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B-spline wavelet boundary element method for three-dimensional problems

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Abstract

This paper aims to propose a wavelet boundary element method (WBEM) to study the three-dimensional elasticity problem and potential problem. In contrast with conventional polynomial interpolation in the BEM, the scaling functions of the B-spline wavelet on the interval (BSWI) are applied to derive calculated formats of the WBEM, construct BSWI elements, discretize the geometric shape, and form BSWI BEM algebraic equations. Because BSWI scaling functions have specific expressions, the integration related to scaling functions can be evaluated directly without other complicated calculation steps like applying other wavelet bases. The Gauss quadrature scheme based on the background cell is implemented to evaluate the integration involved in the WBEM. Furthermore, the singular integration problem appearing in the WBEM can be transformed into that appearing in traditional BEM to solve. Unlike the WBEM in the published literature, arbitrary boundary conditions can be solved directly as the wavelet-based elements are employed to discrete the geometry of structures. Some typical examples with several boundary conditions are provided to verify this method. The numerical solutions illustrate the good convergence, reliability, and flexibility of WBEM by comparison with the traditional BEM and exact solutions.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Nos. U1909217, U1709208), the ZJNSF (No. LD21E050001) and the Zhejiang Special Support Program for High-level Personnel Recruitment of China (No. 2018R52034).

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  1. College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou, 325035, People’s Republic of China

    Qi Wei & Jiawei Xiang

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  1. Qi Wei
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Correspondence to Jiawei Xiang.

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Wei, Q., Xiang, J. B-spline wavelet boundary element method for three-dimensional problems. Acta Mech 232, 3233–3257 (2021). https://doi.org/10.1007/s00707-021-03009-1

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  • DOI: https://doi.org/10.1007/s00707-021-03009-1

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