Geodesic
Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 147-167

Voir la notice de l'article provenant de la source Numdam

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 : 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 },
     pages = {147--167},
     publisher = {EDP-Sciences},
     volume = {41},
     number = {1},
     year = {2007},
     doi = {10.1051/m2an:2007009},
     mrnumber = {2323695},
     zbl = {1123.65117},
     language = {en},
     url = {http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
PY  - 2007
SP  - 147
EP  - 167
VL  - 41
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis 
%D 2007
%P 147-167
%V 41
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/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: Mathematical Modelling and Numerical Analysis , Tome 41 (2007) no. 1, pp. 147-167. doi: 10.1051/m2an:2007009

Cité par Sources :