IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v218y2024icp49-78.html
   My bibliography  Save this article

Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method

Author

Listed:
  • Clain, S.
  • Figueiredo, J.

Abstract

Generalised Finite Difference Methods and similar mesh-free methods (Pointset method, Multipoint method) are based on three main ingredients: a stencil around the reference node, a polynomial reconstruction and a weighted functional to provide the relations between the derivatives at the reference node and the nodes of the stencil. Very few studies were dedicated to the optimal choice of the stencil together with the other parameters that could reduce the global conditioning of the system and bring more stability and better accuracy. We propose a detailed construction of the very high-order polynomial representation and define a functional that assesses the quality of the reconstruction. We propose and implement several techniques of optimisation and demonstrate the advantages in terms of accuracy and stability.

Suggested Citation

  • Clain, S. & Figueiredo, J., 2024. "Stencil and kernel optimisation for mesh-free very high-order generalised finite difference method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 49-78.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:49-78
    DOI: 10.1016/j.matcom.2023.11.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475423004706
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2023.11.009?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.

    References listed on IDEAS

    as
    1. Zhang, Juan & Shuy, Rong-Juin & Chu, Chiung-Lin & Fan, Chia-Ming, 2022. "Generalized finite difference method for three-dimensional eigenproblems of Helmholtz equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 196(C), pages 45-67.
    2. Tinoco-Guerrero, G. & Domínguez-Mota, F.J. & Tinoco-Ruiz, J.G., 2020. "A study of the stability for a generalized finite-difference scheme applied to the advection–diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 176(C), pages 301-311.
    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. Biswas, Chetna & Singh, Anup & Chopra, Manish & Das, Subir, 2023. "Study of fractional-order reaction-advection-diffusion equation using neural network method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 15-27.

    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:218:y:2024:i:c:p:49-78. 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: 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.