IDEAS home Printed from https://ideas.repec.org/a/hin/jnlmpe/7969371.html
   My bibliography  Save this article

Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation

Author

Listed:
  • Guozhen Wang
  • Huanzhen Chen

Abstract

We embed the fractional Allen-Cahn equation into a Galerkin variational framework and thus develop its corresponding finite element procedure and then prove rigorously its mathematical and physical properties for the finite element solution. Combining the merits of the conjugate gradient (CG) algorithm and the Toeplitz structure of the coefficient matrix, we design a fast CG for the linearized finite element scheme to reduce the computation cost and the storage to and respectively. Numerical experiments confirm that the proposed fast CG algorithm recognizes accurately the mass and energy dissipation, the phase separation through a very clear coarse graining process, and the influences of different indices r of fractional Laplacian and different coefficients on the width of the interfaces.

Suggested Citation

  • Guozhen Wang & Huanzhen Chen, 2019. "Efficient Implementation and Numerical Analysis of Finite Element Method for Fractional Allen-Cahn Equation," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-14, July.
    • Handle: RePEc:hin:jnlmpe:7969371
    DOI: 10.1155/2019/7969371
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/MPE/2019/7969371.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/MPE/2019/7969371.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2019/7969371?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
    ---><---

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlmpe:7969371. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.