Dr. Rajendra K. Ray

Dr. Rajendra K. Ray
Phone : 01905-267041
EMail : rajendra[at]iitmandi[dot]ac[dot]in
Address : School of Basic Sciences,
Indian Institute of Technology Mandi,
VPO. Kamand, Mandi - 175005,
Himachal Pradesh, India.

Areas of Interest

  • Numerical Methods for PDEs
  • Computational Fluid dynamics
  • Two-Phase Modeling and Sediment Transport
  • Mathematical Image Processing
  • Stochastic Differential-Algebraic Equations

Education

  • PhD in Mathematics from Indian Institute of Technology Guwahati, 2009.
    Thesis title: Some New Directions in HOC Methodology: Tackling Circular Geometries (Advisor: Dr. Jiten C. Kalita)
  • MSc in Mathematics from Visva-Bharati University, Shantiniketan, 2003
  • BSc in Mathematics (Honours) from Visva-Bharati University, Shantiniketan, 2001

Post-doctoral Research Experience

  • January, 2010–December, 2010 – Laboratoire d’Hydraulique Saint-Venant, University Paris-Est, France (with Prof. Kim Dan NGUYEN).
  • April, 2009 – December, 2009 –Supercomputer Education and Research Centre (SERC), Indian Institute of Science Bangalore, India (with Dr. Soumyendu Raha)

