IDEAS home Printed from https://ideas.repec.org/a/hin/jnlaaa/954658.html
   My bibliography  Save this article

Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes

Author

Listed:
  • Fazal Ghaffar
  • Noor Badshah
  • Saeed Islam

Abstract

A higher order compact difference (HOC) scheme with uniform mesh sizes in different coordinate directions is employed to discretize a two- and three-dimensional Helmholtz equation. In case of two dimension, the stencil is of 9 points while in three-dimensional case, the scheme has 27 points and has fourth- to fifth-order accuracy. Multigrid method using Gauss-Seidel relaxation is designed to solve the resulting sparse linear systems. Numerical experiments were conducted to test the accuracy of the sixth-order compact difference scheme with Multigrid method and to compare it with the standard second-order finite-difference scheme and fourth-order compact difference scheme. Performance of the scheme is tested through numerical examples. Accuracy and efficiency of the new scheme are established by using the errors norms .

Suggested Citation

  • Fazal Ghaffar & Noor Badshah & Saeed Islam, 2014. "Multigrid Method for Solution of 3D Helmholtz Equation Based on HOC Schemes," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, August.
    • Handle: RePEc:hin:jnlaaa:954658
    DOI: 10.1155/2014/954658
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/AAA/2014/954658.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/AAA/2014/954658.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/954658?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
    ---><---

    Citations

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


    Cited by:

    1. Fazal Ghaffar & Noor Badshah & S. Islam, 2017. "Multigrid Solution For The Cauchy Problem Associated With Hel mholtz Type Equation On Non-Uniform Grids," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 1(2), pages 6-10, November.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnlaaa:954658. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.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.