IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i17p3066-d897561.html
   My bibliography  Save this article

A Finite Element Reduced-Dimension Method for Viscoelastic Wave Equation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/17/3066/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/17/3066/
    Download Restriction: no
    ---><---

    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yuejie Li & Zhendong Luo & Changan Liu, 2023. "The Mixed Finite Element Reduced-Dimension Technique with Unchanged Basis Functions for Hydrodynamic Equation," Mathematics, MDPI, vol. 11(4), pages 1-17, February.
    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.
    3. Yuejie Li & Zhendong Luo, 2023. "A Reduced-Dimension Extrapolating Method of Finite Element Solution Coefficient Vectors for Fractional Tricomi-Type Equation," Mathematics, MDPI, vol. 11(22), pages 1-13, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:17:p:3066-:d:897561. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.