Adaptive method for calculating nearly singular integrals in acoustic boundary elements

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (2) : 23-31.

MIAO Yuyue1,2,LI Tianyun1,2,3,ZHU Xiang1,2,ZHANG Guanjun1,2,GUO Wenjie1,2

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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

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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[J]. Journal of Vibration and Shock, 2017, 36(2): 23-31

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