Qualification: 
MPhil, MSc
tm_mamatha@blr.amrita.edu
Phone: 
9902931759

Mamatha T. M. currently serves as Assistant Professor at the Department of Mathematics, School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru Campus, since 2007. She is currently pursuing her Ph.D. research in Numerical Analysis (FEM) at Amrita Vishwa Vidyapeetham University. 

Education

Degree University Year
Ph. D. (Pursuing) Amrita Vishwa Vidyapeetham University 2011 Onwards
M.Phil in Mathematics Sri Venkateswara University, Tirupti 2010
M.Sc. Bangalore University 2007

Professional Appointments

Year Affiliation
Assistant Professor (Sr. Grade) (since 2007) School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru

Membership in Professional Bodies

  • ISTAM

Certificates, Awards & Recognitions

  • Certificate of Excellence in Reviewing from Indian Journal of Library Science and Information Technology, 2017.

Publications

Publication Type: Journal Article

Year of Publication Title

2019

T. M. Mamatha and Dr. B. Venkatesh, “Numerical Integration over arbitrary Tetrahedral Element by transforming into standard 1-Cube”, IOP Conference Series: Materials Science and Engineering, vol. 577, p. 012172, 2019.[Abstract]


In this paper, we are using two different transformations to transform the arbitrary linear tetrahedron element to a standard 1-Cube element and obtain the numerical integration formulas over arbitrary linear tetrahedron element implementing generalized Gaussian quadrature rules, with minimum computational time and cost. We also obtain the integral value of some functions with singularity over arbitrary linear tetrahedron region, without discretizing the tetrahedral region into P3 tetrahedral regions. It may be noted the computed results are converging faster than the numerical results in referred articles and are exact for up to 15 decimal values with minimum computational time. In a tetrahedral sub-atomic geometry, a focal particle is situated at the middle with four substituents that are situated at the sides of a tetrahedron. The bond edges are cos−1(−⅓) = 109.4712206…° ≈ 109.5° when each of the four substituents are the same, as in methane(CH4) and in addition its heavier analogs. The impeccably symmetrical tetrahedron has a place with point amass Td, yet most tetrahedral particles have brought down symmetry. Tetrahedral atoms can be chiral. Mathematically the problem is to evaluate the volume integral over an arbitrary tetrahedron transforming the triple integral over arbitrary linear tetrahedron into the integrals over a standard 1-cube using two different parametric transformations.

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2018

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.[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.

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2015

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.

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Publication Type: Book Chapter

Year of Publication Title

2018

B. Sreevidya, Rajesh M, and Mamatha, T. M., “Design and development of an enhanced security scheme using RSA for preventing false data injection in wireless sensor networks”, in Advances in Intelligent Systems and Computing, vol. 696, , Ed. Springer Verlag, 2018, pp. 225-236.[Abstract]


Wireless sensor networks are largely used in mission-critical applications such as border surveillance, intrusion detection, remote patient monitoring. These applications demand the data to be secured while processing as well as communicating. Data security during the processing phase is a largely researched area, and there exists enough number of techniques to achieve it. On the other hand, techniques to achieve data security during communication phase even though exist in multiple numbers, most of the techniques demand high processing capacity. This requirement leads to high energy consumption which is a challenge in the context of wireless sensor networks. So a technique which will provide data security during communication phase in a wireless sensor network-based application with minimal energy consumption will be a very good solution. The proposed scheme is to prevent false data injection in which malicious or compromised nodes inject false data into the WSN which will influence the decision making of the system. The proposed system provides an enhanced security scheme for preventing false data injection attack in WSN with an efficient reactive routing method. The proposed system addresses two parameters: authenticity of the nodes and the integrity of the data. The proposed system is simulated using Network Simulator 2 (NS2), and the results indicate that the scheme performs better than the existing schemes which provide either integrity of data or authentication of the sender. © Springer Nature Singapore Pte Ltd. 2018.

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Publication Type: Conference Paper

Year of Publication Title

2009

T. M. Mamatha, “Restrained Domination of kth power of a Cycle”, in XVIII International Conference of forum for Inter Disciplinary Mathematics,, Waknaghat,Himachal Pradesh, 2009.

Courses Taught

  • Calculus (Single and Multivariable Calculus)
  • Matrix Algebra
  • Linear Algebra
  • Laplace and Fourier Transforms
  • Ordinary Differential equations
  • Partial Differential equations
  • Complex Analysis
  • Numerical Methods
  • Probability and Statistics