Qualification: 
Ph.D, MSc
v_kesavulu@blr.amrita.edu

Dr. Kesavulu Naidu V. is the Assistant Professor (Selection Grade) in the Department of Mathematics, Amrita School of Engineering, Bangalore. His research interest is Finite Element Methods. He obtained his Ph. D from Amrita Vishwa Vidyapeetham in the year 2013. He has published more than seven technical articles in the reputed international journals, paper presentation at thirteen international conferences and had delivered three invited talks in the reputed workshops.

Qualification

Degree University Year
Ph. D. Amrita University 2013
M.Sc. (Bangalore University) 2003

Publications

Publication Type: Conference Paper

Year of Publication Publication Type Title

2016

Conference Paper

K. Va Nagaraja, Panda, T. Db, and Dr. V. Kesavulu Naidu, “Optimal subparametric finite elements for the computation of cutoff wavenumbers in waveguides”, in AIP Conference Proceedings, 2016, vol. 1715.[Abstract]


In the present work, the computation of cutoff wavenumbers in waveguides with both straight and curved edge boundaries have been carried out using subparametric transformations. As compared to the conventional finite element methods, the subparametric transformation takes the advantage of mapping curved boundaries with greater accuracy. Under this transformation, any triangle with two straight sides and one curved side can be mapped to a standard right-angled triangle. This method has been applied to a regular L-shaped rectangular waveguide and also on an irregular curved geometry. The obtained cutoff frequencies of regular geometry are in close agreement with the existing values found in literature and those of irregular boundary have converged very well. © 2016 AIP Publishing LLC. More »»

2016

Conference Paper

T. Darshi Panda, Dr. Dhanesh G. Kurup, Dr. V. Kesavulu Naidu, Sarada Jayan, and Nagaraja, K. V., “The use of higher order parabolic arcs for the computation of cutoff wavenumbers for TM modes in arbitrary shaped waveguides”, in Communication and Signal Processing (ICCSP), 2016 International Conference on, 2016.[Abstract]


This paper presents the use of Quartic and Quintic order finite elements for computing cutoff wavenumbers of arbitrary shaped waveguides. These finite elements are used for mapping the boundaries of waveguides with the highest accuracy. In the case of waveguides with curve geometries, the mapping is done by quartic and quintic order parabolic arcs. The domain of a particular waveguide is transformed to a suitable isosceles triangle with the help of these finite elements. The above method is found to be highly computationally efficient as compared to other methods found in literature. More »»

Publication Type: Journal Article

Year of Publication Publication Type Title

2015

Journal Article

Dr. V. Kesavulu Naidu, Siddheshwar, P. G., and Dr. K.V. Nagaraja, “Finite Element Solution of Darcy–Brinkman Equation for Irregular Cross-Section Flow Channel Using Curved Triangular Elements”, Procedia Engineering, vol. 127, pp. 301–308, 2015.[Abstract]


The finite element method of solution with optimal subparametric higher-order curved triangular elements is used to solve the 3-D fully developed Darcy–Brinkman flow equation through channel of irregular cross-section. Extensive numerical computation and numerical experimentation are done using the quadratic, cubic, quartic and quintic order triangular elements, which reveals that the parameters’ influence on the velocity distributions are qualitatively similar for all the cross-sections irrespective of whether they are of regular or irregular cross-sections. The quintic order curved triangular element yields the solution of a desired accuracy of 10-6. The method can be easily employed in any other irregular cross-section channels.

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2014

Journal Article

K. Va Nagaraja, Dr. V. Kesavulu Naidu, and Siddheshwar, P. Gb, “Optimal subparametric finite elements for elliptic partial differential equations using higher-order curved triangular elements”, International Journal of Computational Methods in Engineering Science and Mechanics, vol. 15, pp. 83-100, 2014.[Abstract]


This paper presents the finite element method using parabolic arcs for solving elliptic partial differential equations (PDEs) over regular and irregular geometry, which has many applications in science and engineering. Some numerical examples are given to demonstrate the accuracy and efficiency of the proposed method. The results obtained are in excellent agreement with the exact values. © 2014 Copyright Taylor & Francis Group, LLC.

