Assistant Professor, Mathematics, School of Engineering, Bengaluru

Dr. Kesavulu Naidu V. currently serves as the Assistant Professor (Selection Grade) in the Department of Mathematics, School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru. His research interest is Finite Element Methods. He obtained his Ph. D. from Amrita Vishwa Vidyapeetham in the year 2013. He has published several technical articles in the reputed international journals or international conference proceedings, paper presentations at many international conferences and had delivered three invited talks in the reputed workshops.

- 2013:
**Ph.D. in Mathematics**

Amrita Vishwa Vidyapeetham - 2003:
**M.Sc. in Mathematics**

Bangalore University

Year | Affiliation |
---|---|

Since 2006 | Assistant Professor, Amrita Vishwa Vidyapeetham, Bangalore |

2005 - 2006 | GSSIT, Bangalore |

2003 - 2005 | NSVK College, Bangalore |

- Member of ISTAM

- University third Rank Holder in the M. Sc (Mathematics) from Bangalore University

Year | Funding Agency | Title of the Project | Investigators | Status |
---|---|---|---|---|

2021 | NBHM | Finite Element Solution of Partial Differential Equations Using New Higher Order Triangular Elements | Dr. Kesavulu Naidu, Dr. B. Venkatesh, Dr. Murali K. | Ongoing |

- Delivered an invited talk titled “Finite Element Methods using Mathematica” on June 27, 2014, in a “Two-Week International Workshop on Computational Fluid Dynamics” organized by the Department of Mathematics, BMS College of Engineering, Bangalore, held during June 23 -July 5, 2014. The workshop was sponsored by TEQIP-II (Technical Education Quality Improvement Programme-II).
- Delivered an invited talk titled “FEM using Mathematica” on August 1, 2014, in FDP on “Analytical and Numerical Techniques in Applied Mathematics and Engineering” organized by the Department of Mathematics, Malnad College of Engineering, Hassan, Karnataka, held during July 28 - August 2, 2014. The workshop was sponsored by TEQIP-II (Technical Education Quality Improvement Programme-II).
- Delivered an invited talk titled “Finite element analysis using Mathematica” on January 12, 2015, in Faculty Development Program on “Analytical and Numerical Techniques in Applied Mathematics and Engineering” organized by the Department of Mathematics, Malnad College of Engineering, Hassan, Karnataka, held from January 12-13, 2015.

- Matrix Algebra
- Calculus
- Vector Calculus
- Linear Algebra
- Probability and Statistics
- Integral Transforms
- Ordinary Differential Equations
- Partial Differential Equations
- Numerical Methods
- Numerical Solution of Differential Equations.

Research Scholars | |||
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Sl. No. | Name of the Student(s) | Topic | Status – Ongoing/Completed |

1. | Sasikala J. | Finite Element Methods | Ongoing |

2. | Sheryne Jemima Gnanam | Finite Element Methods | Ongoing |

Year of Publication | Title |
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2021 |
G. Shylaja, Venkatesh, B., Dr. V. Kesavulu Naidu, and Dr. K. Murali, “Two-dimensional non-uniform mesh generation for finite element models using MATLAB”, Materials Today: Proceedings, 2021.[Abstract] This paper demonstrates non-uniform mesh generation scheme for two-dimensional domains. For many models in fluid dynamics like turbulent flow, channel flow there is large gradient in the small narrow portion, for example near the wall region. To solve this kind of problems the non-uniform meshing scheme near the wall region helps to capture the fine details of the region. Meshing is carried through MATLAB codes which generate triangular meshes for two dimensional domains. The MATLAB code is based on distmesh2d developed for linear straight sided triangular element by Persson and Gilbert Strang (2004). The proposed meshing scheme is based on nodal relation and subparametric point transformations extracted from parabolic arcs developed by Rathod.et.al (2008). In this work a higher order triangular meshing upto quartic order for two domains the holey pie slice and a circle inscribed in a square has been demonstrated. These in turn finds its application in flow problems, thermodynamics and aerospace engineering. Present meshing scheme provides an improved high quality meshes for these domains and produce accurate results of the nodal position, boundary nodes and element connectivity for the discretized domain. The obtained output is advantageous in executing finite element procedure with less computational efforts. More »» |

