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Title: Stability of boundary element methods for the two dimensional wave equation in time domain revisited
Authors: Fukuhara, Mio
Misawa, Ryota  kyouindb  KAKEN_id
Niino, Kazuki  kyouindb  KAKEN_id
Nishimura, Naoshi
Author's alias: 福原, 美桜
三澤, 亮太
新納, 和樹
西村, 直志
Keywords: Stability
Time domain
BEM
Transmission problems
Eigenvalue problems
Issue Date: Nov-2019
Publisher: Elsevier Ltd
Journal title: Engineering Analysis with Boundary Elements
Volume: 108
Start page: 321
End page: 338
Abstract: This study considers the stability of time domain BEMs for the wave equation in 2D. We show that the question of stability of time domain BEMs 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 that the proposed stability analysis helps to reformulate these equations to obtain stable numerical schemes.
Rights: © 2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/.
The full-text file will be made open to the public on 1 November 2021 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
URI: http://hdl.handle.net/2433/244714
DOI(Published Version): 10.1016/j.enganabound.2019.08.015
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