Spurious Quasi-Resonances in Boundary Integral Equations for the Helmholtz Transmission Problem
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Date
2022
Publication Type
Journal Article
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Abstract
We consider the Helmholtz transmission problem with piecewise-constant material coefficients and the standard associated direct boundary integral equations. For certain coefficients and geometries, the norms of the inverses of the boundary integral operators grow rapidly through an increasing sequence of frequencies, even though this is not the case for the solution operator of the transmission problem; we call this phenomenon that of spurious quasi-resonances. We give a rigorous explanation of why and when spurious quasi-resonances occur and propose modified boundary integral equations that are not affected by them.
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published
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Volume
82 (4)
Pages / Article No.
1446 - 1469
Publisher
SIAM
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Subject
Helmholtz equation; Boundary integral equations; Transmission problem; Quasi resonance
Organisational unit
03632 - Hiptmair, Ralf / Hiptmair, Ralf
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