Publication Type : Journal Article
Publisher : International Journal of Computational Engineering Science and Mechanics
Source : International Journal of Computational Engineering Science and Mechanics, Vol.6, Issue-3, 197- 205
Url : https://onlinelibrary.wiley.com/doi/abs/10.1002/num.20095
Campus : Bengaluru
School : School of Engineering
Department : Mathematics
Year : 2005
Abstract : In this article 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 ≤ ζ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points. The effectiveness of the formulas is demonstrated by applying them to the integration of three nonpolynomial, three polynomial functions and to the evaluation of integrals for element stiffness matrices in linear three-dimensional elasticity. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
Cite this Research Publication : Gauss Legendre Quadrature Formulas for Tetrahedra, International Journal of Computational Engineering Science and Mechanics, Vol.6, Issue-3, 197- 205