IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i9p1486-d407960.html
   My bibliography  Save this article

Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces

Author

Listed:
  • Binhu Xia

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China)

  • Yibao Li

    (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China)

  • Zhong Li

    (School of Humanities and Social Science, Xi’an Jiaotong University, Xi’an 710049, China)

Abstract

This paper describes temporally second-order unconditionally stable direct methods for Allen–Cahn and conservative Allen–Cahn equations on surfaces. The discretization is performed via a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation. We prove that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable. The resulting system of discrete equations is linear and is simple to implement. Several numerical experiments are performed to demonstrate the performance of our proposed algorithm.

Suggested Citation

  • Binhu Xia & Yibao Li & Zhong Li, 2020. "Second-Order Unconditionally Stable Direct Methods for Allen–Cahn and Conservative Allen–Cahn Equations on Surfaces," Mathematics, MDPI, vol. 8(9), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1486-:d:407960
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/9/1486/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/9/1486/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Li, Yibao & Guo, Shimin, 2017. "Triply periodic minimal surface using a modified Allen–Cahn equation," Applied Mathematics and Computation, Elsevier, vol. 295(C), pages 84-94.
    Full references (including those not matched with items on IDEAS)

    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. Jin Wang & Zhengyuan Shi, 2021. "Multi-Reconstruction from Points Cloud by Using a Modified Vector-Valued Allen–Cahn Equation," Mathematics, MDPI, vol. 9(12), pages 1-15, June.
    2. Yu, Qian & Wang, Kunyang & Xia, Binhu & Li, Yibao, 2021. "First and second order unconditionally energy stable schemes for topology optimization based on phase field method," Applied Mathematics and Computation, Elsevier, vol. 405(C).
    3. Li, Yibao & Xia, Qing & Kang, Seungyoon & Kwak, Soobin & Kim, Junseok, 2024. "A practical algorithm for the design of multiple-sized porous scaffolds with triply periodic structures," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 481-495.
    4. Lee, Dongsun & Lee, Chaeyoung, 2022. "Numerical solutions of the Allen–Cahn equation with the p-Laplacian," Applied Mathematics and Computation, Elsevier, vol. 434(C).

    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:8:y:2020:i:9:p:1486-:d:407960. 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.