Research Areas

• Numerical analysis of partial differential equations
• Domain decomposition methods, Parallel computing.
• Mathematical image processing, Artificial intelligence.

Education

• Ph. D. in Mathematics : Department of Mathematics, Indian Institute of Technology Delhi, New Delhi, India.
• M. Sc. in Mathematics : Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India.

Academic Appointments

• Assistant Professor, Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, India, October 2016 to Continuing.
• Assistant Professor, Department of Applied Sciences, National Institute of Technology Delhi, India, March 2015 – October 2016.
• Research Scientist, Max Planck Institute for Solar System Research, Goettingen, Germany, October 2014 – March 2015.
• Postdoctoral Fellow, Department of Mathematics, University of Coimbra, Coimbra, Portugal, June 2012 to September 2014.
• Postdoctoral Fellow, Indian Institute of Science, Bangalore, India, February 2012 to June 2012.

Visiting Positions

• Visiting Professor, Department of Mathematics, University of Coimbra, Portugal, June 17, 2017 to July 14, 2017.

International Journal Publications

• Sumit, S. Kumar, M. Kumar, Optimal fourth-order parameter-uniform convergence of a non-monotone scheme on equidistributed meshes for singularly perturbed reaction-diffusion problems,  International Journal of Computer Mathematics, (2021) https://doi.org/10.1080/00207160.2021.1998467.
• A. Patel, K. Rani, S. Kumar, IN Figueiredo, PN Figueiredo, Automated bleeding detection in wireless capsule endoscopy images based on sparse coding, Multimedia Tools and Applications 80 (2021) 30353–30366.
• S. Kumar, S. Kumar, Sumit, A posteriori error estimation for quasilinear singularly perturbed problems with integral boundary condition, Numerical Algorithms, (2021). https://doi.org/10.1007/s11075-021-01134-5
• Sumit, S. Kumar, J.V. Aguiar, Analysis of a nonlinear singularly perturbed Volterra integro-differential equation, Journal of Computational and Applied Mathematics, (2021), 113410, https://doi.org/10.1016/j.cam.2021.113410.
• S. Kumar, Sumit, H. Ramos, Parameter-uniform approximation on equidistributed meshes for singularly perturbed parabolic reaction-diffusion problems with Robin boundary conditions, Applied Mathematics and Computation,  392 (2021) 125677.
• S. Kumar, Sumit, J. V. Aguiar, A parameter-uniform grid equidistribution method for singularly perturbed degenerate parabolic convection–diffusion problems, Journal of Computational and Applied Mathematics, (2020), 113273, https://doi.org/10.1016/j.cam.2020.113273.
• S. Kumar, S. Kumar, Sumit, High-order convergent methods for singularly perturbed quasilinear problems with integral boundary conditions, Mathematical Methods in the Applied Sciences, 2020; 1– 14. https://doi.org/10.1002/mma.6854.
•  M. Kumar, J. Singh, S. Kumar, Aakansha, A robust numerical method for a coupled system of singularly perturbed parabolic delay problems, Engineering Computations, 38 (2021) 964-988.
• S.C.S. Rao, S. Kumar, J. Singh, A discrete Schwarz waveform relaxation method of higher order for singularly perturbed parabolic reaction–diffusion problems, Journal of Mathematical Chemistry, 58 (2020) 574–594.
• Sumit, S. Kumar, Kuldeep, M. Kumar, A robust numerical method for a two-parameter singularly perturbed time delay parabolic problem, Computational and Applied Mathematics, 39 (2020) 239.
• S. Kumar, J. Singh, M. Kumar, A robust domain decomposition method for singularly perturbed parabolic reaction-diffusion systems, Journal of Mathematical Chemistry, 57 (2019) 1557--1578.
• P. N. Figueiredo, I. N. Figueiredo, L. Pinto, S. Kumar, Y.-H. R. Tsai, A. V. Mamonov, Polyp detection with computer aided diagnosis in white light colonoscopy: comparison of three different methods, Endosc Int Open, 7 (2019) E209-E215.
• J. Singh, S. Kumar, M. Kumar, A domain decomposition method for solving singularly perturbed parabolic reaction-diffusion problems with time delay, Numerical Methods for Partial Differential Equations, 34 (2018) 1849-1866.
