1. A coupled double boundary Burton-Miller method without hypersingular integral.
- Author
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Shi, Ziyu, Xiang, Yu, Chen, Jie, and Bao, Yingchao
- Subjects
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BOUNDARY element methods , *INTEGRAL equations , *SOUND wave scattering , *ACOUSTIC radiation , *INTEGRALS , *HYPERGRAPHS , *SINGULAR integrals - Abstract
The Burton-Miller method is widely used to solve the problem of solution non-uniqueness in a conventional boundary element method (CBEM). Although this method is very robust, the hypersingular integral kernel contained in its normal derivative equation increases the computational complexity and reduces the computational accuracy. In this paper, a coupled double boundary Burton-Miller method with unique solutions at full wave numbers is proposed. The aforementioned process is done by replacing the normal integral equation of the Burton-Miller method with the virtual indirect boundary element method (VIBEM) integral equation of combined layer potential and using the equivalent relationship between their coefficient matrices. The proposed method inherits the high-precision advantages of VIBEM and avoids the hypersingular integrals of traditional Burton-Miller methods. In particular, no singular integral is present when the plane element is used for discretization. The numerical results of acoustic radiation and scattering show that the calculation accuracy of the coupled double boundary Burton-Miller method is higher than that of CBEM and the conventional Burton-Miller method. Moreover, the condition number of the coefficient matrix is much lower than that of VIBEM. Lastly, the computation time is less than that of the conventional Burton-Miller method. • Avoiding the calculation of hypersingular integrals in the Burton-Miller method. • Significantly improved the computational accuracy of the Burton-Miller method. • The non-uniqueness of the solution of the boundary integral equation is overcome. • The matrix condition number of the virtual boundary element method is reduced. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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