On the identification of symmetric quadrature rules for finite element methods. (May 2015)

• Record Type: Journal Article
• Authors: Witherden, F.D.; Vincent, P.E.
• Is Part Of: Computers & mathematics with applications. Volume 69:issue 10(2015)
• Page Start: 1232
• Page End: 1241
• Publication Date: 2015-05
• Subjects: Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2015.03.017
• Languages: English
• ISSNs: 0898-1221

Abstract

<abstract xml:lang="en" abstract-type="author" id="a000005"> <title id="st000005">Abstract</title> <sec> <p id="sp000050">In this paper we describe a methodology for the identification of symmetric quadrature rules inside of quadrilaterals, triangles, tetrahedra, prisms, pyramids, and hexahedra. The methodology is free from manual intervention and is capable of identifying a set of rules with a given strength and a given number of points. We also present <italic>polyquad</italic> which is an implementation of our methodology. Using polyquad v1.0 we proceed to derive a complete set of symmetric rules on the aforementioned domains. All rules possess purely positive weights and have all points inside the domain. Many of the rules appear to be new, and an improvement over those tabulated in the literature.</p> </sec> </abstract>