2020 |
G. Shylaja, Venkatesh, B., Dr. V. Kesavulu Naidu, and Dr. K. Murali, “Improved finite element triangular meshing for symmetric geometries using MATLAB”, Materials Today: Proceedings, 2020.[Abstract] A MATLAB code for generation of curved triangular elements in two dimensions is presented. The method is based on the MATLAB meshing scheme distmesh2d provided by Persson and Strang. The meshing scheme generates triangular meshing for three symmetric geometries circle, ellipse and annular ring. Meshing scheme procedures are performed for linear (3-noded), quadratic (6-noded) and cubic (10-noded) curved triangular elements. As an output, we get a triangular meshing of symmetric geometry, node position, element connectivity and boundary edges. These outputs can be used to solve some class of partial differential equations (PDEs) by using finite element method (FEM). More »» |

2019 |
G. Shylaja, Dr. B. Venkatesh, and Dr. V. Kesavulu Naidu, “Finite Element Method to Solve Poisson’s Equation Using Curved Quadratic Triangular Elements”, IOP Conference Series: Materials Science and Engineering, vol. 577, p. 012165, 2019.[Abstract] The paper discusses the finite element method to solve Poisson’s equation using quadratic order curved triangular elements. We use quadratic order point transformation to solve the partial differential equation. We observe that with quadratic order as the discretization of the domain element is increased, the error of the solution decreases. More »» |

2019 |
K. Murali, Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “Darcy–Brinkman–Forchheimer flow over irregular domain using finite elements method”, IOP Conference Series: Materials Science and Engineering, vol. 577, p. 012158, 2019.[Abstract] The finite element method of solution with curved triangles to solve the three-dimensional, fully-developed Darcy–Brinkman–Forchheimer flow equation in channel with curved side is solved using quasi-linearization and Gauss-Seidel iteration method. Exhaustive numerical computation and numerical experimentation reveals the parameters’ influence on the velocity distributions.. A salient feature of the method adopted in the present paper is that it ensures that the errors are almost equally distributed among all the nodes. It is found that the irregular cross-section channel with upward concave boundary decelerates the flow. Numerical experimentation involved different order curved triangular elements and extensive computation revealed that the quintic order curved triangular element yields the desired solution to an accuracy of 10−5. The finite element method is found to be very effective in capturing boundary and inertia effects in the three-dimensional, fully-developed flow through porous media. Further, it succeeds in giving the required solution for large values of Forchheimer number when shooting method fails to do so. The method can be easily employed in any other irregular cross-section channel. More »» |

2019 |
Dr. K. Murali, Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “Solution of Darcy-Brinkman Flow Over an Irregular Domain by Finite Element Method”, Journal of Physics: Conference Series, vol. 1172, p. 012091, 2019.[Abstract] The problem of finding the numerical solution for the flow through a sporadic geometry includes a considerable measure of calculation time. In this article a finite element approach which involves sub-parametric finite element technique with bended triangular elements and with less number of degrees of freedom is used for finding solution of Darcy Brinkman flow through a rectangular duct with one bended side. This reduces the computational time considerably. The showing of the viability of the strategy is the target in this article. Results acquired are in great concurrence with the previous works that has been carried out. More »» |

2018 |
Dr. V. Kesavulu Naidu, Banerjee, D., and Nagaraja, K. V., “Optimal subparametric finite element method for elliptic PDE over circular domain”, Proceedings of the Jangjeon Mathematical Society, vol. 21, pp. 77-81, 2018.[Abstract] This paper gives us an insight into the usefulness of the proposed method in Finite Element Analysis (FEM) for solving an elliptic Partial Differential Equation (PDE) over circular domain. We are using quadratic and cubic order curved triangular elements to solve the problem of stress concentration on a circular plate, which is governed by Poisson's equation. The proposed FEM solution matches very well with the exact solution. This shows the efficiency and effectiveness of the method in various mechanical applications. © 2018 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved. More »» |

2016 |
Dr. K.V. Nagaraja, Panda, T. Darshi, and Dr. V. Kesavulu Naidu, “Optimal subparametric finite elements for the computation of cutoff wavenumbers in waveguides”, AIP Conference Proceedings, vol. 1715, p. 020048, 2016.[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. More »» |

2015 |
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. More »» |

2014 |
Dr. K.V. Nagaraja, Dr. V. Kesavulu Naidu, and Siddheshwar, P. G., “Optimal Subparametric Finite Elements for Elliptic Partial Differential Equations Using Higher-Order Curved Triangular Elements”, International Journal for 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. More »» |

2013 |
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. More »» |

2010 |
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 »» |

2010 |
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. More »» |

2010 |
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 »» |

2008 |
H. T. Rathod, Nagaraja, K. V., Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “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. More »» |

