Nouvelles formulations intégrales pour les problèmes de diffraction d'ondes

@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 -