# Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

- Volume: 41, Issue: 1, page 147-167
- ISSN: 0764-583X

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topAntoine, Xavier, and Darbas, Marion. "Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation." ESAIM: Mathematical Modelling and Numerical Analysis 41.1 (2007): 147-167. <http://eudml.org/doc/250044>.

@article{Antoine2007,

abstract = {
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.
},

author = {Antoine, Xavier, Darbas, Marion},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Acoustic scattering; Helmholtz equation; second-kind Fredholm integral equation; Krylov iterative solution.; Dirichlet, Neumann boundary conditions; second-kind Fredholm operator; Galerkin boundary element method; Brakhage-Werner integral equation; acoustic scattering; combined field integral equations; Krylov subspace iterative solver; GMRES without restart; convergence; numerical experiments},

language = {eng},

month = {4},

number = {1},

pages = {147-167},

publisher = {EDP Sciences},

title = {Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation},

url = {http://eudml.org/doc/250044},

volume = {41},

year = {2007},

}

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

DA - 2007/4//

PB - EDP Sciences

VL - 41

IS - 1

SP - 147

EP - 167

AB -
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.

LA - eng

KW - Acoustic scattering; Helmholtz equation; second-kind Fredholm integral equation; Krylov iterative solution.; Dirichlet, Neumann boundary conditions; second-kind Fredholm operator; Galerkin boundary element method; Brakhage-Werner integral equation; acoustic scattering; combined field integral equations; Krylov subspace iterative solver; GMRES without restart; convergence; numerical experiments

UR - http://eudml.org/doc/250044

ER -

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