Specialization

Application of wavelets, Partial differential equations, Machine Learning

Email

kavita@thapar.edu

Contact No.

+91-9654-040-633

Associate Professor

kavita@thapar.edu

Biography

Dr. Kavita is currently serving as an Associate Professor in the Department of Mathematics. She earned her Ph.D. from the Department of Mathematics at IIT Delhi in 2014. Following her doctorate, she pursued postdoctoral research at the Department of Aerospace and Mechanical Engineering, University of Liège, Belgium. In 2015, she joined the Thapar Institute of Engineering and Technology. Dr. Kavita’s research expertise lies in differential equations, wavelet analysis, and uncertainty quantification. She has published approximately 25 research papers in prestigious journals, with one of her recent works featured in the ASME (American Society of Mechanical Engineers) journal. She successfully completed a research project funded by the Department of Science and Technology (DST), titled "Compression and Representation of Biological Signals Using Diffusion Wavelets." To stay abreast of the latest advancements in artificial intelligence and machine learning, Dr. Kavita has begun exploring how her research can contribute to these emerging fields. She has presented her research at various international conferences and has visited several universities in the USA, Canada, Australia, Japan, Argentina, Germany, and Vietnam. In addition to her research, Dr. Kavita is deeply committed to teaching. She integrates technology-driven methods to make learning more engaging for her students. She has created over 600 educational videos, covering a broad range of courses for Thapar students. Please visit the following page for more details. https://sites.google.com/site/drkavitagoyalmathematics/home

Education

• Ph.D. (Mathematics) IIT Delhi
• M.Sc. (Hons. School) from Panjab University, Chandigarh

Experience: Total Teaching Experience: More than 10 years

• Associate Professor: Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, India from July, 2022 to Present.
• Assistant Professor: Department of Mathematics, Thapar Institute of Engineering and Technology, Patiala, India from October, 2015 to June, 2022
• Post doctorate Fellow: Department of Aerospace and Mechanical Engineering, University of Liege, Belgium, from October, 2014 to September, 2015

Teaching Interests:

• Machine Learning
• Numerical Analysis
• Linear Algebra
• Differential Equations
• Calculus

Research Interest:

• Applications of wavelets
• Numerical Analysis
• Differential Equations
• Machine Learning

