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A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics

Author

Listed:
  • Xiaofei Qin

    (School of Science, Harbin Institute of Technology, Shenzhen 518055, China)

  • Youhua Fan

    (School of Science, Harbin Institute of Technology, Shenzhen 518055, China)

  • Hongjun Li

    (Urban and Rural Construction Institute, Hebei Agricultural University, Baoding 071001, China)

  • Weidong Lei

    (School of Civil and Environmental Engineering, Harbin Institute of Technology, Shenzhen 518055, China)

Abstract

The analytically time integrable time-space domain (ATI-TSD) is discovered based on which the minimum time-space domain is identified for treatment on singularities in the three-dimensional time-domain boundary element method (3D TD-BEM) formulation. A direct method to solve singular integrals in the 3D TD-BEM formulation for elastodynamic problems is proposed. The wavefront singularity can be analytically eliminated in ATI-TSD, while the dual singularity can be treated by the direct method using Kutt’s quadrature in the identified minimum time-space domain. Three benchmark examples are presented to verify the correctness and the applicability of the direct method for solving the singular integrals in 3D TD-BEM.

Suggested Citation

  • Xiaofei Qin & Youhua Fan & Hongjun Li & Weidong Lei, 2022. "A Direct Method for Solving Singular Integrals in Three-Dimensional Time-Domain Boundary Element Method for Elastodynamics," Mathematics, MDPI, vol. 10(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:286-:d:726929
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    References listed on IDEAS

    as
    1. Xuan Liu & Muhammad Ahsan & Masood Ahmad & Muhammad Nisar & Xiaoling Liu & Imtiaz Ahmad & Hijaz Ahmad, 2021. "Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schr ö dinger Equation with Energy and Mass Conversion," Energies, MDPI, vol. 14(23), pages 1-17, November.
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    Cited by:

    1. Nikolaos L. Tsitsas, 2023. "Analytical Methods in Wave Scattering and Diffraction Volume I," Mathematics, MDPI, vol. 11(4), pages 1-5, February.

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