Darbas, Marion TI - Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2007 SP - 147 EP - 167 VL - 41 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/m2an:2007009/ DO - 10.1051/m2an:2007009 LA - en ID - M2AN_2007__41_1_147_0 ER -
%0 Journal Article %A Antoine, Xavier %A Darbas, Marion %T Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation %J ESAIM: Modélisation mathématique et analyse numérique %D 2007 %P 147-167 %V 41 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/m2an:2007009/ %R 10.1051/m2an:2007009 %G en %F 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: Modélisation mathématique et analyse numérique, Tome 41 (2007) no. 1, pp. 147-167. doi: 10.1051/m2an:2007009
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