Numerical integration of some functions over an arbitrary linear tetrahedra in Euclidean three-dimensional space

摘要

In this paper it is proposed to compute the volume integral of certain functions whose antiderivates with respect to one of the variates (say either x or y or z) is available. Then by use of the well known Gauss Divergence theorem, it can be shown that the volume integral of such a function is expressible as sum of four integrals over the unit triangle. The present method can also evaluate the triple integrals of trivariate polynomials over an arbitrary tetrahedron as a special case. It is also demonstrated that certain integrals which are nonpolynomial functions of trivariates x; y; z can be computed by the proposed method. We have applied Gauss Legendre Quadrature rules which were recently derived by Rathod et al. [H.T. Rathod, K.V. Nagaraja, B. Venkatesudu, N.L. Ramesh, Gauss Legendre Quadrature over a Triangle, J. Indian Inst. Sci. 84 (2004) 183-188] to evaluate the typical integrals governed by the proposed method. (C) 2007 Elsevier Inc. All rights reserved.