Qualification: 
Ph.D, MPhil, MSc
Email: 
b_venkatesh@blr.amrita.edu
Phone: 
9036399837

Dr. B. Venkatesh currently serves as Associate Professor and Head of the Department of Mathematics at the Amrita School of Engineering, Bengaluru Campus. He was conferred with a Ph. D. in Mathematics, Central College, Bangalore University, Bengaluru. Prior to joining Amrita, he served as Senior Lecturer and Lecturer at The Oxford College of Engineering and BTL Institute of Technology respectively. He has a teaching experience of 19 years.

Qualification

Degree University Year
Ph. D Bangalore University 2006
M.Phil Bangalore University 1998
M.Sc Bangalore University 1996

Publications

Publication Type: Journal Article

Year of Publication Publication Type Title

2015

Journal Article

T. M. Mamatha and Dr. B. Venkatesh, “Gauss quadrature rules for numerical integration over a standard tetrahedral element by decomposing into hexahedral elements”, Applied Mathematics and Computation, vol. 271, pp. 1062–1070, 2015.[Abstract]


In recent years hexahedral elements have gained more importance than compared to tetrahedral elements (e.g. importance in the study of aero-acoustic equations using hexahedral elements to check the computational efficiency between tetrahedral and hexahedral elements). Also among the various integration schemes, Gauss Legendre quadrature which can evaluate exactly the (2n−1)th order polynomial with n-Gaussian points is most commonly used in view of the accuracy and efficiency of calculations. In this paper, we present a Gauss quadrature method for numerical integration over a standard tetrahedral element T[0,1]3 by decomposing into hexahedral elements H[−1,1]3. The method can be used for computing integrals of smooth functions, as well as functions with end-point singularities. The performance of the method is demonstrated with several numerical examples. By the proposed method, with less number of divisions we are obtaining the exact solutions with minimum errors and number of computations is reduced drastically. We have evaluated the aspect ratio value of each hexahedral element which is in the range 1–5, as per the element quality check these elements can be used for mesh generation in FEM.

More »»

2013

Journal Article

H. T. Rathod, Dr. B. Venkatesh, T, S. K., and M, M. T., “Numerical integration over polygonal domains using convex quadrangulation and gauss legendre quadrature rules”, Inernational journal of engineering and computer science, vol. 2, no. 8, pp. 2576–2610, 2013.

2011

Journal Article

H. T. Rathod, Dr. B. Venkatesh, Nagabhushan, C. S., and Hariprasad, A. S., “On quintic splines with applications to quadrature over curved domains”, International electronic engineering mathematical society, vol. 6, pp. 126–146, 2011.

2010

Journal Article

H. T. Rathod, Nagabhushan, C. S., Dr. B. Venkatesh, and , “On quintic splines with applications to function and integrable function approximations”, International electronic engineering mathematical society, vol. 4, pp. 73–103, 2010.

2010

Journal Article

H. T. Rathod, Hariprasad, A. S., Dr. B. Venkatesh, and Nagabhushan, C. S., “The use of quintic splines for high accracy function and integrable function approximations”, International electronic engineering mathematical society, vol. 4, pp. 104–128, 2010.

2007

Journal Article

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.[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. More »»

2005

Journal Article

H. T. Rathod, Dr. B. Venkatesh, and Nagaraja, K. V., “Symmetric Gauss Legendre quadrature rules for composite numerical integration over a tetrahedral region”, Journal of Bulletin of Mathematics, vol. 24, pp. 51–79, 2005.

2005

Journal Article

H. T. Rathod, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Gauss Legendre Quadrature Formulae for Tetrahedra”, International Journal for Computational Methods in Engineering Science and Mechanics, vol. 6, no. 3, pp. 179–186, 2005.[Abstract]


In this paper 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 ≤ ξ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions. More »»
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