Rathan Samala

Assistant Professor, Department of Mathematics

Research Interest:

Computational Methods for (Partial) Differential Equations:

1. Hyperbolic conservation laws

2. Nonlocal conservation laws: applications to traffic flows

3. Shock capturing schemes: ENO and WENO
   

Connect


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


Teaching Interests

  • Calculus
  • Numerical Methods 
  • Differential Equations

Education

  • Ph.D. Visvesvaraya National Institute of Technology, Nagpur, July, 2015-Dec, 2018
  • M.Sc. Mathematics, IIT Kharagpur, 2011-13
  • B.Sc. Vaagdevi Degree & P.G. College, Kakatiya University, Warangal. 2008-11

Professional Experience


  • Assistant Professor, Indian Institute of Petroleum and Energy, Visakhapatnam, July-2019 to till date
  • Postdoctoral fellow, Department of Mathematics, IIT Bombay, Jan-2019 to July-2019 [Advisor: Prof. S. Baskar]
  • Adhoc faculty, Visvesvaraya National Institute of Technology, Nagpur, July-2013 to Dec-2024.

Member of Professional Bodies

  • Life member of Indian Society of Theoretical and Applied Mechanics(ISTAM)
  • Life member of Indian Mathematical Society(IMS)
  • Life member of Andhra Pradesh and Telangana Society for Mathematical Sciences (APTSMS)
  • SIAM Early career member, 2020

Journal Publications

17. Arun Govind Neelan, Raimund Burger, Manoj T Nair, Samala Rathan, 

     Higher-order conservative discretizations on arbitrarily varying non-uniform grids,  
      Computational and Applied Mathematics, Springer, 44, Article No.  27 (2025). [SCIE, IF: 2.5]

16. Shipra Mahata, Samala Rathan, Juan Ruiz Alverez, Dionisio F. Yanez, 
      A general correction for numerical integration rules over piece-wise continuous functions, 
      Journal of Computational and Applied Mathematics, Vol. 459, 116378, 2025. [SCIE, IF:2.1]

15. Lavanya V Salian, Samala Rathan, 
      Exponential approximation space reconstruction weighted essentially nonoscillatory scheme for dispersive partial differential equations, 
      Mathematical Methods in the Applied Sciences, Wiley, Vol. 47(4), 1823-1851, (2024). [SCIE, IF:2.1]

14. Samala Rathan, Deepit Shah, T. Hemanth Kumar, K. Sandeep Charan, 
      Adaptive IQ and IMQ-RBFs for solving initial value problems: Adam-Bashforth and Adam-Moulton methods, 
      International Journal of Computational Methods, World Scientific,  Vol. 21, No. 03, 2350032, (2024). [SCIE, IF:1.4]

13. Jan Friedrich, Sanjibanee Sudha, Samala Rathan, 
      Numerical schemes for a class of nonlocal conservation laws: a general approach, 
      Networks and Heterogenous Media, AIMS Press, 18(3), 1335-1354, (2023). [SCIE, IF:1.2]

12. Samala Rathan, Jiaxi Gu, 
      A sixth-order central WENO scheme for nonlinear degenerate parabolic equations, 
      Computational and Applied Mathematics, Springer, 42, Article No. 182 (2023). [SCIE, IF:2.5]

11. 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,  Springer, 8(4), 203, (2022). [SCOPUS]

10. Samala Rathan, Biswarup Biswas. 
      Arc-length based WENO scheme for Hamilton-Jacobi Equations. 
      Communications on Applied Mathematics and Computation, Springer, 3(3), 481-496, (2021). [ESCI, IF:1.4]

9.  Samala Rathan, G. Naga Raju, Ashlesha A. Bhise, 
     Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws, 
     Applied Numerical Mathematics, Elsevier, Vol 157, 255-275, (2020).  [SCI, IF:2.2]

8. Samala Rathan, 
    L1-type smoothness indicators based weighted essentially non-oscillatory scheme for Hamilton-Jacobi equations, 
    International Journal for Numerical Methods in Fluids,  Wiley, Vol. 92(12), 1927-1947, (2020). [SCI, IF:1.7]

7. Samala Rathan, Rakesh Kumar, Ameya D. Jagtap. 
   L1-type smoothness indicators based weno scheme for nonlinear degenerate parabolic equations. 
   Applied Mathematics and Computation, Elsevier, Vol.375, Article No.125112, (2020). [SCI, IF:3.5]

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, Wiley, 91(1), 1-28, (2019). [SCI, IF:1.7]

5. Samala Rathan, G. Naga Raju, 
    Improved weighted eno scheme based on parameters involved in nonlinear weights, 
     Applied Mathematics and Computation, Elsevier, 331, 120-129, (2018). [SCI,IF:3.5]

4. Samala Rathan, G. Naga Raju, 
    A modified fifth-order weno scheme for hyperbolic conservation laws, 
    Computers & Mathematics with Applications, Elsevier, 75(5), 1531-1549, (2018). [SCI, IF:2.9]

3. G. Naga Raju, Yogita Rathod, Samala Rathan, 
   Improved third-order weighted essentially non-oscillatory scheme. 
    International Journal for Numerical Methods in Fluids, Wiley, 87(7), 329-342, (2018).  [SCI,IF:1.7]

2. G. Naga Raju, Yogita Rathod, Samala Rathan, 
    Third-order weno scheme with a new smoothness indicator, 
    International Journal for Numerical Methods in Fluids, Wiley, 85(2), 90-112, (2017). [SCI,IF:1.7]

