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Gauss legendre quadrature formulas over a tetrahedron

Publication Type : Journal Article

Publisher : Numerical Methods for Partial Differential Equations, Wiley Online Library,

Source : Numerical Methods for Partial Differential Equations, Wiley Online Library, Volume 22, Number 1, p.197–219 (2006)

Url : http://onlinelibrary.wiley.com/doi/10.1002/num.20095/full

Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Year : 2006

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 : H. T. Rathod, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Gauss legendre quadrature formulas over a tetrahedron”, Numerical Methods for Partial Differential Equations, vol. 22, pp. 197–219, 2006.



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