Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes
David P. Levadoux; Bastiaan L. Michielsen
ESAIM: Mathematical Modelling and Numerical Analysis (2010)
- Volume: 38, Issue: 1, page 157-175
- ISSN: 0764-583X
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topLevadoux, David P., and Michielsen, Bastiaan L.. "Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes." ESAIM: Mathematical Modelling and Numerical Analysis 38.1 (2010): 157-175. <http://eudml.org/doc/194204>.
@article{Levadoux2010,
abstract = {
We present an integral equation method for solving boundary value
problems of the Helmholtz equation in unbounded domains. The
method relies on the factorisation of one of the
Calderón projectors by an operator approximating the exterior
admittance (Dirichlet to Neumann) operator of the scattering
obstacle. We show how the pseudo-differential calculus allows us
to construct such approximations and that this yields integral
equations without internal resonances and being well-conditioned
at all frequencies. An implementation technique is elaborated,
where again reasonings from pseudo-differential calculus play an
important rôle. Some numerical examples are presented which appear
to confirm that the new integral equation leads to linear systems
which are much better conditioned than the classical ("direct")
integral equations and hence have much better behaviour when
solved with iterative techniques and matrix sparsification.
},
author = {Levadoux, David P., Michielsen, Bastiaan L.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Équations intégrales; opérateurs pseudo-différentiels; équation de Helmholtz.},
language = {eng},
month = {3},
number = {1},
pages = {157-175},
publisher = {EDP Sciences},
title = {Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes},
url = {http://eudml.org/doc/194204},
volume = {38},
year = {2010},
}
TY - JOUR
AU - Levadoux, David P.
AU - Michielsen, Bastiaan L.
TI - Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 38
IS - 1
SP - 157
EP - 175
AB -
We present an integral equation method for solving boundary value
problems of the Helmholtz equation in unbounded domains. The
method relies on the factorisation of one of the
Calderón projectors by an operator approximating the exterior
admittance (Dirichlet to Neumann) operator of the scattering
obstacle. We show how the pseudo-differential calculus allows us
to construct such approximations and that this yields integral
equations without internal resonances and being well-conditioned
at all frequencies. An implementation technique is elaborated,
where again reasonings from pseudo-differential calculus play an
important rôle. Some numerical examples are presented which appear
to confirm that the new integral equation leads to linear systems
which are much better conditioned than the classical ("direct")
integral equations and hence have much better behaviour when
solved with iterative techniques and matrix sparsification.
LA - eng
KW - Équations intégrales; opérateurs pseudo-différentiels; équation de Helmholtz.
UR - http://eudml.org/doc/194204
ER -
References
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- D. Levadoux and B. Michielsen, Analysis of a boundary integral equation for high frequency Helmholtz problems. Fourth International Conf. Mathematical and Numerical Aspects of Wave Propagation, Colorado, 1–5 June (1998).
- V. Rokhlin, Diagonal form of translation operators for the Helmholtz equation in three dimensions. Rapport technique YALEU/DCS/RR-894, Yale University, Department of Computer Science (1992).
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Citations in EuDML Documents
top- Xavier Antoine, Hélène Barucq, Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
- Xavier Antoine, Hélène Barucq, Approximation by generalized impedance boundary conditions of a transmission problem in acoustic scattering
- Xavier Antoine, Marion Darbas, Generalized combined field integral equations for the iterative solution of the three-dimensional Helmholtz equation
- David P. Levadoux, Proposition de préconditionneurs pseudo-différentiels pour l’équation CFIE de l’électromagnétisme
- David P. Levadoux, Proposition de préconditionneurs pseudo-différentiels pour l'équation CFIE de l'électromagnétisme
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