Journal Publications

  • Jain SK, Ray RK., Bhavsar A. A Non-Linear Coupled Diffusion System For Image Despeckling and Application to Ultrasound Images. Circuits, Systems, and Signal Processing (Springer), Accepted, 2018.
  • Tyagi S, Abbas S, Meherrem S, Ray RK.. Time-delay-induced instabilities and Hope bifurcation analysis in 2-neuron network model with reaction-diffusion term. Neurocomputing (Elsevier), (https://doi.org/10.1016/j.neucom.2018.06.008) , 2018.
  • Mittal HVR, Ray RK.. Solving Immersed Interface Problems Using a New Interfacial Points Based Finite Difference Approach. SIAM Journal of Scientific Computing 40(3): A1860-A1884, 2018.
  • Mittal HVR, Qasem MA, Ray RK.. Locked-on vortex shedding modes from a rotationally oscillating circular cylinder. Ocean engineering (Elsevier), 146: 324-338, 2017.
  • Mittal HVR, Ray RK., Qasem MA. A numerical study of initial flow past an impulsively started rotationally oscillating circular cylinder using a transformation-free HOC scheme. Physics of Fluids (AIP), 29(9): 093603, 2017.
  • Tyagi S, Abbas S, Ray RK.. Stability and Bifurcation analysis of Cellular Neural Networks with Discrete and Distributed delays. Proceedings of the National Academy of Sciences, India Section A: Physical Sciences (Springer), 1-17, 2017.
  • Ray RK., Kumar A. Numerical study of shear rate effect on unsteady flow separation from the surface of the square cylinder using structural bifurcation analysis. Physics of Fluids (AIP), 29(8): 083604, 2017.
  • Kumar A, Ray RK.. A Numerical simulation of shear flow past two equal sized square cylinders arranged in parallel at Re=500. AIP Conf. Proc., 1863:490003-1-490003-4, 2017.
  • Mittal HVR, Ray RK.. Solving Moving Interface Problems Using a Higher Order Accurate Finite Difference Scheme. AIP Conf. Proc., 1863:490002-1-490002-4, 2017.
  • Jain SK, Ray RK.. Edge Detectors Based Telegraph Total Variational Model for Image Filtering. Information Systems Design and Intelligent Applications. Advances in Intelligent Systems and Computing (Springer), 433:119-126, 2016.
  • Mittal HVR, Kalita JC, Ray RK.. A class of finite difference schemes for interface problems with an HOC approach. International Journal for Numerical Methods in Fluids (Wiley), 82:567-606, 2016.
  • Ray RK, Kalita JC. Higher-Order-Compact Simulation of Unsteady Flow Past a Rotating Cylinder at Moderate Reynolds Numbers. Computationl and Applied Mathematics (Springer), 35(1):219-250, 2016.
  • Mittal HVR, Ray RK.. A Cartesian Grid Method for Solving Stokes Equations with Discontinuous Viscosity and Singular Sources. Advanced Computing and Communication Technologies. Advances in Intelligent Systems and Computing (Springer), 452:315-323, 2016.
  • Kumar A, Ray RK.. Higher order compact numerical simulation of shear flow past inclined square cylinder. Advanced Computing and Communication Technologies. Advances in Intelligent Systems and Computing (Springer), 452:305-313, 2016.
  • Mittal HVR, Ray RK.. A New Direction To Higher Order Compact Scheme For Solving Immersed Interface Problems. Mathematical Sciences International Research Journal (IMRF), 4(1):51-54, 2015.
  • Tyagi S, Abbas S, Ray RK.. Stability Analysis of an Integro Differential Equation Model of Ring Neural Network with Delay. Mathematical Analysis and its Applications (Springer), 143:37-49, 2015.
  • Kumar A, Ray RK.. Numerical Study of Shear Flow Past a Square Cylinder at Reynolds Numbers 100, 200. Procedia Engineering (Elsevier), 127:102-109, 2015.
  • Mittal HVR, Ray RK.. An HOC Based Immersed Interface Scheme for Uniform Flow Past a Circular Cylinder. Procedia Engineering (Elsevier), 127:244-249, 2015.
  • Jain SK, Ray RK., Bhavsar A. Iterative Solvers for Image Denoising with Diffusion Models: A Comparative Study. Computers and Mathematics with Applications (Elsevier), 70:191-211, 2015.
  • Jain SK, Ray RK.. A Non-Linear Diffusion based Partial Differential Equation Model For Noise Reduction in Images. Information Systems Design and Intelligent Applications. Advances in Intelligent Systems and Computing (Springer), 340:429-438, 2015.
  • Jain SK, Ray RK., Bhavsar A. A Comparative Study of Iterative Solvers for Image De-noising. Proceedings of the 3rd International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA). Advances in Intelligent Systems and Computing (Springer), 328:307-314, 2015.
  • Mittal HVR, Ray RK. A Transform Free Higher Order Compact Finite Difference Scheme for Simulating the Flow behind a Rotationally Oscillating Circular Cylinder at Reynolds number 500. Applied Mechanics and Materials, 367:126-131, 2013.
  • Shi Yu-e, Ray RK, Nguyen KD. A Projection Method-based model with the exact C-property for shallow-water flows over dry and irregular bottom using unstructured finite-volume technique. Computers & Fluids (Elsevier), 76:178-195, 2013.
  • Ray RK, Mittal HVR. A Transform-Free HOC Scheme for Incompressible Viscous Flow past a Rotationally Oscillating Circular Cylinder. World Academy of Science, Engineering and Technology. International Journal of Physical and Mathematical Sciences, 6(12):1763-1769, 2012.
  • Ray RK. A Transformation-free HOC Scheme for Incompressible viscous Flow Past a Rotating and Translating Circular Cylinder. Journal of Scientific Computing (Springer), 46(2):265-293, 2011.
  • Ray RK, Nguyen KD. An Unstructured Finite-volume Technique for Shallow-water Flows with Wetting and Drying Fronts. World Academy of Science, Engineering and Technology, 71:682-687, 2010.
  • Ray RK, Kalita JC. A transformation-free HOC scheme for incompressible viscous flows on nonuniform polar grids. International Journal for Numerical Methods in Fluids (Wiley), 62:683-708, 2010.
  • Kalita JC, Ray RK. A transformation-free HOC scheme for incompressible viscous flow past an impulsively started circular cylinder. Journal of Computational Physics (Elsevier), 228:5207-5236, 2009.
  • Ray RK, Kalita JC, Dass AK. An efficient HOC scheme for transient convection-diffusion-reaction equations with discontinuous coefficients and singular source terms. Proc. Appl. Math. Mech., 7(1):1025603-1025604, 2007.

