IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i5p510-d508685.html
   My bibliography  Save this article

New Preconditioned Iteration Method Solving the Special Linear System from the PDE-Constrained Optimal Control Problem

Author

Listed:
  • Yan-Ran Li

    (Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China)

  • Xin-Hui Shao

    (Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China)

  • Shi-Yu Li

    (Department of Mathematics, College of Sciences, Northeastern University, Shenyang 110819, China)

Abstract

In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We propose the three-block splitting (TBS) iterative method and proved that it is unconditionally convergent. At the same time, the corresponding TBS preconditioner is derived from the TBS iteration method, and we studied the spectral properties of the preconditioned matrix. Finally, numerical examples in two-dimensions is applied to demonstrate the advantages of the TBS iterative method and TBS preconditioner with the Krylov subspace method.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:5:p:510-:d:508685
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/5/510/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/5/510/
    Download Restriction: no
    ---><---

    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. 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.
    2. 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).
    3. 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).

    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:9:y:2021:i:5:p:510-:d:508685. 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.