IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v63y2016i1p69-95.html
   My bibliography  Save this article

A leapfrog semi-smooth Newton-multigrid method for semilinear parabolic optimal control problems

Author

Listed:
  • Jun Liu
  • Mingqing Xiao

Abstract

A new semi-smooth Newton multigrid algorithm is proposed for solving the discretized first order necessary optimality systems that characterizing the optimal solutions of a class of two dimensional semi-linear parabolic PDE optimal control problems with control constraints. A new computational scheme (leapfrog scheme) in time associated with the standard five-point stencil in space is established to achieve the second-order finite difference discretization. The convergence (or unconditional stability) of the proposed scheme is proved when assuming time-periodic solutions. Moreover, the derived well-structured discretized Jacobian matrices greatly facilitate the development of effective smoother in our multigrid algorithm. Numerical simulations are provided to illustrate the effectiveness of the proposed method, which validates the second-order accuracy in solution approximations and the optimal linear complexity of computing time. Copyright Springer Science+Business Media New York 2016

Suggested Citation

  • Jun Liu & Mingqing Xiao, 2016. "A leapfrog semi-smooth Newton-multigrid method for semilinear parabolic optimal control problems," Computational Optimization and Applications, Springer, vol. 63(1), pages 69-95, January.
    • Handle: RePEc:spr:coopap:v:63:y:2016:i:1:p:69-95
    DOI: 10.1007/s10589-015-9759-z
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10589-015-9759-z
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10589-015-9759-z?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zhang, Zemian & Chen, Xuesong, 2021. "A conjugate gradient method for distributed optimal control problems with nonhomogeneous Helmholtz equation," Applied Mathematics and Computation, Elsevier, vol. 402(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:spr:coopap:v:63:y:2016:i:1:p:69-95. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.