Boundary integral equation methods for the two dimensional wave equation in time domain revisited

This study considers the stability of time domain BIEMs for the wave equation in 2D. We show that the stability of time domain BIEMs is reduced to a nonlinear eigenvalue problem related to frequency domain integral equations. We propose to solve this non-linear eigenvalue problem numerically with th...

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Bibliographic Details
Published in:arXiv.org 2019-02
Main Authors: Fukuhara, Mio, Misawa, Ryota, Niino, Kazuki, Nishimura, Naoshi
Format: Article
Language:English
Subjects:
Boundary integral method
Dimensional stability
Dirichlet problem
Eigenvalues
Frequency domain analysis
Integral equations
Mathematical analysis
Time domain analysis
Wave equations
Online Access:Get full text
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Summary:This study considers the stability of time domain BIEMs for the wave equation in 2D. We show that the stability of time domain BIEMs is reduced to a nonlinear eigenvalue problem related to frequency domain integral equations. We propose to solve this non-linear eigenvalue problem numerically with the Sakurai-Sugiura method. After validating this approach numerically in the exterior Dirichlet problem, we proceed to transmission problems in which we find that some time domain counterparts of "resonance-free" integral equations in frequency domain lead to instability. We finally show how to reformulate these equations to obtain stable numerical schemes.
ISSN:2331-8422