声学边界元拟奇异积分计算的自适应方法

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摘要提出一种自适应方法计算声学边界元中的拟奇异积分，通过单元分级细分将总积分转移到子单元上以消除拟奇异性。在此方法基础上深入研究拟奇异性，进一步提出接近度的概念，其中临界接近度可作为拟奇异积分计算的理论依据，并可用于预估拟奇异性是否存在。此方法的积分精度可调控，且不受场点位置限制，相比于已有方法更加灵活高效。数值分析表明拟奇异性强弱由场点与单元的相对位置决定,单元上远离场点的区域拟奇异性很弱，无需处理。研究结果为处理边界元法中的拟奇异性问题提供了新的选择和参考。

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关键词 ：边界元, 拟奇异性, 自适应, 接近度

Abstract：An adaptive method was presented to calculate nearly singular integrals in acoustic boundary elements. The element was subdivided into subelements hierarchically so as to remove the near singularity by transforming the integral over the initial element to Gauss integrals over subelements. Based on this method,the near singularity was thoroughly studied and the concept of proximity was described. The critical proximity can be used as the criterion for calculating nearly singular integrals and to predict the existence of near singularity. Compared with previous methods,the adaptive method is more flexible and efficient. The integral precision can be adjusted and is not restricted by the positions of near-field points. It is found that the positional relationships between near-field points and the element have important effect on nearly singular integrals. The work provides more understanding and choice to the problem of near singularity in acoustic boundary elements.

Key words： boundary elements; nearly singularity; adaptivity; proximity

收稿日期: 2015-09-09 出版日期: 2017-01-15

引用本文:

缪宇跃1,2 李天匀1,2,3 朱翔1,2 张冠军1,2 郭文杰1,2. 声学边界元拟奇异积分计算的自适应方法[J]. 振动与冲击, 2017, 36(2): 23-31.
MIAO Yuyue1,2,LI Tianyun1,2,3,ZHU Xiang1,2,ZHANG Guanjun1,2,GUO Wenjie1,2. Adaptive method for calculating nearly singular integrals in acoustic boundary elements. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(2): 23-31.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2017/V36/I2/23

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