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Gauss Legendre–Gauss Jacobi quadrature rules over a tetrahedral region

Publication Type : Journal Article

Publisher : Applied mathematics and computation

Source : Applied mathematics and computation, Elsevier, Volume 190, Number 1, p.186–194 (2007)

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Keywords : Finite element method, Gauss Legendre–Gauss Jacobi quadrature rules, Orthogonal polynomials, Standard 1-cube, Tetrahedral Regions

Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Year : 2007

Abstract : This paper presents a Gaussian Quadrature method for the evaluation of the triple integral View the MathML source, where f(x,y,z) is an analytic function in x, y, z and T refers to the standard tetrahedral region: {(x,y,z)|0⩽x,y,z⩽1,x+y+z⩽1} in three space (x,y,z). Mathematical transformation from (x,y,z) space to (U,V,W) space map the standard tetrahedron T in (x,y,z) space to a standard 1-cube: {(U,V,W)/0⩽U,V,W⩽1} in (U,V,W) space. Then we use the product of Gauss Legendre and Gauss Jacobi weight coefficients and abscissas to arrive at an efficient quadrature rule over the standard tetrahedral region T. We have then demonstrated the application of the derived quadrature rules by considering the evaluation of some typical triple integrals over the region T.

Cite this Research Publication : H. T. Rathod, Dr. B. Venkatesh, Nagaraja, K. V., and Islam, M. Shafiqul, “Gauss Legendre–Gauss Jacobi quadrature rules over a tetrahedral region”, Applied Mathematics and Computation, vol. 190, pp. 186-194, 2007.

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