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The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media

Author

Listed:
  • Cong Liu

    (College of Naval Architecture and Ocean Engineering, Naval University of Engineering, Wuhan 430033, China)

  • Shaosong Min

    (College of Naval Architecture and Ocean Engineering, Naval University of Engineering, Wuhan 430033, China)

  • Yandong Pang

    (College of Weapon Engineering, Naval University of Engineering, Wuhan 430033, China)

  • Yingbin Chai

    (School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China
    State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China)

Abstract

This work presents a novel simulation approach to couple the meshfree radial point interpolation method (RPIM) with the implicit direct time integration method for the transient analysis of wave propagation dynamics in non-homogeneous media. In this approach, the RPIM is adopted for the discretization of the overall space domain, while the discretization of the time domain is completed by employing the efficient Bathe time stepping scheme. The dispersion analysis demonstrates that, in wave analysis, the amount of numerical dispersion error resulting from the discretization in the space domain can be suppressed at a very low level when the employed nodal support domain of the interpolation function is adequately large. Meanwhile, it is also mathematically shown that the amount of numerical error resulting from the time domain discretization is actually a monotonically decreasing function of the non-dimensional time domain discretization interval. Consequently, the present simulation approach is capable of effectively handling the transient analysis of wave propagation dynamics in non-homogeneous media, and the disparate waves with different speeds can be solved concurrently with very high computation accuracy. This numerical feature makes the present simulation approach more suitable for complicated wave analysis than the traditional finite element approach because the waves with disparate speeds always cannot be concurrently solved accurately. Several numerical tests are given to check the performance of the present simulation approach for the analysis of wave propagation dynamics in non-homogeneous media.

Suggested Citation

  • Cong Liu & Shaosong Min & Yandong Pang & Yingbin Chai, 2023. "The Meshfree Radial Point Interpolation Method (RPIM) for Wave Propagation Dynamics in Non-Homogeneous Media," Mathematics, MDPI, vol. 11(3), pages 1-27, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:523-:d:1040028
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    References listed on IDEAS

    as
    1. Chai, Yingbin & Li, Wei & Liu, Zuyuan, 2022. "Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Yancheng Li & Sina Dang & Wei Li & Yingbin Chai, 2022. "Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
    3. Li, Yancheng & Liu, Cong & Li, Wei & Chai, Yingbin, 2023. "Numerical investigation of the element-free Galerkin method (EFGM) with appropriate temporal discretization techniques for transient wave propagation problems," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. You, Xiangyu & Li, Wei & Chai, Yingbin, 2020. "A truly meshfree method for solving acoustic problems using local weak form and radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 365(C).
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    Cited by:

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