IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v271y2015icp1062-1070.html
   My bibliography  Save this article

Gauss quadrature rules for numerical integration over a standard tetrahedral element by decomposing into hexahedral elements

Author

Listed:
  • Mamatha, T.M.
  • Venkatesh, B.

Abstract

In recent years hexahedral elements have gained more importance than compared to tetrahedral elements (e.g. importance in the study of aero-acoustic equations using hexahedral elements to check the computational efficiency between tetrahedral and hexahedral elements). Also among the various integration schemes, Gauss Legendre quadrature which can evaluate exactly the (2n−1)th order polynomial with n-Gaussian points is most commonly used in view of the accuracy and efficiency of calculations. In this paper, we present a Gauss quadrature method for numerical integration over a standard tetrahedral element T[0,1]3 by decomposing into hexahedral elements H[−1,1]3. The method can be used for computing integrals of smooth functions, as well as functions with end-point singularities. The performance of the method is demonstrated with several numerical examples. By the proposed method, with less number of divisions we are obtaining the exact solutions with minimum errors and number of computations is reduced drastically. We have evaluated the aspect ratio value of each hexahedral element which is in the range 1–5, as per the element quality check these elements can be used for mesh generation in FEM.

Suggested Citation

  • Mamatha, T.M. & Venkatesh, B., 2015. "Gauss quadrature rules for numerical integration over a standard tetrahedral element by decomposing into hexahedral elements," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 1062-1070.
    • Handle: RePEc:eee:apmaco:v:271:y:2015:i:c:p:1062-1070
    DOI: 10.1016/j.amc.2015.09.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300315012199
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2015.09.001?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:271:y:2015:i:c:p:1062-1070. 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.