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arXiv · 1902.06480

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

Mio Fukuhara·Ryota Misawa·Kazuki Niino·Naoshi Nishimura
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Abstract

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.

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Mio Fukuhara, Ryota Misawa, Kazuki Niino, Naoshi Nishimura. 2019-02-18. Boundary integral equation methods for the two dimensional wave equation in time domain revisited. https://arxiv.org/abs/1902.06480

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