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2013

Journal Article

Dr. V. Kesavulu Naidu and Dr. K.V. Nagaraja, “Advantages of cubic arcs for approximating curved boundaries by subparametric transformations for some higher order triangular elements”, Applied Mathematics and Computation, vol. 219, pp. 6893-6910, 2013.[Abstract]


In the finite element method, the most popular technique for dealing with curved boundaries is that of isoparametric coordinate transformations. In this paper, the 10-node (cubic), 15-node (quartic) and 21-node (quintic) curved boundary triangular elements having one curved side and two straight sides are analyzed using the isoparametric coordinate transformations. By this method, these curved triangles in the global coordinate system are mapped into a isosceles right angled unit triangle in the local coordinate system and the curved boundary of these triangular elements are implicitly replaced by cubic, quartic, and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. Relations are deduced for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a cubic arc which passes through four points of the original curve, thus ensuring a good approximation. The point transformations thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangles will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements. Numerical examples are given to demonstrate the accuracy and efficiency of the method. © 2013 Elsevier Inc. All rights reserved.

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2010

Journal Article

Dr. V. Kesavulu Naidu and Dr. K.V. Nagaraja, “The use of parabolic arc in matching curved boundary by point transformations for septic order triangular element and its applications”, Advanced Studies in Contemporary Mathematics (Kyungshang), vol. 20, pp. 437-456, 2010.[Abstract]


This paper is concerned with curved boundary triangular element having one curved side and two straight sides. The curved element considered here is the 36-node (septic) triangular element. On using the isoparametric coordinate transformation, the curved triangle in the global (x,y) coordinate system is mapped into a standard triangle: {(ξ, & etal)/0 ≤ ξ,η ≤ l,ξ+ η ≤ 1} in the local coordinate system (ξ,η). Under this transformation curved boundary of this triangular element is implicitly replaced by septic arc. The equation of this arc involves parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in septic arc in such a way that the arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters inthe interior of curved triangle will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides. We have considered an application example, which consists of the quarter ellipse: {(x, y)/x = 0, y = 0, x2/36+y2/4 =1}. We take this as a curved triangle in the physical coordinate system (x, y). We have demonstrated the use of point transformations to determine the points along the curved boundary of the triangle and also the points in the interior of the curved triangle. We have next demonstrated the use of point transformation to determine the arc length of the curved boundary. An additional demonstration which uses the point transformation and the Jacobian is considered. We have thus evaluated certain integrals, for example, ∫/A t αdxdy, (t = x,y,α = 0,1) A and found the physical quantities like area and centroid of the curved triangular elements. We hope that this study gives us the required impetus in the use of higher order curved triangular elements under the subparametric coordinate transformation. More »»

2010

Journal Article

Dr. K.V. Nagaraja, Dr. V. Kesavulu Naidu, and Rathod, H. Tb, “The use of parabolic arc in matching curved boundary by point transformations for sextic order triangular element”, International Journal of Mathematical Analysis, vol. 4, pp. 357-374, 2010.[Abstract]


This paper is concerned with curved boundary triangular element having one curved side and two straight sides. The curved element considered here is the 28-node (sextic) triangular element. On using the isoparametric coordinate transformation, the curved triangle in the global (x, y) coordinate system is mapped into a standard triangle: {(ξ,η) / 0 ≤ ξ,η ≤ 1,ξ + η ≤ 1}in the local coordinate system(ξ,η). Under this transformation curved boundary of this triangular element is implicitly replaced by sextic arc. The equation of this arc involves parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in sextic arc in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangle will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides.

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2010

Journal Article

H. T. Rathod, Shrivalli, H. Y., Dr. K.V. Nagaraja, and Dr. V. Kesavulu Naidu, “On a New Cubic Spline Interpolation with Application to Quadrature”, Int. Journal of Math. Analysis, vol. 4, no. 28, pp. 1387–1415, 2010.[Abstract]


This paper presents a formulation and a study of an interpolatory cubic spline which is new and akin to the Subbotin quadratic spline. This new cubic spline interpolates at the first and last knots and at the two points located at trisections between the knots. Application of the proposed spline to integral function approximations and quadrature over curved domains are investigated. Numerical illustrations, sample outputs and MATLAB programs are appended.. More »»

2008

Journal Article

H. Ta Rathod, Dr. K.V. Nagaraja, Dr. V. Kesavulu Naidu, and Venkatesudu, Bb, “The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements”, Finite Elements in Analysis and Design, vol. 44, pp. 920-932, 2008.[Abstract]


This paper is concerned with curved boundary triangular elements having one curved side and two straight sides. The curved elements considered here are the 6-node (quadratic), 10-node (cubic), 15-node (quartic) and 21-node (quintic) triangular elements. On using the isoparametric coordinate transformation, these curved triangles in the global (x, y) coordinate system are mapped into a standard triangle: { (ξ, η) / 0 ≤ ξ, η ≤ 1, ξ + η ≤ 1 } in the local coordinate system (ξ, η). Under this transformation curved boundary of these triangular elements is implicitly replaced by quadratic, cubic, quartic and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangles will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides. © 2008 Elsevier B.V. All rights reserved.

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