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A hybrid smoothed moving least-squares interpolation method for acoustic scattering problems

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Abstract

The discrete model in the traditional finite element method (FEM) inevitably behaves more stiffly than the corresponding continuous model. This results in an unavoidable dispersion error that increases rapidly with the wavenumber. To overcome this problem in acoustic scattering computations, a hybrid smoothed moving least-squares interpolation method (HSMLSIM) is developed to control the dispersion error. In the HSMLSIM, a hybrid stiffness is created by combining a standard FEM model and a node-based locally smoothed FEM model to soften the acoustic stiffness. To accurately calculate the entries of the softened acoustic stiffness, an improved mesh-free interpolation method is adopted for shape function construction. A discrete model that has very close to the actual stiffness of the original model can be achieved using the HSMLSIM. The major benefit of the HSMLSIM is that, for a given mesh, the accuracy is significantly improved compared to that of FEM without introducing extra degrees of freedom. The performance of the proposed method is numerically studied. Numerical experiments are conducted to investigate the properties of the proposed method. The simulation results indicate that the HSMLSIM can effectively suppress the dispersion error and achieve superior computational performance and is, therefore, competitive for acoustic scattering computations.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51909016), the Natural Science Foundation of Chongqing, China (Grant No. cstc2020jcyj-msxmX0070) and the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJZD-K202100702 and KJQN201900705).

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  1. School of Shipping and Naval Architecture, Chongqing Jiaotong University, Chongqing, 400074, China

    Shaowei Wu

  2. School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan, 430063, Hubei, China

    Yang Xiang

  3. College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, Heilongjiang, China

    Wanyou Li

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  1. Shaowei Wu
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  2. Yang Xiang
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Correspondence to Shaowei Wu.

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Wu, S., Xiang, Y. & Li, W. A hybrid smoothed moving least-squares interpolation method for acoustic scattering problems. Engineering with Computers 39, 3651–3669 (2023). https://doi.org/10.1007/s00366-022-01780-w

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