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Gauss Legendre Quadrature Formulas For Tetrahedra

Publication Type : Journal Article

Publisher : International Journal of Computational Engineering Science and Mechanics

Source : International Journal of Computational Engineering Science and Mechanics,Vol.6, No.3,179-186(2005)

Url : https://www.semanticscholar.org/paper/Gauss-Legendre-Quadrature-Formulae-for-Tetrahedra-Rathod-Venkatesudu/48901f03bd2e21df8d8ade5d5c8cae133f541b53

Campus : Bengaluru

School : School of Engineering

Year : 2005

Abstract : In this paper we consider the Gauss Legendre quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)| 0 ≤ x, y, z ≤ 1, x + y + z ≤ 1} in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: {(ξ, η, ζ)| − 1 ≤ ξ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions.

Cite this Research Publication : H.T.Rathod ,B.Venkatesudu, K.V.Nagaraja, Gauss Legendre Quadrature Formulas For Tetrahedra , International Journal of Computational Engineering Science and Mechanics,Vol.6, No.3,179-186(2005).Publisher: Taylor & Francis, UK, Indexed in Scopus

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