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B. V. Rathish Kumar
PhD (SSSIHL, Prasanthinilayam)
Professor, Department of Mathematics and Statistics
Research Interest
Finite Element Analysis, Numerical Methods for PDEs, Numerical Analysis, Wavelets, Applied Mathematics, Computational Biology, High Performance Computing, Parallel Numerical Methods, CFD, Complete Flux Scheme, Financial Mathematics, Convection in Porous Media, AI/ML methods for PDEs, BioMedical Image processing, Monsoon Dynamics, Cardiac Electric Activity
FB571
Department of Mathematics and Statistics
IIT Kanpur,
Kanpur 208016
Specialization
Numerical Analysis, Applied Mathematics, Scientific Computing, computational Biomechanics, PDEs, CFD, HPC, Image Processing
Education
Thesis Title: Finite Element Analysis of Bio-Fluid FlowsThesis Supervisor: Prof. K.B. Naidu PhD (IIT Madras)
Current Teaching
Courses (UG/PG) taught
New courses introduced & taught:Finite Element Error EstimationMathematical Foundations for Cardiac ElectrophysiologyPDE Based Image ProcessingWavelet Methods for Elliptic PDEsPDE Based Computational Financial MathematicsParallel Numerical AlgorithmsAI/ML Methods for Differential EquationsParallel Numerical Methods for PDEsMathematical Modeling of Cardiovascular Fluid DynamicsReduced Basis Methods for PDEsOther courses taught:
Basics of Computers & Programming LanguagesLinear Algebra & ODEComplex Analysis & PDEContinuum MechanicsCalculus of Variations & Integral EquationsComputational Fluid DynamicsBasics and Applications of Finite Element MethodAdvanced Finite element ComputationsParallel Numerical AlgorithmsNumerical Analysis / Principles of Numerical ComputationNumerical solutions to Partial Differential EquationsParallel Numerical Methods for PDE sData StructuresAlgorithmsMathematical Modelling of Cardio Vascular DynamicsMTH: 203 (ODE &PDE)Finite Element MethodMathematical ModelingTheory of ODEComputer Programming and Data StructuresFluid DynamicsTheory of ComputationSelected Publications
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 RameshKalamkar, 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 domainsJournal 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 modelEuropean 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
Awards & Fellowships
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