IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v231y2025icp128-143.html
   My bibliography  Save this article

A study on fractional centered difference scheme for high-dimensional integral fractional Laplacian operator with {ω}-circulant preconditioner

Author

Listed:
  • Chou, Lot-Kei
  • Qu, Wei
  • Huang, Yuan-Yuan
  • Lei, Siu-Long

Abstract

Fundamental properties for the coefficients of a second-order finite difference approximation of the fractional Laplacian in d≥2 dimensions are derived in this paper. The obtained decay rate of the coefficients implies that the coefficients (with no closed-form expression) can be approximated via d-dimensional inverse fast Fourier transform of size K per dimension with accuracy O(K−d−α), where α∈(0,2) is the order of the fractional Laplacian. For solving fractional partial differential equations on regular grids, the coefficient matrix is a d-level Toeplitz matrix that can be preconditioned by the d-level {ω}-circulant matrix. Here, a spectral analysis of the difference matrix is derived. The purpose of this work is also to justify some observations presented by Hao et al. (2021). Numerical experiments in two-dimension and three-dimension illustrate that {ω}-circulant preconditioner has better performance over T. Chan’s circulant preconditioner.

Suggested Citation

  • Chou, Lot-Kei & Qu, Wei & Huang, Yuan-Yuan & Lei, Siu-Long, 2025. "A study on fractional centered difference scheme for high-dimensional integral fractional Laplacian operator with {ω}-circulant preconditioner," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 231(C), pages 128-143.
    • Handle: RePEc:eee:matcom:v:231:y:2025:i:c:p:128-143
    DOI: 10.1016/j.matcom.2024.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424004737
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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:eee:matcom:v:231:y:2025:i:c:p:128-143. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.