• New courses introduced & taught:

• Finite Element Error Estimation

• Mathematical Foundations for Cardiac Electrophysiology

• PDE Based Image Processing

• Wavelet Methods for Elliptic PDEs

• PDE Based Computational Financial Mathematics

• Parallel Numerical Algorithms

• AI/ML Methods for Differential Equations

• Parallel Numerical Methods for PDEs

• Mathematical Modeling of Cardiovascular Fluid Dynamics

• Reduced Basis Methods for PDEs

• Other courses taught:

• Basics of Computers & Programming Languages

• Linear Algebra & ODE

• Complex Analysis & PDE

• Continuum Mechanics

• Calculus of Variations & Integral Equations

• Computational Fluid Dynamics

• Basics and Applications of Finite Element Method

• Advanced Finite element Computations

• Parallel Numerical Algorithms

• Numerical Analysis / Principles of Numerical Computation

• Numerical solutions to Partial Differential Equations

• Parallel Numerical Methods for PDE s

• Data Structures

• Algorithms

• Mathematical Modelling of Cardio Vascular Dynamics

• MTH: 203 (ODE &PDE)

• Finite Element Method

• Mathematical Modeling

• Theory of ODE

• Computer Programming and Data Structures

• Fluid Dynamics

• Theory of Computation

• B.V.Rathish Kumar and Parul Pathak, Linear stability analysis of convection in a solid partitioned inhomogeneous multilayered porous structure, Physics of Fluids 34, 076601 (2022); https://doi.org/10.1063/5.0090512

• Sourabh P. Bhat, B. V. Rathish Kumar, Shainath Ramesh Kalamkar, Vinay Kumar, Sudhir Pathak and Walter Schneider, Modeling and simulation of the potential indoor airborne transmission of SARS-CoV-2 virus through respiratory droplets, Physics of Fluids 34, 031909 (2022); https://doi.org/10.1063/5.0085495

• Vinay Kumar, V. S. S. N. V. G. Krishna Murthy and B. V. Rathish Kumar, Entropy generation in a chemically and thermally reinforced doubly stratified porous enclosure in a magnetic field, Physics of Fluids 34, 013307 (2022); https://doi.org/10.1063/5.0077870

• V. Rathish Kumar and Manisha Chowdhury, Variational multiscale stabilized finite element analysis of non-Newtonian Casson fluid flow model fully coupled with Transport equation with variable diffusion coefficients, Comput. Methods Appl. Mech. Engrg. 388 (2022) 114272, www.elsevier.com/locate/cma.

• Vinay Kumar, V.S.S.N.V.G. Krishna Murthy, B.V. Rathish Kumar, Multi-force effect on fluid flow, heat and mass transfer, and entropy generation in a stratified fluid- saturated porous enclosure, Mathematics and Computers in Simulation 203 (2023) 328– 367 www.elsevier.com/locate/matcom

• Sumit Kumar, Sanjay Kumar, V.Rathish Kumar, Om Shankar, The pulsatile 3D- Hemodynamics in a doubly afflicted human descending abdominal artery with iliac branching, Computer Methods in Biomechanics and Biomedical Engineering (2022) (https://doi.org/10.1080/10255842.2022.2082839).

• Shweta Raturi and V. Rathish Kumar, Effect of insoluble surfactants on the motion of Reiner–Rivlin fluid sphere in a spherical container with Newtonian fluid, Z. Angew. Math. Phys. (2021) 72:172 c 2021 The Author(s), under exclusive licence to Springer Nature Switzerland AG 0044-2275/21/040001-16 published online August 11, 2021 rhttps://doi.org/10.1007/s00033-021-01600-z

• Kumar, Somanchi V. S. S. N. G. Krishna Murthy, and B V R. Kumar, “Entropy and multiphysics analysis in a viscous dissipative non-Darcian porous enclosure," The EuropeanPhysical Journal Plus, vol. 136, no. 7, 2021.

• Mohapatra, P. Dutt, B.V.Rathish Kumar, Marc I. Gerritsima, Non-conforming least- squares spectral element method for Stokes equations on non-smooth domains Journal of  Computational and Applied MathematicsVolume 372July 2020Article 112696

• Abdul Halim and V. Rathish Kumar,An anisotropic PDE model for image inpainting Computers & Mathematics with Applications (In press) 2020

• Manisha Chowdhury and V.Rathish Kumar, On subgrid multiscale stabilized finite element method for advection-diffusion-reaction equation with variable coefficients  Applied Numerical MathematicsVolume 150April 2020Pages 576-586

• Abdul Halim , B.V. Rathish Kumar, A TV − L2 − H−1 PDE model for effective denoising, Computers and Mathematics with Applications 80 (2020) 2176–2193

• V. Rathish Kumar, Sunil Kumar, Convergence of three-step Taylor Galerkin finite element scheme based monotone Schwarz iterative method for singularly perturbed differential-difference equation, Numerical Functional Analysis & Optimization, 36:1029-1024, 2015.