•  M. Kumar, S. Kumar, Higher order numerical approximation for time dependent singularly perturbed differential-difference convection-diffusion equations, Numerical Methods for Partial Differential Equations, 34 (2018) 357-380.
• S. Kumar and M. Kumar, A Second Order Uniformly Convergent Numerical Scheme for Parameterized Singularly Perturbed Delay Differential Problems, Numerical Algorithms, 76 (2017) 349-360. 
• S. Kumar and S.C.S. Rao, A Robust Domain Decomposition Algorithm for Singularly Perturbed Semilinear Systems, International Journal of Computer Mathematics, 94 (2017) 1108-1122.
• C. Graca, G. Falcao, and I. N. Figueiredo, and S. Kumar, Hybrid Multi-GPU Computing: Accelerated Kernels for Segmentation and Object Detection with Medical Image Processing Applications, Journal of Real-Time Image Processing, 13 (2017) 227-244.
• I. N. Figueiredo, S. Moura, J. S. Neves, L. Pinto, S. Kumar, C. M. Oliveira, J. D. Ramos Automated retina identification based on multiscale elastic registration, Computers in Biology and Medicine, 79 (2016) 130-143.
• S. Kumar and M. Kumar, Analysis of Some Numerical Methods on Layer-Adapted Meshes for Singularly Perturbed Quasilinear Systems, Numerical Algorithms, 71 (2016) 139-150.
• I.N. Figueiredo, S. Kumar, C. M. Oliveira, J. D. Ramos, and B. Engquist, Automated Lesion Detectors in Retinal Fundus Images, Computers in Biology and Medicine, 66 (2015) 47-65.
• S. Kumar and M. Kumar, An Analysis of Overlapping Domain Decomposition Method for Singularly Perturbed Reaction-Diffusion Systems, Journal of Computational and Applied Mathematics, 281 (2015) 250-262.
• S. Kumar and M. Kumar, High Order Parameter-Uniform Discretization for Singularly Perturbed Delay Parabolic Partial Differential Equations with Time Delay, Computers & Mathematics with Applications, 68 (2014) 1355-1367.
• S. Kumar, Layer-Adapted Methods for Quasilinear Singularly Perturbed Delay Differential Problems, Applied Mathematics and Computation, 233 (2014) 214-221.
• S. Kumar and S. C. S. Rao, A Robust Overlapping Schwarz Domain Decomposition algorithm for Time-Dependent Singularly Perturbed Reaction-Diffusion Problems, Journal of Computational and Applied Mathematics, 261 (2014) 127-138.
• I. N. Figueiredo, S. Kumar, C. Leal, and P. N. Figueiredo, Computer-Assisted Bleeding Detection in Wireless Capsule Endoscopy Images, Computer Methods in Biomechanics and Biomedical Engineering: Imaging & Visualization, 1 (2013) 198-210.
• S. C. S. Rao and S. Kumar, Robust High Order Convergence of a Overlapping Schwarz Method for a Singularly Perturbed Semilinear Reaction-Diffusion Problems, Journal of Computational Mathematics, 31 (2013) 509-521.
• S. C. S. Rao and S. Kumar, A Hybrid Difference Scheme for Singularly Perturbed Semilinear Reaction-Diffusion Problems, Neural Parallel Scientific Computations, 21 (2013) 335-346.
• S. C. S. Rao and S. Kumar, Second Order Global Uniformly Convergent Numerical Method for a System of Coupled Singularly Perturbed Initial Value Problems, Applied Mathematics and Computation, 219 (2012) 3740-3753.
• S. Kumar and M. Kumar, Parameter-Robust Numerical Method for a System of Singularly Perturbed Initial Value Problems, Numerical Algorithms, 59 (2012) 185-195.
• M. Kumar and S. Kumar, High Order Robust Approximations for Singularly Perturbed Semilinear Systems, Applied Mathematical Modelling, 36 (2012) 3570-3579.
• S. C. S. Rao and S. Kumar, An Almost Fourth Order Uniformly Convergent Domain Decomposition Method for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations, Journal of Computational and Applied Mathematics, 235 (2011) 3342-3354.
• S. C. S. Rao, S. Kumar, and M. Kumar Uniform Global Convergence of a Hybrid Scheme for Singularly Perturbed Reaction-Diffusion Systems, Journal of Optimization Theory and Applications, 151 (2011), 338-352.
• S. C. S. Rao and S. Kumar, A Robust NumericalMethod for Singularly Perturbed Semilinear Convection-Diffusion Problems, Neural, Parallel and Scientific Computations, 18 (2010) 155-165.
• S. C. S. Rao, S. Kumar, and M. Kumar A Parameter Uniform B-Spline Collocation Method for Singularly Perturbed Semilinear Reaction-Diffusion Problems, Journal of Optimization Theory and Applications, 146 (2010) 795-809.

