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A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis

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  • Sun, Linlin
  • Fu, Zhuojia
  • Chen, Zhikang

Abstract

This paper presents the localized collocation solver based on fundamental solutions to 3D elastic wave propagation analysis. In the proposed collocation solver, the approximated solution at the considered node is represented by a linear combination of the solutions at a few nearest nodes in the stencil support of the considered node instead of the whole discretization nodes. The related weighting functions are determined by solving a system of linear equations, which is constructed as a linear combination of fundamental solutions in the related stencil support. Therefore, the proposed collocation solver produces sparse resultant matrix, which makes it possible to perform large-scale elastic wave propagation simulations on a desktop computer. Furthermore, it avoids highly ill-conditioned dense matrix encountered in most of collocation methods. The efficiency and accuracy of the proposed method have been verified under several benchmark examples.

Suggested Citation

  • Sun, Linlin & Fu, Zhuojia & Chen, Zhikang, 2023. "A localized collocation solver based on fundamental solutions for 3D time harmonic elastic wave propagation analysis," Applied Mathematics and Computation, Elsevier, vol. 439(C).
    • Handle: RePEc:eee:apmaco:v:439:y:2023:i:c:s0096300322006737
    DOI: 10.1016/j.amc.2022.127600
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    References listed on IDEAS

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    1. 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.
    2. Weiwei Li & Fajie Wang, 2022. "Precorrected-FFT Accelerated Singular Boundary Method for High-Frequency Acoustic Radiation and Scattering," Mathematics, MDPI, vol. 10(2), pages 1-9, January.
    3. Xi, Qiang & Fu, Zhuojia & Wu, Wenjie & Wang, Hui & Wang, Yong, 2021. "A novel localized collocation solver based on Trefftz basis for potential-based inverse electromyography," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    4. Ureña, Francisco & Gavete, Luis & Gómez, Ángel García & Benito, Juan José & Vargas, Antonio Manuel, 2020. "Non-linear Fokker-Planck equation solved with generalized finite differences in 2D and 3D," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    5. Wang, Fajie & Zhao, Qinghai & Chen, Zengtao & Fan, Chia-Ming, 2021. "Localized Chebyshev collocation method for solving elliptic partial differential equations in arbitrary 2D domains," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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    1. 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.
    2. 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.

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