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Analyzing three-dimensional wave propagation with the hybrid reproducing kernel particle method based on the dimension splitting method

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Abstract

By introducing the dimension splitting method into the reproducing kernel particle method (RKPM), a hybrid reproducing kernel particle method (HRKPM) for solving three-dimensional (3D) wave propagation problems is presented in this paper. Compared with the RKPM of 3D problems, the HRKPM needs only solving a set of two-dimensional (2D) problems in some subdomains, rather than solving a 3D problem in the 3D problem domain. The shape functions of 2D problems are much simpler than those of 3D problems, which results in that the HRKPM can save the CPU time greatly. Four numerical examples are selected to verify the validity and advantages of the proposed method. In addition, the error analysis and convergence of the proposed method are investigated. From the numerical results we can know that the HRKPM has higher computational efficiency than the RKPM and the element-free Galerkin method.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (no. 11571223).

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Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Piaopiao Peng & Yumin Cheng

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  1. Piaopiao Peng
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  2. Yumin Cheng
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Correspondence to Yumin Cheng.

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Peng, P., Cheng, Y. Analyzing three-dimensional wave propagation with the hybrid reproducing kernel particle method based on the dimension splitting method. Engineering with Computers 38 (Suppl 2), 1131–1147 (2022). https://doi.org/10.1007/s00366-020-01256-9

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