Year of Publication | Title |
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2019 |
Dr. K. Murali, Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “Solution of Darcy-Brinkman-Forchheimer Equation for Irregular Flow Channel by Finite Elements Approach”, in Journal of Physics: Conference Series, 2019, vol. 1172.[Abstract] The finite element method of solution with curved triangles to solve the three-dimensional, fully-developed Darcy-Brinkman-Forchheimer flow equation in channel with curved side is solved using quasi-linearization and Gauss-Seidel iteration method. Exhaustive numerical computation and numerical experimentation reveals the parameters' influence on the velocity distributions. A salient feature of the method adopted in the present paper is that it ensures that the errors are almost equally distributed among all the nodes. It is found that the irregular cross-section channel with upward concave boundary decelerates the flow. Numerical experimentation involved different order curved triangular elements and extensive computation revealed that the quintic order curved triangular element yields the desired solution to an accuracy of 10 -5 . The finite element method is found to be very effective in capturing boundary and inertia effects in the three-dimensional, fully-developed flow through porous media. Further, it prevails with regards to giving the required answer for vast estimations of Forchheimer number when shooting technique fails to do as such. The technique can be effortlessly utilized in some other sporadic cross-area channel. © Published under licence by IOP Publishing Ltd. More »» |

2018 |
Dr. V. Kesavulu Naidu, Banerjee, D., Siddheshwar, P. G., and , “Optimal sub-parametric finite element approach for a Darcy-Brinkman fluid flow problem through a circular channel using curved triangular elements”, in IOP Conference Series: Materials Science and Engineering, 2018, vol. 310.[Abstract] In this paper a proposed sub-parametric finite element method is used to solve a Darcy Brinkman flow problem through a circular channel using curved triangular elements. The flow through an irregular geometry requires a very tedious computation. In order to solve the flow problem with a much effective computational process, a finite element approach with curved triangular elements and with less number of degrees of freedom is used. The usefulness of the method is the objective of the paper. Results are in good agreement with previous works done. © Published under licence by IOP Publishing Ltd. More »» |

Year of Publication | Title |
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2018 |
T. Darshi Panda, Dr. K.V. Nagaraja, and Dr. V. Kesavulu Naidu, “A Simple and Efficient Higher Order Finite Element Scheme for Helmholtz Waveguides”, in Advances in Electronics, Communication and Computing, vol. 443, A. Kalam, Das, S., and Sharma, K., Eds. Singapore: Springer Singapore, 2018, pp. 421-43.[Abstract] This paper presents a simple and efficient finite element scheme for computing the cutoff wave numbers of arbitrary-shaped waveguides using higher order triangular elements. The waveguide geometry is divided into a set of triangular elements and each of these elements is mapped to a standard isosceles triangle by discritizing with subparametric finite elements. For waveguides containing arbitrary cross sections, the transformation is done using a series of higher order parabolic arcs. In this case, the curve boundaries are approximated by curved triangular finite elements and then transformed to an isosceles triangle. Numerical results are illustrated to validate the present approach. The obtained results have converged very well with the existing literature with minimum number of triangular elements, degree of freedoms, order of computational matrix, etc. More »» |

Year of Publication | Title |
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2017 |
D. T. Panda, Dr. K.V. Nagaraja, Dr. V. Kesavulu Naidu, and Sarada Jayan, “Application of quintic order parabolic arcs in the analysis of waveguides with arbitrary cross-section”, Proceedings of the International Conference on Communication and Electronics Systems, ICCES 2016. Institute of Electrical and Electronics Engineers Inc., 2017.[Abstract] A simple and efficient higher order finite element scheme is presented for obtaining highly accurate numerical solution for the two-dimensional Helmholtz equation in waveguides of arbitrary cross-section subjected to dirichlet boundary conditions. The above approach makes use of the Quintic order (5th order) parabolic arcs for accurately mapping the irregular cross section of the waveguide and then transforming the entire waveguide geometry to a standard isosceles triangle. In case of waveguides with regular geometry the transformation is done by straight sided quintic order finite elements. A unique and accurate point transformation technique is developed that ensures high accuracy of mapping by this quintic order curved triangular elements. This point transformation procedure gives a simple interpolating polynomial that defines the transformation from the global coordinate system to the local coordinate system. The above higher order finite element method is found to be highly optimal and accurate considering the various computational parameters like the number of triangular elements, degrees of freedom, nodal point distribution on the entire geometry, etc. © 2016 IEEE. More »» |

Faculty Research Interest: