IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v356y2019icp338-346.html
   My bibliography  Save this article

A new fast method of solving the high dimensional elliptic eigenvalue problem

Author

Listed:
  • Huang, Ruihao
  • Mu, Lin

Abstract

In this paper, we develop a novel method to solve the elliptic eigenvalue problem. The univariate multi-wavelet approach provides a simple diagonal preconditioner for second order elliptic problems, which gives an almost constant condition number for efficiently solving the corresponding linear system. Here, we shall consider a new fast numerical approach for approximating the smallest elliptic eigenvalue by using the multi-wavelet basis in the multi-grid discretization scheme. Moreover, we develop a new numerical scheme coupled with sparse grids method in the calculation. This new approach saves storage in degrees of freedom and thus is more efficient in the computation. Several numerical experiments are provided for validating the proposed numerical scheme, which show that our method retains the optimal convergence rate for the smallest eigenvalue approximation with much less computational cost comparing with ’eigs’ in full grids.

Suggested Citation

  • Huang, Ruihao & Mu, Lin, 2019. "A new fast method of solving the high dimensional elliptic eigenvalue problem," Applied Mathematics and Computation, Elsevier, vol. 356(C), pages 338-346.
    • Handle: RePEc:eee:apmaco:v:356:y:2019:i:c:p:338-346
    DOI: 10.1016/j.amc.2019.03.035
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319302425
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.03.035?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.

    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:356:y:2019:i:c:p:338-346. 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: 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.