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Publication Type : Journal Article
Publisher : Applied Mathematics and Computation
Source : Applied Mathematics and Computation, Volume 191, Number 2, p.397-409 (2007)
Keywords : Extended numerical integration, Finite element method, Gauss Legendre quadrature, Numerical integration, Tetrahedron, Triangular elements
Campus : Bengaluru
School : School of Engineering
Department : Mathematics
Year : 2007
Abstract : 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.
Cite this Research Publication : H. T. Rathod, Nagaraja, K. V., and Dr. B. Venkatesh, “Numerical integration of some functions over an arbitrary linear tetrahedra in Euclidean three-dimensional space”, Applied Mathematics and Computation, vol. 191, pp. 397-409, 2007.