Publications

Journals

1. Detection of multiple tumors through temperature response of a human brain using inverse bioheat transfer based on swarm optimization, M. Singhal, R. K. Singla, K. Goyal, Thermal Science and Engineering Progress, volume 47, 2024
2. A review of regularization strategies and solution techniques for ill-posed inverse problems, with application to inverse heat transfer problems, M. Singhal, K. Goyal and R. K. Singla, ‘Reviews in Mathematical Physics’, volume 36, pages 2330007, 2023
3. Review of solution methodologies for structural analysis of composites. Mohit Dhuria, Neeraj Grover, Kavita Goyal, European Journal of Mechanics-A/Solids, volume 103, pages 105157, 2024.
4. An adaptive stochastic investigation of partial differential equations using wavelet collocation generalized polynomial chaos method. Navjot Kaur and Kavita Goyal, Communications in Nonlinear Science and Numerical Simulation, volume 119, page 107110, 2023.
5. Inverse optimization based non-invasion technique for multiple tumor detection in brain tissue. M. Singhal, R. K. Singla, K. Goyal and S. Singh, ‘International Communications in Heat and Mass Transfer’, volume 141, 106596, 2023.
6. A new shear deformation theory in axiomatic framework for bending and buckling analysis of cross-ply and angle-ply laminated composite plates. Mohit Dhuria, Neeraj Grover and Kavita Goyal, ‘Journal of Applied Mechanics’, volume 90, page 051004, 2023.
7. An Adaptive Wavelet Optimized Finite Difference B-spline Polynomial Chaos Method for Random Partial Differential Equations, Navjot Kaur and Kavita Goyal, Applied Mathematics and Computation, volume 415, page 126738, 2022.
8. Influence of porosity distribution on static and buckling responses of porous functionally graded plates, Mohit Dhuria, Neeraj Grover and Kavita Goyal, Structures, volume 34, page 1458-1474, 2021.
9. Uncertainty Quantification of Stochastic Epidemic SIR Models using B-spline Polynomial Chaos, Navjot Kaur and Kavita Goyal, Regular and Chaotic Dynamics, volume 26, page 22-38, 2021.
10. A novel comparative approach on inverse heat transfer analysis of an experimental setup of an extended surface, Meenal Singhal, Rohit Kumar Singla and Kavita Goyal, International Communications in Heat and mass Transfer, volume 118, pages 104822, 2020.
11. Hybrid Hermite polynomial chaos SBP-SAT technique for stochastic advection-diffusion equations, Navjot Kaur and Kavita Goyal, International Journal of Modern Physics-C, volume 31, pages 2050128 (2020).
12. Uncertainty propagation using Wiener-Linear B-spline wavelet expansion, Navjot Kaur and Kavita Goyal, Computers & Mathematics with Applications, volume 79, pages 2598-2623 (2020).
13. Convective and radiative thermal analysis of composite wall with non-linear, temperature-dependent properties, Meenal Singhal, Rohit Kumar Singla and Kavita Goyal, Heat Transfer Research, volume 51, pages 275-296, 2020.
14. A MATLAB suite for second generation wavelets on an interval and the corresponding adaptive grid, Kavita Goyal and Deepika Sharma, Acta Applicandae Mathematicae, volume 31, pages 279-321, 2020.
15. A curvelet method for numerical solution of Partial Differential Equations, Deepika Sharma, Kavita Goyal and Rohit Kumar Singla, Applied Numerical Mathematics, volume 148, pages 28-44, 2020.
16. Experimental and computational inverse thermal analysis of transient, non-linear heat flux in circular pin fin with temperature-dependent thermal properties, Meenal Singhal, Sarvjeet Singh, Rohit Kumar Singla, Kavita Goyal and Deepak Jain, Applied Thermal Engineering, volume 168, 114721, 2020.
17. Wavelet optimized upwind conservative method for traffic flow problems, Deepika Sharma and Kavita Goyal, International Journal of Modern Physics-C, volume 31, pages 2050086, 2020.
18. An adaptive grid based curvelet optimized solution for nonlinear Schrodinger equation, Deepika Sharma, Rohit Kumar Singla and Kavita Goyal, International Journal of Modern Physics-C, volume 30, 1950101 (1-28), 2019.
19. Spectral graph wavelet optimized finite difference method for solution of Burger’s equation with different boundary conditions, Deepika Sharma and Kavita Goyal, Journal of Difference Equations and Applications, volume 25, pages: 373-395, 2019.
20. Second generation wavelet optimized finite difference method (SGWOFD) for solution of Burger’s equation with different boundary conditions, Deepika Sharma and Kavita Goyal, International journal of wavelets, multiresolution and information processing, volume 16, pages: 1850032:1-29, 2018.
21. Sensitivity analysis of parametric uncertainties and modeling errors in computational-mechanics models by using a generalized probabilistic modeling approach, Maarten Arnst and Kavita Goyal, Reliability Engineering and System Safety, volume 167, pages 394–405, 2017.
22. An adaptive meshfree spectral graph wavelet method for partial differential equations, Kavita Goyal and Mani Mehra, Applied Numerical Mathematics, volume 113, pages: 168–185, 2017.
23. Fast diffusion wavelet method for partial differential equations, Kavita Goyal and Mani Mehra, Applied Mathematical Modelling, volume 40, pages: 5000–5025, 2015.
24. An adaptive meshfree diffusion wavelet method for partial differential equations on the sphere, Kavita Goyal and Mani Mehra, Journal of Computational Physics, volume: 272, pages: 747–771, 2014.
25. A Fast Adaptive diffusion wavelet method for Burger’s equation, Kavita Goyal and Mani Mehra, Computers & Mathematics with Applications, volume: 68, pages: 568–577, 2014.
26. Algorithm 929: A Suite on Wavelet Differentiation Algorithms, Mani Mehra and Kavita Goyal, ACM-Transactions on Mathematical Software, volume: 39, pages: 27:1–27:28, 2013.