An interpolation-based fast-multipole accelerated boundary integral equation method for the three-dimensional wave equation
An interpolation-based fast-multipole accelerated boundary integral equation method for the three-dimensional wave equation
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DOI：
10.1016/j.jcp.2013.11.008
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发表时间：
2014-02
期刊：
影响因子：
--
通讯作者：
Toru Takahashi
中科院分区：
文献类型：
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作者：
Toru Takahashi
提出了一种新的快速多极子方法（FMM）来加速三维波动方程的时域边界积分方程方法（TDBIEM）。该算法是一个增强的插值为基础的FMM的时域情况下，采用平面波时域算法的概念。针对低频区域的应用，本文提出的基于时域插值的FMM算法可以将TDBIEM的计算复杂度从O（Ns 2Nt）降低到O（Ns 1+ δ Nt）（其中δ= 1/3或1/2），其中Ns和Nt分别为空间和时间自由度.通过数值实验，与传统的（直接）TDBIEM的计算精度和速度的建议加速TDBIEM进行了验证。
A new fast multipole method (FMM) is proposed to accelerate the time-domain boundary integral equation method (TDBIEM) for the three-dimensional wave equation. The proposed algorithm is an enhancement of the interpolation-based FMM for the time-domain case, adopting the notion of the plane-wave time-domain algorithm. With the application being targeted at a low-frequency regime, the proposed time-domain interpolation-based FMM can reduce the computational complexity of the TDBIEM from O (N s 2 N t) to O (N s 1+ δ N t)(where δ= 1/3 or 1/2) with the help of multilevel space–time hierarchy, where N s and N t are the spatial and temporal degrees of freedom, respectively. The computational accuracy and speed of the proposed accelerated TDBIEM are verified in comparison with those of the conventional (direct) TDBIEM via numerical experiments.