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Analysis of transient wave propagation dynamics using the enriched finite element method with interpolation cover functions

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  • Chai, Yingbin
  • Li, Wei
  • Liu, Zuyuan

Abstract

To improve the performance of the low-order linear triangular element for solving transient wave propagation problems, this paper presents a novel enriched finite element method (EFEM) for wave analysis. The original linear nodal shape functions are enriched by using the additional interpolation cover functions over patches of elements. To effectively solve the wave problems, the used interpolation cover function is constructed by using the Lagrangian functions plus the harmonic trigonometric functions. The present approach can be regarded as a combination of the classical finite elements and the spectral techniques, but individual strengths of the two methods are synergized, so more accurate results can be obtained compared to the standard finite elements. In this work the root of the linear dependence (LD) issue in the present EFEM is investigated detailedly, and then an effective approach is proposed to completely eliminate the LD problem. By performing the dispersion analysis, it is found that the present EFEM possesses the attractive monotonic convergence property for transient wave propagations, that is the obtained numerical solutions will monotonically converge to the exact solutions with the decreasing time steps for time integration as long as the reasonably fine meshes are used. Several typical numerical examples are solved to illustrate the capacities of the present method.

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  • 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).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006482
    DOI: 10.1016/j.amc.2021.126564
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    References listed on IDEAS

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    1. 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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    4. S.M. Dsouza & T. Khajah & X Antoine & S.P.A. Bordas & S. Natarajan, 2021. "Non Uniform Rational B-Splines and Lagrange approximations for time-harmonic acoustic scattering: accuracy and absorbing boundary conditions," Mathematical and Computer Modelling of Dynamical Systems, Taylor & Francis Journals, vol. 27(1), pages 263-294, January.
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    Cited by:

    1. Gui, Qiang & Li, Wei & Chai, Yingbin, 2023. "The enriched quadrilateral overlapping finite elements for time-harmonic acoustics," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    2. Qiang Wang & Pyeoungkee Kim & Wenzhen Qu, 2022. "A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    3. Jue Qu & Hao Guo & Hongjun Xue & Sina Dang & Yingchun Chen, 2022. "Experimental Study on Manned/Unmanned Thermal Environment in Radar Electronic Shelter Based on Different Air Supply Conditions," Energies, MDPI, vol. 15(4), pages 1-29, February.
    4. 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).
    5. Yingbin Chai & Kangye Huang & Shangpan Wang & Zhichao Xiang & Guanjun Zhang, 2023. "The Extrinsic Enriched Finite Element Method with Appropriate Enrichment Functions for the Helmholtz Equation," Mathematics, MDPI, vol. 11(7), pages 1-25, March.
    6. 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.
    7. Xunbai Du & Sina Dang & Yuzheng Yang & Yingbin Chai, 2022. "The Finite Element Method with High-Order Enrichment Functions for Elastodynamic Analysis," Mathematics, MDPI, vol. 10(23), pages 1-27, December.
    8. Lin Chen & Wenzhi Xu & Zhuojia Fu, 2022. "A Novel Spatial–Temporal Radial Trefftz Collocation Method for 3D Transient Wave Propagation Analysis with Specified Sound Source Excitation," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    9. Sina Dang & Gang Wang & Yingbin Chai, 2023. "A Novel “Finite Element-Meshfree” Triangular Element Based on Partition of Unity for Acoustic Propagation Problems," Mathematics, MDPI, vol. 11(11), pages 1-21, May.
    10. Cheng Chi & Fajie Wang & Lin Qiu, 2023. "A Novel Coupled Meshless Model for Simulation of Acoustic Wave Propagation in Infinite Domain Containing Multiple Heterogeneous Media," Mathematics, MDPI, vol. 11(8), pages 1-15, April.
    11. Yang Zhang & Qiang Gui & Yuzheng Yang & Wei Li, 2022. "The Instability and Response Studies of a Top-Tensioned Riser under Parametric Excitations Using the Differential Quadrature Method," Mathematics, MDPI, vol. 10(8), pages 1-23, April.
    12. Liyuan Lan & Suifu Cheng & Xiatao Sun & Weiwei Li & Chao Yang & Fajie Wang, 2022. "A Fast Singular Boundary Method for the Acoustic Design Sensitivity Analysis of Arbitrary Two- and Three-Dimensional Structures," Mathematics, MDPI, vol. 10(20), pages 1-13, October.
    13. Tingting Sun & Peng Wang & Guanjun Zhang & Yingbin Chai, 2022. "A Modified Radial Point Interpolation Method (M-RPIM) for Free Vibration Analysis of Two-Dimensional Solids," Mathematics, MDPI, vol. 10(16), pages 1-20, August.
    14. Dongdong Liu & Xing Wei & Chengbin Li & Chunguang Han & Xiaxi Cheng & Linlin Sun, 2022. "Transient Dynamic Response Analysis of Two-Dimensional Saturated Soil with Singular Boundary Method," Mathematics, MDPI, vol. 10(22), pages 1-19, November.
    15. Jue Qu & Hongjun Xue & Yancheng Li & Yingbin Chai, 2022. "An Enriched Finite Element Method with Appropriate Interpolation Cover Functions for Transient Wave Propagation Dynamic Problems," Mathematics, MDPI, vol. 10(9), pages 1-12, April.
    16. Xingxing Yue & Buwen Jiang & Xiaoxuan Xue & Chao Yang, 2022. "A Simple, Accurate and Semi-Analytical Meshless Method for Solving Laplace and Helmholtz Equations in Complex Two-Dimensional Geometries," Mathematics, MDPI, vol. 10(5), pages 1-9, March.

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