skumar.mat's picture
Dr. Sunil Kumar
Assistant Professor
Department of Mathematical Sciences
skumar.mat@iitbhu.ac.in
+91-7835014019
Area of Interest: 
Numerical analysis of partial differential equations, Domain decomposition methods, Mathematical image processing, Medical image processing, Computer Vision, Biometrics.

Dr. Sunil Kumar is an Assistant Professor in the Department of Mathematical Sciences, IIT (BHU), Varanasi, India. He earned his masters degree from IIT Roorkee and doctorate degree from IIT Delhi. He carried out his postdoctoral research at IISc Bangalore (2012) and University of Coimbra, Portugal (2012-2014). He was then a research scientist at Max Planck Institute for Solar System Research, Germany (2014-2015). He also served as Assistant Professor at NIT Delhi (2015-2016). His research interests span the broad areas of Numerical Analysis and Image Processing. Mainly, he focus on the following topics. 
 

Research Areas

  • Numerical analysis of partial differential equations, Singularly perturbed problems, Delay differential equations.
  • Domain decomposition methods, Parallel computing.
  • Mathematical image processing, Medical image processing, Computer Vision, Biometrics.

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

  • 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.
  • V. Gupta, 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

  • S. Kumar,Overlapping Schwarz Domain Decomposition Methods for Singularly Perturbed Reaction-Diffusion Problems, Ph.D Thesis, I.I.T. Delhi,New Delhi, India, 2012.

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

Even Semester, 2018-19 Academic Session

  • MA 101: Mathematics 
  • MA 104: Information Technology and Computing Workshop

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

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
Project  Title  Sonsoring Agency Duration Amount Role
Robust Adaptive Mesh Methods for Singularly Perturbed Problems in Ordinary and Partial Differential Equations SERB 2018-2021 Rs. 20.95 Lakhs PI
Schwarz Waveform Relaxation Methods for Singularly Perturbed Parabolic Problems SERB 2018-2021 Rs. 6.6 Lakhs PI
Automated Algorithms for Analysis of Wireless Capsule Endoscopy Images IIT (BHU) 2016-2018 Rs. 10 Lakhs PI

Ph.D. 

 Name  Topic  Status  Registration Year
 Sumit Adaptive Grid Methods for Singularly Perturbed Problems  Ongoing  2016
 Joginder Singh Domain Decomposition Methods for Singularly Perturbed Parabolic  Problems  Ongoing  2017
 Aakansha   Singularly Perturbed Differential Equations Ongoing 2018
 Kuldeep  Singularly Perturbed Differential Equations Ongoing 2018

 

M. Tech.

 Name  Topic  Status  Year
 Indu Joshi Automated Analysis of Wireless Capsule Endoscopy Images  Completed  2016
Sumit Sahrawat Convolutional Neural Network Based Image Dehazing Methods Completed 2018
R. Ronith Reddy A numerical study of singularly perturbed parabolic systems Completed 2019

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
    • 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 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.
  • Warden, Vivekananda Hostel, IIT (BHU), May 2018-Continuing
  • 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
 

One JRF Position: Applications are invited from highly motivated and eligible candidates for the post of JRF for the research project entitled “Robust Adaptive Mesh Methods for Singularly Perturbed Problems in Ordinary and Partial Differential Equations,” funded by Science & Engineering Research Board (SERB). For more details, see the job advertisement.  
 
Ph.D. Positions
 
Prospective Ph.D. Students of my Group must have sound knowledge in mathematics  (especially, in Numerical Analysis, Partial Differential Equations, and Analysis) and excellent programming skills. Ph.D students interested to work on mathematical image processing is desired to have knowledge of image processing.
 

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.

Postdoctoral Positions
 
Several postdoctoral funding options are available through external agencies, for example NBHM, SERB , etc. If you are interested to apply for any of these fellowships with me as host, please do not hesitate to contact me via email at skumar.mat@iitbhu.ac.in