Development and application of the fast algorithm for the time-domain boundary element method for transient wave problems

瞬态波问题时域边界元法快速算法的开发与应用

• 批准号: 24656072
• 负责人: TAKAHASHI Toru
• 金额: $ 2.58万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012-04-01 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-24656072/
• 关键词: 境界要素法; 高速多重極法; 波動方程式; 関数補間; 反復解法; 音響問題; 高速解法; 非定常問題; 補間

The bottleneck of the boundary element method is its high computational cost, although the method is very accurate for the transient wave problems. To overcome this difficulty, the present study proposed an FMM-like fast algorithm and developed a fast boundary element method for wave problems in time domain. Specifically, the idea to approximate a two-body interaction function with polynomials in order to obtain its representation in the separation of variables, which originates from the black-box fast multiple method, is applied to the time-dependent Green's function for the three-dimensional scalar wave equation of interest. As a result, a time-domain interpolation-based fast multipole method was developed successfully. Through the numerical experiments with the implemented computer program, the proposed method was validated.

边界元素方法的瓶颈是其高计算成本，尽管该方法对于瞬态波问题非常准确。为了克服这一困难，本研究提出了一种类似FMM的快速算法，并开发了一种快速边界元素方法，以解决时间域中的波浪问题。具体而言，为了在变量的分离中获得其表示的三体相互作用函数的想法，该函数源自black-box快速多种方法，该函数适用于三个依赖的绿色函数。尺寸标量波方程感兴趣。结果，成功开发了基于时间域插值的快速多极方法。通过实现的计算机程序的数值实验，已验证了所提出的方法。

项目成果

An interpolation-based fast multipole boundary integral equation method for wave equation

基于插值的波动方程快速多极边界积分方程方法

• 发表时间: 2013
• 作者: Toru Takahashi

An interpolation-based fast multipole integral equation method for wave equation

基于插值的波动方程快速多极积分方程法

• 发表时间: 2013
• 作者: Emmanuel Agullo;Bérenger Bramas;Olivier Coulaud;Eric Darve;Matthias Messner;Toru Takahashi;Wei Gao;南野宏紀，藤垣元治;Toru Takahashi
• 通讯作者: Toru Takahashi

An interpolation-based fast-multipole accelerated boundary integral equation method for the three-dimensional wave equation

• DOI: 10.1016/j.jcp.2013.11.008
• 发表时间: 2014-02
• 期刊: J. Comput. Phys.
• 作者: Toru Takahashi

TASK-BASED FMM FOR MULTICORE ARCHITECTURES

• DOI: 10.1137/130915662
• 发表时间: 2014-01-01
• 期刊: SIAM JOURNAL ON SCIENTIFIC COMPUTING
• 影响因子: 3.1
• 作者: Agullo, Emmanuel;Bramas, Berenger;Takahashi, Toru
• 通讯作者: Takahashi, Toru

A time-domain BIEM for wave equation accelerated by fast multipole method using interpolation

使用插值的快速多极子法加速波动方程的时域 BIEM

• 发表时间: 2013
• 作者: So Ito;Zhigang Jia;Shigeaki Goto;Gaofa He;Keiichiro Hosobuchi;Yuki Shimizu;Wei Gao;Toru Takahashi
• 通讯作者: Toru Takahashi