International Conference Publications​

• S. Kumar, J. Singh, and M. Kumar, A Robust Domain Decomposition Method for  Singularly Perturbed Parabolic Systems, Proc. of the 18th International Conference on Computational and Mathematical Methods in Science and Engineering, CMMSE 2018, Rota, Cadiz, Spain, July 9–14, 2018.
• J. Singh, S. Kumar, and M. Kumar, A high order accurate overlapping domain decomposition method for singularly perturbed reaction-diffusion systems, Lecture Notes in Computer Science,  (2018), Proc. of 7-th Conference on Finite Difference Methods: Theory and Applications (FDM: T&A’ 2018), Lozenetz, Bulgaria, June 11-16, 2018.
• I. Joshi, S. Kumar, and I. N. Figueiredo Bag of Visual Words Approach for Bleeding Detection in Wireless Capsule Endoscopy Images, Lecture Notes in Computer Science, 9730 (2016) 575-582, Proceedings of International Conference on Image Analysis and Recognition, Povoa de Varzim, Portugal, July 13-15, 2016.
• C. Graca, G. Falcao, S. Kumar, and I. N. Figueiredo, Cooperative Use of Parallel Processing with Time or Frequency-Domain Filtering for Shape Recognition, Proc. IEEE, European Signal Processing Conference (EUSIPCO 2014), Lisbon, Portugal, 2014.
• I. N. Figueiredo, S. Kumar, C. Leal, and L. Pinto, Fall detection modeling based on inverse problems, International Conference on Engineering Optimization (EngOpt 2014), Lisbon, Portugal, Sept. 8-11, 2014, Proc. Taylor & Francis Group (CRC/Balkema).
• I. N. Figueiredo and S. Kumar, Automatic Optic Disc Detection in Retinal Fundus Images Based on Geometric Features, Lecture Notes in Computer Science, 8815 (2014) 285-292, Proceedings of International Conference on Image Analysis and Recognition, Algarve, Portugal, Oct. 22-24, 2014.
• I. N. Figueiredo and S. Kumar, Wavelet-based computer-aided detection of bright lesions in retinal fundus images, Lecture Notes in Computer Science, 8641 (2014) 234-240, Proceedings of CompImage'14 conference, Pittsburgh, USA, Sept. 3-5, 2014.
• I. N. Figueiredo, S. Kumar, and P. N. Figueiredo An Intelligent System for Polyp detection in Wireless Capsule Endoscopy Images, Computational Vision andMedical Image Processing IV, Taylor & Francis Group, London, (2013), 229-235, Proceedings of IV ECCOMAS Thematic Conference on Computational Vision andMedical Image Processing:VipIMAGE2013, Funchal, Portugal.
• I. N. Figueiredo, S. Kumar, C Leal, and P. N. Figueiredo, An Automatic Blood Detection Algorithm for Wireless Capsule Endoscopy Images, Computational Vision and Medical Image Processing IV, Taylor & Francis Group, London, (2013), 237-241, Proceedings of IV ECCOMAS Thematic Conference on Computational Vision and Medical Image Processing:VipIMAGE2013, Funchal, Portugal.
• S. C. S. Rao and S. Kumar, Numerical Solution of a Nonlinear System of Singularly Perturbed Initial Value Problems, Dynamic Systems and Applications, 6 (2012) 367-371, Proceedings of Sixth International Conference on Dynamic Systems and Applications, Atlanta, Georgia,USA.
• S. C. S. Rao and S. Kumar, An Efficient Numerical Method for a System of Singularly Perturbed Semilinear Reaction-Diffusion Equations, Lecture Notes in Computer Science, 6046 (2011) 486-493, Proc. of 7th International Conference, NMA 2010, Borovets, Bulgaria, August 20-24, 2010.

