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A Finite Element Reduced-Dimension Method for Viscoelastic Wave Equation

Author

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  • Zhendong Luo

    (School of Digitalized Intelligence Engineering, Hunan Sany Polytechnic College, Changsha 410129, China)

Abstract

In this study, we mainly employ a proper orthogonal decomposition (POD) to lower the dimension for the unknown Crank–Nicolson finite element (FE) (CNFE) solution coefficient vectors of the viscoelastic wave (VW) equation so as to build a reduced-dimension recursive CNFE (RDRCNFE) algorithm, adopt matrix analysis to analyze the stability together with errors to the RDRCNFE solutions, and utilize some numerical experimentations to verify the effectiveness of the RDRCNFE algorithm.

Suggested Citation

  • Zhendong Luo, 2022. "A Finite Element Reduced-Dimension Method for Viscoelastic Wave Equation," Mathematics, MDPI, vol. 10(17), pages 1-12, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3066-:d:897561
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    References listed on IDEAS

    as
    1. Zhendong Luo, 2022. "The Dimensionality Reduction of Crank–Nicolson Mixed Finite Element Solution Coefficient Vectors for the Unsteady Stokes Equation," Mathematics, MDPI, vol. 10(13), pages 1-11, June.
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    Cited by:

    1. Zhendong Luo & Yuejie Li, 2022. "A Preserving Precision Mixed Finite Element Dimensionality Reduction Method for Unsaturated Flow Problem," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    2. Xiaoyong Yang & Zhendong Luo, 2022. "An Unchanged Basis Function and Preserving Accuracy Crank–Nicolson Finite Element Reduced-Dimension Method for Symmetric Tempered Fractional Diffusion Equation," Mathematics, MDPI, vol. 10(19), pages 1-13, October.

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