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

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	961-983
Number of pages	23
Journal	IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)
Volume	81
Issue number	6
DOIs	https://doi.org/10.1093/imamat/hxw019
Publication status	Published - 1 Dec 2016

Keywords

Boundary integral equation
Multi-domain
Multi-trace
Wave propagation

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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.",

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AU - Claeys, Xavier

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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

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

Abstract

Keywords

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