Analysis of Nearly Singular Integral Problem in 3D Acoustic Field Boundary Element Method

Abstract

Abstract: Taking 3D acoustic analysis as an example, a semi-analytic algorithm is proposed which can be used to compute nearly singular integrals with high order element exactly. With analysis of geometry features of high order elements, approximate geometric parameters are constructed. Then, a kernel function of nearly singular integral is decomposed into two parts using subtraction method. One is regular part and the other is singular part. Integral of regular part is computed accurately using conventional Gauss quadrature. For integral of the singular part, semi-analytic algorithm gives exact result. Classical examples are given including 3D acoustic internal and external problems. Sound pressures at points near boundary are calculated with different methods. Comparisons of results demonstrate accuracy and effectiveness of the algorithm.

Key words: BEM, nearly singular integral, regularization, high order element, semi-analytic algorithm

CLC Number:

O348.8

SUN Rui, HU Zongjun, NIU Zhongrong. Analysis of Nearly Singular Integral Problem in 3D Acoustic Field Boundary Element Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2017, 34(5): 611-618.

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