Conference Publications

  • Kumar A, Ray RK.. Numerical simulation of flow around square cylinder with an inlet shear in a close channel. Applications of Fluid Dynamics. Lecture Notes in Mechanical Engineering, pp.: 297-304, 2017.
  • Mittal HVR, Ray RK. A New Direction to Higher Order Compact (HOC) Scheme for Solving Immersed Interface Problems. In: Multiphase Flows with Phase Change Challenges and Opportunities, IIT Hyderabad, India.
  • Mittal HVR, Ray RK. An efficient higher order accurate finite difference scheme for solving two dimensional elliptic equations with discontinuities. In International Congress of Mathematicians (ICM); Seoul, South Korea, 2014.
  • Jain SK, Ray RK. A comparative study of iterative solvers for image de-noising using Crank-Nicolson scheme. In International Congress of Mathematicians (ICM); Seoul, South Korea, 2014.
  • Ray RK, Mittal HVR. Numerical study of transition flows over a rotationally oscillating circular cylinder. In International Congress of Mathematicians (ICM); Seoul, South Korea, 2014.
  • Nguyen KD, Ray RK, Pham Van Bang D. Modeling of Sediment Transport and Turbidity Maximum in the Gironde Estuaries (France) by Single- and Two-Phase Approaches. In: The 10th Int. Conf. on Hydroscience and Engineering (ICHE); Orlando, USA, 2012.
  • Nguyen KD, Ray RK, Pham Van Bang D. Modeling of Sediment Transport and Turbidity Maximum in the Gironde Estuaries (france) by a Two-Phase Non-Hydrostatic Model. In: American Geophysical Union, Fall Meeting; San Francisco, USA, 2012.
  • Ray RK, Kalita JC. An efficient higher order accurate scheme for two-dimensional Immersed Interface problems. In: Third International Conference on MetaComputing (ICoMeC), Bhubaneswer, India, 2012.
  • Nguyen KD, Ray RK. An Unstructured Finite-volume Technique for Shallow-water Flows with Wetting and Drying Fronts. In: ASME-JSME-KSME 2011 Joint Fluids Engineering Conference (AJK2011-FED), Hamamatsu, Japan, 2011.
  • Ray RK. New findings on Alpha-Beta Phenomena for Unsteady Flow Past an Impulsively Started Circular Cylinder. In: IUTAM Symposium on Bluff Body Flows (Blubof); IIT Kanpur, India, 2011.
  • Nguyen KD, Levy F, Ray RK, Pham Van Bang D. Modeling of Sediment Transport and Turbidity Maximum in the Gironde Estuaries (France) by Single- and Two-Phase Approaches. In: River, Coastal and Estuarine Morphodynamics (RCEM), Beijing, China, 2011.
  • Levy F, Ray RK, Nguyen KD and Pham Van Bang D. Two-phase modelling for turbidity maximum transport in the Gironde Estuary (France). In: Two-pHase modElling for Sediment dynamIcS (THESIS), Paris, France, 2011.
  • Ray RK, Kalita JC, Dass AK. An efficient HOC scheme for 1D elliptic equations with discontinuous coefficients and singular source terms using nonuniform space grids. In: Indo-Australian Workshop and Symposium in CFD, IIT Roorkee, India, 2007.

Sponsored Projects

  • Development of an efficient numerical method for solving stochastic Partialdifferential equation and its application to turbulent flow analysis; Sponsored by SERB (DST).
    Duration: 3 years (08/2018 - 07/2021); Project Value: 20.09 Lakh.
  • Modelling of Contaminated sediment transport in lake/river; Sponsored by BRNS (DAE).
    Duration: 3 years (07/2014 - 10/2018); Project Value: 21.07 Lakh (with Dr. O. P. Singh (Co-PI)).
  • Development of Higher Order Accurate Numerical Schemes for Elliptic Equations with various Discontinuities and its Application to Immersed Interface Problems ; Sponsored by NBHM (DAE).
    Duration: 3 years (01/2015 - 01/2018); Project Value: 2.99 Lakh.
  • Development of a class of Higher Order Compact (HOC) Finite Difference schemes and its application to Linear Shear Flows; Sponsored by SERB (DST).
    Duration: 3 years (02/2014 - 02/2017); Project Value: 13.32 Lakh.
  • Higher Order Compact (HOC) Finite Difference scheme for Elliptic Equations with Discontinuous Coefficients and Singular Source Terms; Sponsored by IIT Mandi (Seed Grant) .
    Duration: 3 years (2011 - 2014); Project Value: 5.00 Lakh.