• Sunil Kumar, V. Rathish Kumar, A domain decomposition Taylor Galerkin finite element approximation of a singularly perturbed semilinear differential-difference equation, Numerical Mathematics and Advanced Applications ENUMATH, 2015.

• JHM ten Thije Boonkkamp, BVR Kumar, S Kumar, M Pargaei, “Complete flux scheme for conservation laws containing a linear source”, Numerical Mathematics and Advanced Applications, ENUMATH 2015, 112, 23-31.

• V.S.S.N.V.G. Krishna Murthy, B. V. Rathish Kumar, A Parallel Finite Element Study of 3D Mixed Convection in a Fluid Saturated Cubic Porous Enclosure under Injection/ Suction E_ect, Applied Mathematics and Computation, 269: pp. 841 - 862, 2015.

• V.S.S.N.V.G. Krishna Murthy, B. V. Rathish Kumar, A Parallel Finite Element Study of 3D Mixed Convection in a Fluid Saturated Cubic Porous Enclosure under Injection/ Suction E_ect, Applied Mathe-matics and Computation, 269: pp. 841 - 862, 2015.

• H. M. ten Thije Boonkkamp, B. V. Rathish Kumar, Sunil Kumar, M. Pargaei, Complete flux scheme for conservation laws containing a linear source, Numerical Mathematics & Advanced Applications ENUMATH-2015, Springer, 112:23-31, 2016.

• Akash Anand, Ambuj Pandey V. Rathish Kumar and Jagabandhu Paul ) An e_cient high-order Nystrom scheme for acoustic scattering by inhomogeneous penetrable media with discontinuous material interface, Journal of Computational Physics, 311 (2016),

• Gopal Priyadarshi and V. Rathish Kumar, An approximate solution of Fredholm in- tegral equation of the second kind by band-limited scaling function, Int. J. Pure. Appl.Math., 107:23{34, 2016

• Sunil Kumar, V. Rathish Kumar, A domain decomposition Taylor Galerkin finite element approximation of a parabolic singularly perturbed differential equation, Applied Mathematics & Computation, 293:508-522, 2017.

• Sunil Kumar, V. Rathish Kumar, A finite element domain decomposition approximation for a semilinear parabolic singularly perturbed differential equation, International Journal of Nonlinear Sciences & Numerical Simulation, 18:41-55, 2017.

• Abdul Halim, V. Rathish Kumar,Fourier Spectral Method for Image Denoising, Int.

• Image VideoProcess. Theor. App. 2017.

• K. Murthy, F. Magoulès, B V R. Kumar, and V. Kumar, “Double diffusive free convection along a vertical surface in a doubly stratified porous medium with Soret and Dufour effects under MHD forces,” Journal of Porous Media, vol. 20, no. 10, 2017.

• Rowthu Vijayakrishna, V. Rathish Kumar, Abdul Halim, A PDE Based Image Segmentation UsingFourier Spectral Method, Differential Equations and Dynamical Systems, (March 2018) https://doi.org/10.1007/s12591-018-0414-x

• Gopal Priyadarshi and V. Rathish Kumar, Wavelet Galerkin schemes for higher order time dependent partial di_erential equations, Numer. Meth. Partial. Di_. Eqn., 34: 982-1008, 2018.

• Gopal Priyadarshi and V. Rathish Kumar, Wavelet Galerkin method for fourth order linear and nonlinear di_erential equations, Appl. Math. Comput., 327:8{21, 2018.

• V. Rathish Kumar and Gopal Priyadarshi, Wavelet Galerkin method for fourth order multidimensional elliptic partial di_erential equations, Accepted in Int. J. Wavelets Multiresolution. 2018.

• Gopal Priyadarshi and V. Rathish Kumar, On the existence and approximate solution of Fredholm integral equation of the first kind by band-limited scaling function, Diff. Eqn.Dyn. Sys, doi.org/10.1007/s12591-018-0416-8, 2018.

• Kumar, S. K. Murthy, and B V R. Kumar, “Influence of MHD forces on Bejan’s heatlines and masslines in a doubly stratified fluid saturated Darcy porous enclosure in the presence of Soret and Dufour effects–a numerical study,” International Journal of Heat and Mass Transfer, vol. 117, pp. 1041–1062, 2018.

• Kumar, S. K. Murthy, and B V R. Kumar, “Bejan’s heatline and massline visualization of multi-force effect on convection in a porous enclosure,” International Journal of Mechanical Sciences, vol. 146, pp. 249–271, 2018.

• Shweta Raturi, Sunil Dutta and V.Rathishkumar, Slow viscous flow past cylindrical particles with thin liquid layer: Cell model European Journal of Mechanics -B/Fluids, Volume 71, September–October 2018, Pages 151-159

• V.Rathish Kumar and Manisha A priori and a posteriori error estimation for finite element approximation of advection-diffusion-reaction equation with spatially variable coefficients (accepted and to appear in in Journal of Applied & Computational Mathematics, 2020)

• Sunil Kumar, V. Rathish Kumar, J. H. M. ten Thije Boonkkamp, Complete flux scheme for parabolic singularly perturbed differential-difference equations, Numerical Methods for Partial Differential Equations, 35:790-804, 2019.

