Publication Type : Journal Article
Publisher : International Journal for Computational Methods in Engineering Science and Mechanics, Taylor & Francis
Source : International Journal for Computational Methods in Engineering Science and Mechanics, Taylor & Francis, Volume 6, Issue 3, Number 3, p.179–186 (2005)
Url : http://www.tandfonline.com/doi/abs/10.1080/15502280590923711#.VuksitJ94dU
Campus : Bengaluru
School : Center for Nanosciences, School of Engineering
Department : Mathematics
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, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Gauss Legendre Quadrature Formulae for Tetrahedra”, International Journal for Computational Methods in Engineering Science and Mechanics, vol. 6, no. 3, pp. 179–186, 2005.