IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v436y2023ics0096300322005902.html
   My bibliography  Save this article

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Author

Listed:
  • Voet, Yannis

Abstract

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated reassemblage of finite element matrices for nonlinear PDEs is frequently pointed out as one of the bottlenecks in the computations. The second bottleneck being the large and numerous linear systems to be solved arising from the use of Newton’s method to solve nonlinear systems of equations. In this paper, we will address the first issue. We will see how under mild assumptions the assemblage procedure may be rewritten using a completely loop-free algorithm. Our approach leads to a small matrix-matrix multiplication for which we may count on highly optimized algorithms.

Suggested Citation

  • Voet, Yannis, 2023. "On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005902
    DOI: 10.1016/j.amc.2022.127516
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322005902
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127516?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. Anjam, I. & Valdman, J., 2015. "Fast MATLAB assembly of FEM matrices in 2D and 3D: Edge elements," Applied Mathematics and Computation, Elsevier, vol. 267(C), pages 252-263.
    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. Yan-Ran Li & Xin-Hui Shao & Shi-Yu Li, 2021. "New Preconditioned Iteration Method Solving the Special Linear System from the PDE-Constrained Optimal Control Problem," Mathematics, MDPI, vol. 9(5), pages 1-13, March.
    2. Miroslav Frost & Jan Valdman, 2022. "Vectorized MATLAB Implementation of the Incremental Minimization Principle for Rate-Independent Dissipative Solids Using FEM: A Constitutive Model of Shape Memory Alloys," Mathematics, MDPI, vol. 10(23), pages 1-17, November.
    3. Moskovka, Alexej & Valdman, Jan, 2022. "Fast MATLAB evaluation of nonlinear energies using FEM in 2D and 3D: Nodal elements," Applied Mathematics and Computation, Elsevier, vol. 424(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:eee:apmaco:v:436:y:2023:i:c:s0096300322005902. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.