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

Xavier Antoine; Marion Darbas

ESAIM: Mathematical Modelling and Numerical Analysis (2007)

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

Abstract

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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.

How to cite

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Antoine, 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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