Book Chapters

• S. Kumar, I. N. Figueiredo, C. Graca, and G. Falcao, A GPU Accelerated Algorithm for Blood Detection in Wireless Capsule Endoscopy Images, Developments in Medical Image Processing and Computational Vision, Lecture Notes in Computational Vision and Biomechanics, Springer, 2015, pp. 55 -71.

Thesis

"I touch the future.... I teach" - Christa McAuliffe

Odd Semester, 2020-21 Academic Year

• .

See below for a list of all courses that I have taught since March, 2015.

 Courses taught at IIT (BHU), Varanasi, India

• MA 101: Mathematics I
• MA 102: Mathematics II
• MA 104: Information Technology and Computing Workshop
• MA 201: Numerical Techniques
• CSM 421: Numerical Solution of Partial Differential Equations
• MA 203: Mathematical Methods
• MA 423: Integral Equations and Calculus of Variation

Courses taught at NIT Delhi, New Delhi, India

• MH 110: Mathematics II
• MAL 101: Advanced Calculus
• MAL 151: Linear Algebra and Complex Analysis
• AS 650: Research Methodology
• AS 602: Advanced Numerical Analysis
• MEL 551: Computational Methods in Engineering

Ph.D. 

M. Tech.

Conferences/Workshops/Short-term Courses

• Organized
  • Coordinator, QIP and CEP STC on Computational Methods for Integral and Differential Equations, December 10-16, 2018, Department of Mathematical Sciences, IIT (BHU) Varanasi, India
  • Coordinator, Workshop on Theory and Computation of Singularly Perturbed Differential Equations, December 04 - 08, 2017, Department of Mathematical Sciences, IIT (BHU) Varanasi, India (funded by MHRD, Govt. of India, under GIAN scheme).
  • Coordinator, Workshop on Isogeometric Methods using B-Splines and NURBS, December 16 - 20, 2017, Department of Mathematical Sciences, IIT (BHU) Varanasi, India (funded by MHRD, Govt. of India, under GIAN scheme).
• ​Attended
  • 19th International Conference on Computational and Mathematical Methods in Science and Engineering, June 30 - July 06, 2019, Rota, Cadiz, Spain.
  • International Conference on Differential Equations and Control Problems: Modeling, Analysis and Computations, June 17 – June 19, 2019, IIT Mandi, India.
  • 18th International Conference on Computational and Mathematical Methods in Science and Engineering, July 09 - 13, 2018, Rota, Cadiz, Spain.
  • International Conference on PDEs: Theory and Computations, December 28 – December 30, 2015, South Asian University, New Delhi, India.
  • IV ECCOMAS Thematic Conference on Computational Vision and Medical Image Processing: VipIMAGE 2013, October14 – October 16, 2013, Funchal, Portugal.
  • Workshop on Modeling and Simulation of Physiological Systems, December 05 – December 08, 2012, IST Lisbon, Lisbon, Portugal.
  • ​International Congress of Mathematicians, August 19 – August 27, 2010, Hyderabad, India.
  • International Conference Boundary and Interior Layers: Computational and Asymptotic Methods, July 05 – July 09, 2010, Zaragoza, Spain.
  • Instructional School on Computational Methods for Partial Differential Equations, May 27 – June 23, 2007, Department of Mathematics, IIT Bombay, Mumbai, India.
  • Workshop on Practical Aspects of Parallel Processing , Organized by CDAC, February 05 – February 08, 2007, CSC IIT Delhi, New Delhi, India.
  • International High Performance Computing (HPC) Users Conference on Leadership Computing for Science and Industry, February 28 – March 02, 2006, IIT Delhi, New Delhi, India.