Teaching

Teaching at IIT Mandi

  • MA-101: Mathematics I.
  • MA-201: Mathematics III.
  • IC-110: Engineering Mathematics.
  • IC-111: Linear algebra.
  • IC-150P: Computation for Engineers Lab.
  • CS-203: Discrete Mathematics.
  • MA-607: Numerical Analysis.
  • MA-608: Computational Fluid Dynamics.
  • MA-609: Numerics of PDEs.
  • MA-709: Numerical Linear Algebra.
  • MA-565: Numerical Methods in Quantitative Finance
  • IC-201P: Design Practicum
  • MA-514: Computer Programming
  • MA-514P: Computer Programming Lab
  • MA-523: Numerical Analysis

Student Supervision

Graduated Ph.D. Students

  • Hari Vansh Rai Mittal (Registration No.: D11023, Thesis defended on July, 2016)
  • Thesis title: A CLASS OF HIGHER ORDER ACCURATE SCHEMES FOR FLUID INTERFACE PROBLEMS

  • Subit Kumar Jain (Registration No.: D12070, Thesis defended on June, 2018)
  • Thesis title: A CLASS OF NON-LINEAR COUPLED PARTIAL DIFFERENTIAL EQUATION BASED MODELS FOR IMAGE RESTORATION WITH ITS NUMERICAL REALIZATION

Ongoing Ph.D. Students

  • Atendra Kumar (Registration No.: D14033)
  • Sudeb Majee (Registration No.: D15028)
  • Amarjit Hayt (Registration No.: D16022)
  • Abhishek Tripathi (Registration No.: D17041)
  • Pankaj (Registration No.: PTD1601)

Awards and Scholarships

  • Achieved First class 2nd position in M.Sc. (in Mathematics).
  • Achieved First class 2nd position in B.Sc. (in Mathematics).
  • 96.19 percentile (57th all India rank) in GATE 2004 (in Mathematical Sciences).
  • National Merit Scholarship for 10+2 Examination.
  • National Merit Scholarship for B.Sc. (in Mathematics) Examination.
  • University Merit Scholarship Visva-Bharati University, India (1998, 2000–2003).
  • Gold Medal in Cricket in the 21st Inter IIT Staff Sport Meet, IIT Guwahati, 2013.
  • Included in Marquis Who's Who in the World 2015 - 32nd Edition.

Professional Experience

As a Faculty

  • Chairman, Student Affairs Panel, IIT Mandi, India (2017-present).
  • Chairman, Advisory Board, Hospitality and Guest House Service, IIT Mandi, India (2017-18).
  • Coordinator, M.Sc. in Applied Mathematics program, IIT Mandi, India (2015-17).
  • Sports Advisor, IIT Mandi, India (2015-17).
  • Coordinator, Hiking and Trekking Club, IIT Mandi, India (2011-14).
  • Warden, Nako Hostel, IIT Mandi, India (2011-14).
  • Chairman, Transport Advisory Board, IIT Mandi, India (2016).
  • Chairman, Student/Hostel Related Purchases committee, IIT Mandi, India (2013-14).
  • Chairman, PhD admission committee in Mathematics, IIT Mandi, India (Dec.-2012, July-2013, July-2014).
  • Co-Advisor, Institute Transport Committee, IIT Mandi, India (2015).
  • Faculty In-charge, Staff Contingents for Inter-IIT Staff Sport Meet, IIT Mandi, India (2013-18).

As a Students

  • Student Representative, Departmental Postgraduate Programme Committee (DPPC), Department of Mathematics, Indian Institute of Technology Guwahati, India, (2005–2008).
  • Member, American Mathematical Society (AMS).
  • Member, Society for Industrial and Applied Mathematics (SIAM).
  • Cultural Secretary, Siang Hostel, Indian Institute of Technology Guwahati, India (2006-2007).
  • Member, Mess Management Committee, Siang Hostel, Indian Institute of Technology Guwahati, India(2004-2005).
  • StudentWarden, Shantishree Boys’ Hostel, Visva-Bharati University, India (2002–2003).
  • Mess Convenor, Nanda Sadan Boys’ Hostel, Visva-Bharati University, India (2000–2001).
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