Rathan S

Assistant Professor, Department of Mathematics

Research Interest:

Broad Area: Numerical Analysis and Scientific Computing; Computational methods for PDEs

Current Interests:
  • Numerical Methods for Hyperbolic Conservation Laws and Related Models
  • Shock Capturing 
  • ENO and WENO Schemes
  • Numerical Approximations and Integration
  • Finite-Difference, Finite-Volume Schemes
  • Nonlocal Conservation Laws
  • Stability Analysis of PDEs
  • Implicit-Explicit Time Integration Techniques
Contact:

Email: rathans.math@iipe.ac.in, samalarathan2@gmail.com
   

Connect


Office: 0891-285-6046

Teaching Interests


B.Tech. Courses:
  • Numerical Methods 
  • Engineering Mathematics-I 
  • Engineering Mathematics-II
PhD Courses:

  • Topics in Numerical Analysis
  • High-Resolution Schemes for Nonlinear PDEs-I
  • High-Resolution Schemes for Nonlinear PDEs-II

Education

  • Ph.D. Visvesvaraya National Institute of Technology, Nagpur, July, 2015-Dec, 2018
  • M.Sc. Mathematics, IIT Kharagpur, 2011-2013
  • B.Sc. vaagdevi Degree & P.G. College, Kakatiya University, Warangal.

Professional Experience

  • Assistant Professor, Indian Institute of Petroleum and Energy, Visakhapatnam, July-2019 to present
  • Postdoctoral fellow, Department of Mathematics, IIT Bombay, Jan-2019 to July-2019
  • Direct CSIR-SRF, Department of Mathematics, VNIT Nagpur, March 2018-Nov 2018
  • JRF, Department of Mathematics, VNIT Nagpur, Jan 2015-Jan 2018
  • Teaching Assistant, Department of Mathematics, VNIT Nagpur, July 2013-Dec 2014

Member of Professional Bodies

  • Life member of Indian Society of Theoretical and Applied Mechanics(ISTAM)
  • SIAM Early career member, 2020

Journal Publications

1. Samala Rathan, Deepit Shah*.
    Construction and comparative study of second order time stepping methods based on IQ and IMQ-RBFs.
   International Journal of Applied and Computational Mathematics,  8(4), 203, 2022.

2. Samala Rathan, Biswarup Biswas.
    Arc-length based WENO scheme for Hamilton-Jacobi Equations.
    Communications on Applied Mathematics and Computation, 3(3), 481-496, (2021).

3. Samala Rathan, G. Naga Raju, Ashlesha A. Bhise.
    Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws.
    Applied Numerical Mathematics, Vol 157, 255-275, (2020). 

4. Samala Rathan.
   L1-type smoothness indicators based weighted essentially non-oscillatory scheme for Hamilton-Jacobi equations.
   International Journal for Numerical Methods in Fluids, Vol. 92(12), 1927-1947, 2020

5. Samala Rathan, Rakesh Kumar, Ameya D. Jagtap.
    L1-type smoothness indicators based weno scheme for nonlinear degenerate parabolic equations.
    Applied Mathematics and Computation, Vol.375, Article No.125112, (2020). 

6. Ashlesha A. Bhise, G. Naga Raju, Samala Rathan, M. Devakar.
    An efficient hybrid weno scheme with a problem independent discontinuity locator.
    International Journal for Numerical Methods in Fluids, 91(1), 1-28, (2019). 

7.  Samala Rathan, G. Naga Raju.
     Improved weighted eno scheme based on parameters involved in nonlinear weights.
     Applied Mathematics and Computation, 331, 120-129, (2018). 

8. Samala Rathan, G. Naga Raju.
    A modified fifth-order weno scheme for hyperbolic conservation laws.
    Computers & Mathematics with Applications, 75(5), 1531-1549, (2018). 

9.  G. Naga Raju, Yogita Rathod, Samala Rathan.
     Improved third-order weighted essentially non-oscillatory scheme. 
     International Journal for Numerical Methods in Fluids, 87(7), 329-342, (2018). 

10. G. Naga Raju, Yogita Rathod, Samala Rathan.
      Third-order weno scheme with a new smoothness indicator.
       International Journal for Numerical Methods in Fluids 85(2), 90-112, (2017). 

11. Samala Rathan, G. Naga Raju.
      An improved non-linear weights for seventh-order weighted essentially non-oscillatory scheme. 
      Computers & Fluids, 156, 496-514, (2017). 

* Indicates Under-Graduate student

Conference Publications

  •  “Seventh-order WENO scheme with L1−norm type smoothness indicators” in the Conference on Latest Advances in Computational and Applied Mathematics at Mahindra Ecole Centrale, Hyderabad, December, 15−17, 2016. (Only abstract)
  •   “Investigation of weighted essentially non-oscillatory scheme at critical points and near discontinuities” in the conference on Computational PDE at TIFR-CAM, Bengaluru, 2015.(Only abstract)

Research Projects

1. Title of the project: Design and Development of Numerical Schemes for Hyperbolic Systems of Conservation Laws
    Sponsoring agency: NBHM, DAE
    Project duration: 3 years 
    Cost of the Project: Rs. 16, 20, 400.00/-

Awards & Honors

  • Institute Postdoctoral fellowship, IIT Bombay, 01-01-2019 to 31-12-2020.
  • Selected for NBHM Postdoctoral fellowship for the year 2018. (Not availed)
  • Direct CSIR SRF fellowship in Mathematics for the year 2017-18. (One of the two selected candidates from all over India )
  • All India rank 144, IIT-JAM 2011.
  • Mandal level third topper in S.S.C., 2006.

Administrative Responsibilities:

Professor-in-Charge, Admissions, from 2021 to till date

Phd Students:

Ongoing:

1. Lavanya V Salian (Area of Research: Stability Analysis of PDEs)

2. Sanjibanee Sudha (Area of Research: Nonlocal Conservation Laws)

3. Shipra Mahata (Area of Research: Implicit-Explicit Time Integration Techniques)

4. Sudipta Sahu (Area of Research: Higher-order Numerical Methods for Conservation Laws)

Reviewer

  • AMS Mathematical Reviews
  • Applied Numerical Mathematics(Elsevier )
  • Computers & Fluids (Elsevier )
  • International Journal for Numerical Methods in Fluids(Wiley)
  • International Journal of Computer Mathematics(Taylor & Francis)
  • International Journal of Computational Fluid Dynamics(Taylor & Francis)
  • Computational and Applied Mathematics(Springer)
  • Indian Journal of Pure and Applied Mathematics(Springer)