Essential spectrum of local multi-trace boundary integral operators

Xavier Claeys

doi:10.1093/imamat/hxw019

Essential spectrum of local multi-trace boundary integral operators

Xavier Claeys

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers are equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented.

langue originale	Anglais
Pages (de - à)	961-983
Nombre de pages	23
journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	81
Numéro de publication	6
Les DOIs	https://doi.org/10.1093/imamat/hxw019
état	Publié - 1 déc. 2016

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10.1093/imamat/hxw019

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title = "Essential spectrum of local multi-trace boundary integral operators",

abstract = "Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers are equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented.",

keywords = "Boundary integral equation, Multi-domain, Multi-trace, Wave propagation",

author = "Xavier Claeys",

year = "2016",

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T1 - Essential spectrum of local multi-trace boundary integral operators

AU - Claeys, Xavier

PY - 2016/12/1

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N2 - Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers are equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented.

AB - Considering pure transmission scattering problems in piecewise constant media, we derive an exact analytic formula for the spectrum of the corresponding local multi-trace boundary integral operators in the case where the geometrical configuration does not involve any junction point and all wave numbers are equal. We deduce from this the essential spectrum in the case where wave numbers vary. Numerical evidences of these theoretical results are also presented.

KW - Boundary integral equation

KW - Multi-domain

KW - Multi-trace

KW - Wave propagation

UR - https://www.scopus.com/pages/publications/85014446875

U2 - 10.1093/imamat/hxw019

DO - 10.1093/imamat/hxw019

M3 - Article

AN - SCOPUS:85014446875

SN - 0272-4960

VL - 81

SP - 961

EP - 983

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 6

ER -

Essential spectrum of local multi-trace boundary integral operators

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