​
Invited Talks/Contributed Talks

• Invited Talk on A spline collocation method for a fractional sub-diffusion model, FDTCA 2021, IIT (BHU) Varanasi, November 12-14, 2021.
• Invited Talk on Introduction to Boundary Layer Problems, Refresher Course on Mathematical tools for Physical and Computational Sciences, Dr. Harisingh Gour Vishwavidyalaya, Sagar, September 24 - October 08, 2021.
• Invited Talk on Introduction to Singularly Perturbed Differential Equations and their Numerical Methods, DETAAM 2021, DIT University, July 12-16, 2021.
• Invited Talk on Introduction to Singularly Perturbed Problems and their Numerical Analysis, NTSC-2019 Workshop, KNIT Sultanpur, UP, India.
• Contributed Talk on A Discrete Schwarz Waveform Relaxation Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems, 19th International Conference on Computational and Mathematical Methods in Science and Engineering, June 30 - July 06, 2019, Rota, Cadiz, Spain.
• Invited Talk on A Domain Decomposition Method for Singularly Perturbed Parabolic Reaction-Diffusion Problems, ICDECP19, June 17 – June 19, 2019, IIT Mandi, India.
• Contributed Talk on A Robust Domain Decomposition Method for Singularly Perturbed Parabolic Systems, 18th International Conference on Computational and Mathematical Methods in Science and Engineering, July 09 - 13, 2018, Rota, Cadiz, Spain.
• Invited Talk on Overlapping Domain Decomposition Algorithms for Singularly Perturbed Parabolic Problems, June 28, 2017,  Department of Mathematics, University of Coimbra, Coimbra, Portugal.
• Guest Speaker QIP on Advanced Numerical and Analytical Methods for Engineers and Scientists, January 12 – January 18, 2016, IIT BHU,Varanasi.
• Invited Talk at International Conference on PDEs: Theory and Computations, December 28 – December 30, 2015, South Asian University, New Delhi, India.
• Chaired a session at IV ECCOMAS Thematic Conference on Computational Vision and Medical Image Processing: VipIMAGE 2013, October14 – October 16, 2013, Funchal, Portugal.
• Contributed Talk on An Intelligent System for Polyp detection in Wireless Capsule Endoscopy Images, IV ECCOMAS Thematic Conference on Computational Vision and Medical Image Processing: VipIMAGE 2013, October 14 – October 16, 2013, Funchal, Portugal.
• Keynote speaker at Workshop on Modeling and Simulation of Physiological Systems, December 05 – December 08, 2012, IST Lisbon, Lisbon, Portugal.
• Contributed Talk on A Uniformly Convergent Numerical Method for a Coupled System of Singularly Perturbed Initial-Value Problems, International Conference Boundary and Interior Layers: Computational and Asymptotic Methods, July 05 – July 09, 2010, Zaragoza, Spain.

• Member, DPGC, Department of Mathematical Sciences, IIT (BHU) Varanasi, September 2021 to continuing.
• DUGC Convener, Department of Mathematical Sciences, IIT (BHU) Varanasi, September 2019 to August 2020.
• Warden, Vivekananda Hostel, IIT (BHU), May 2018- May 2021.
• Deputy Controller of Examination, NIT Delhi, July 2016 – October 2016.
• Chairman, Library Committee, NIT Delhi, July 2016 – October 2016.
• Deputy Chief Warden, NIT Delhi, August 2015 – July 2016.
• Chairman, Literary Club, NIT Delhi, August 2015 – July 2016.
• Chairman, Sports Club, NIT Delhi, August 2015 – July 2016.
• Chairman, Time Table Committee, NIT Delhi, August 2015 – July 2016.
• DPGC Convener, Department of Applied Sciences, NIT Delhi, August 2015 – October 2016.
• Member, Institute Annual Report Committee, NIT Delhi, August 2015 – July 2016.
• Chairman, SRC Club, NIT Delhi, May 2015 – August 2015.
• Assistant Warden, New Boys Hostel, Indian Institute of Science, Bangalore, May 01, 2012-June 08, 2012.

Current Openings
 

Ph.D. interviews at IIT (BHU), in general, are held two times a year;  in May/June for odd semester and in November/December for even semester. The admission procedure details can be found on IIT (BHU) website, see Application Process.