• Sunil Kumar, V. Rathish Kumar, J. H. M. ten Thije Boonkkamp, Complete flux scheme for elliptic singularly perturbed differential-difference equations, Mathematics& Computers in Simulation, 165:255-270, 2019.

• Meena Pargei, V.Rathish Kumar, Luca Pavarino, Modeling and simulation of cardiac electric activity in a human cardiac tissue with multiple ischemic zones, J. Math. Biology, Springer, 2019.( https://doi.org/10.1007/s00285-019-01403-x)

• V. Rathish Kumar, Abdul Halim, A Linear Fourth Order PDE Based Gray Scale Image Inpainting Model, Computational and Applied Mathematics https://doi.org/10.1007/s40314-019-0768-x (2019)

• Meena pargei and V.Rathish Kumar, On the Existence-Uniqueness and Computation of Solution of a Class of Cardiac Electric Models, International Journal of Advances in Engineering Sciences and Applied Mathematics, 2019.

• Alpesh Kumar, Akansha Bhardwaj and V.Rathish kumar, A meshless local collocation method for time fractional diffusion wave equation, Computers & Mathematics with Applications, Volume 78, Issue 6, 15 September 2019, Pages 1851- 1861

• Abdul Halim and V.Rathish Kumar, Higher Oder PDE based Model for Segmenting Noisy Image, IET Image Processing Journal, Jan 2020 (Accepted)

• Mohapatra, P. Dutt, B.V.Rathish Kumar, Marc I. Gerritsima, Non-conforming least- squares spectral element method for Stokes equations on non-smooth domains Journal of Computational and Applied MathematicsVolume 372July 2020Article 112696

• Abdul Halim and V. Rathish Kumar,An anisotropic PDE model for image inpainting Computers & Mathematics with Applications (In press) 2020

• Manisha Chowdhury and V.Rathish Kumar, On subgrid multiscale stabilized finite element method for advection-diffusion-reaction equation with variable coefficients Applied Numerical MathematicsVolume 150April 2020Pages 576-586

• Gopal Priyadarshi and V.Rathish Kumar, Haar Wavelet method for 2D Parabolic Inverse problem with a control parameter, Rendiconti del circolo di Palermo Series, 69(3), 2020

• Gopal Priyadarshi and V.Rathis Kumar, Reconstruction of the Parameter in Parabolic Partial Differential Equations using Haar Wavelet Method, Engineering Computations, 2020 (in press).

• Abdul Halim and V.Rathish Kumar, A TV-L2-H^(-1) method for effective de- noising of images, Computers and Mathematics with Applications, 2020

• Shweta Raturi and V.Rathish Kumar, The Effect of Surfactant on the Drag and Wall Correction Factor of a drop in a bounded medium, ZAMM , 2020

• Pradip Sindhu Chair Professorship, IITK, 2014-17

• President, Indian Society Of Theoretical and Applied Mechanics(ISTAM), 2016

• General Secretary, Indian Academy of Mathematical Modeling and Simulation (IAMMS), 2015-2018

• Vice-President, Indian Association of Biomedical Engineers and Scientists, (IABMES), 2014-till date

• Adjunct Professor, SSSIHL, Prasanthinilayam, 2019-2022

• DST-SERB Co-opted PAC member for Mathematical Sciences, 2016-2020

• A.S.Gupta Memorial Speaker in ISTAM, IIT Bhubaneswar, 2019

• CIJK-Math Biology Plenary speaker, Beijing, China, 2019

• China-India-Japan-Korea Math-Biology executive council member, 2015-till date

• Member of Editorial Board of Contemporary Mathematics & Statistics, 2012-till date

• Member of the Editorial Board of Int. J. Applied Mathematics, 2010-2012

• Member of the National Advisory Committee for National Programme for Differential Equations: Theory, Computation &Application, IIT Bombay under the aegis of DST, Govt. of India, 2011-2016

• Member of the Steering Committee for National Network for Mathematical and Computational Biology, 2013-2016

• Board Member of Academic Committee for Applied Mathematics & Scientific Computing of Baroda University, 2012-Till date

• BOS member for Mathematical sciences of a) SRM University, b) SSSIHL, Prasanthinilayam, c) HBTI, Kanpur, d) DIAT, Pune, 2017-till date (a), 2019-till date (b), 2018-till date(c), 2018-till date(d)

• DST-SERB-NNMCB Regional Coordinator, 2014-2017

• Plenary Speaker ICCPDE-2022, 2022

• Best Mathematical Modeler, 2021

Office

FB571
Department of Mathematics and Statistics
IIT Kanpur,
Kanpur 208016

Office Phone: 0512-259-7660 (O)

Email: bvrk[AT]iitk.ac.in