Stability of boundary element methods for the two dimensional wave equation in time domain revisited
Stability of boundary element methods for the two dimensional wave equation in time domain revisited
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DOI：
10.1016/j.enganabound.2019.08.015
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发表时间：
2019-11
影响因子：
3.3
通讯作者：
Mio Fukuhara;Ryota Misawa;K. Niino;N. Nishimura
中科院分区：
文献类型：
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作者：
Mio Fukuhara;Ryota Misawa;K. Niino;N. Nishimura
本文研究二维波动方程时域边界元法的稳定性。我们表明，时域边界元的稳定性问题减少到一个非线性特征值问题的频域积分方程。我们建议用Sakurai-Sugiura方法数值求解这个非线性特征值问题。在外部Dirichlet问题数值验证这种方法后，我们继续传输问题，我们发现，一些时域对应的“共振自由”积分方程在频域导致不稳定。我们最后表明，建议的稳定性分析有助于重新制定这些方程，以获得稳定的数值方案。
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.