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Numerical Integration over Ellipsoid by transforming into 10-noded Tetrahedral Elements

Publication Type : Journal Article

Publisher : IOP Conference Series: Materials Science and Engineering, IOP Publishing,

Source : IOP Conference Series: Materials Science and Engineering, IOP Publishing, Volume 310, p.012144 (2018)

Url : https://doi.org/10.1088/1757-899x/310/1/012144

Campus : Bengaluru

School : School of Engineering

Department : Mathematics

Year : 2018

Abstract : In this paper we try to obtain the numerical integration formulas to evaluate volume integrals over an ellipsoid by transforming into a 10-noded standard tetrahedral element. We first transform the ellipsoid to a sphere of radius one. A sphere of radius one in the first octant is divided into six tetrahedral elements (with three straight edges and three curved edges) by choosing a point P on the surface of the sphere. Later we consider each curved tetrahedral element to be 10-noded elements and transform them to standard tetrahedral elements (10-noded) with straight edges. Then we evaluate numerical integral values of some integrands by applying these transformations over the ellipsoid using MATHEMATICA-software. The performance of the proposed method with that of the generated meshes over ellipsoid is analyzed using some example problems. We observe that the ellipsoid has been discretized into 48 standard 10-noded tetrahedral elements and the results are converging to the exact integral values with minimum computational time.

Cite this Research Publication : T. M. Mamatha, Dr. B. Venkatesh, and R. Pramod, “Numerical Integration over Ellipsoid by transforming into 10-noded Tetrahedral Elements”, IOP Conference Series: Materials Science and Engineering, vol. 310, p. 012144, 2018.


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