Publication Type:

Journal Article

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

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.

207
PROGRAMS
OFFERED
5
AMRITA
CAMPUSES
15
CONSTITUENT
SCHOOLS
A
GRADE BY
NAAC, MHRD
9th
RANK(INDIA):
NIRF 2017
150+
INTERNATIONAL
PARTNERS