1. Samala Rathan, G. Naga Raju, 

    An improved non-linear weights for seventh-order weighted essentially non-oscillatory scheme,

    Computers & Fluids, Elsevier, 156, 496-514, (2017). [SCI, IF:2.5]


Submitted:

  • Sanjibanee Sudha, Jan Friedrich, Samala Rathan, Central schemes for systems of non-local balance laws, [arXiv]. 
  • Lavanya V Salian, Samala Rathan, Debojyoti Ghosh. A novel central compact finite difference scheme for third derivatives with a high spectral resolution, [arXiv].
  •  Lavanya V Salian, Samala Rathan, Rakesh Kumar. Compact FD scheme for some Sobolev-type equations with Dirichlet boundary conditions, [arXiv].
  • Samala Rathan, Rakesh Kumar, Lavanya V Salian. A high-resolution third-order hybrid WENO scheme for solving hyperbolic conservation laws. 
  • Lavanya V Salian, Vivek S Yadav, Samala Rathan, Rakesh Kumar. Spectral Analysis of Node- and Cell-Centered Higher-Order Compact Schemes for Fully Discrete One and Two Dimensional Convection-Dispersion Equation. 
  • Sudipta Sahu, Emanuele Macca, Rathan Samala,  Semi-Implicit Central scheme for Hyperbolic systems of balance laws with Relaxed Source Term.


Conference Publications

  • A. Arun G Neelan, S. Rathan, Triplet Order Adaptive Seventh-Order WENO Scheme for Compressible Flows, Journal of Physics: Conference Series, Volume 2844, 012021, 5th International Conference on Recent Advancement in Physics Sciences, IoP Publishing, 2024. DOI: 10.1088/1742-6596/2844/1/012021

Research Projects

1. Design and development of numerical scheme for nonlocal conservation laws in multi-dimension,

2. Design and Development of Numerical Schemes for Hyperbolic Systems of Conservation Laws, 
    Role: Principal Investigator;  Funding Agency: NBHM, DAE, Duration: 3 years (Dec, 2021 to Feb, 2025), 
    Budget: ~Rs. 18,31,794.00/-, Status: Completed.

3. Design and Analysis of Numerical Techniques for Hyperbolic Systems of Conservation Laws, 
    Role: Principal Investigator; Funding Agency: IRG, IIPE Visakhapatnam; Duration: 3 years (06/2021to 06/2024), 
    Budget: ~Rs. 8,31,070.00/-; Status: Completed.

Workshops/Conferences/Short_Courses organized:

  • Local organizer, "NCM ATM workshop on Numerical Methods for Partial Differential Equations," December 16-27, 2024, IIPE, Visakhapatnam, India.
  • Convener, "Shortcourse in Applications of Scalar Hyperbolic Conservation Laws," March 1-5, 2024, IIPE, Visakhapatnam, India.
  • Treasurer, A four-day workshop on "Research Opportunities in Petroleum, Energy and Natural Gas (ReOPEN)," Feb 24-27, 2020, IIPE, Visakhapatnam, India.

Awards & Honors

  • PECFAR-2024 award from IGSTC.
  • ANRF-ITS Travel Grant award-2024. 
  • 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. 
  • All India rank 144, IIT-JAM 2011.
  • Mandal level third topper in S.S.C., 2006.

Administrative Responsibilities:


Current:

  1. Dean's council coordinator-Faculty Affairs, from August 23rd, 2023 to till date
  2. Member, EAA-Activities committee, from Mar 7th 2022 to till date
  3. In-charge, H&S departmental website design and maintenance committee, June 17th, 2022 to till date


Previous:

  1. PIC-Admissions committee, from Jan 5th, 2021 to 19-05-2024.
  2. Member, Scholarship committee, from Jan 5th 2021 to Mar 6th 2022. 
  3. Member, EAA-Sports Events committee, from Jan 5th 2021 to Mar 6th 2022. 
  4. Member, EAA-News letter and Magazine committee, from Jan 5th 2021 to Mar 6th 2022. 
  5. Member, EAA-Class committee, from Jan 5th 2021 to Mar 6th 2022. 
  6. Member, Library committee, from Jan 5th 2021 to Mar 6th 2022. 
  7. Member, EAA-Sports Events committee, from March 5th 2020 to Jan 4th 2021. 
  8. Member, EAA-Class committee, from March 5th 2020 to Jan 4th 2021. 
  9. Member, Library committee, from August 6th 2019 to Jan 4th 2021. 
  10. Member, EAA-Cultural Events committee, from August 6th 2019 to March 4th 2020. 
  11. Member, EAA-Technical Events committee, from August 6th 2019 to March 4th 2020.
  12. Member, EAA-Scholarship and Awards committee, from August 6th 2019 to March 4th 2020. 
  13. Member, Transport committee, from August 6th 2019 to March 4th 2020. 

Phd Students:

Ongoing:

1. Lavanya V Salian: Joined in July 2021

2. Sanjibanee Sudha: Joined in July 2021, (Co-supervisor: Dr. C.V. Rao)

3. Shipra Mahata: Joined in July 2022.

4. Sudipta Sahu : Joined in December 2022.

Invited Lecture

  • Presented an invited talk titled "Hybridization of a third-order WENO for solving hyperbolic conservation laws" at Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Germany(17-06-2025)

  • Presented an invited talk titled "Hybridization of a third-order WENO for solving hyperbolic conservation laws" at School of Business Informatics and Mathematics, University of Mannheim, Germany(27-05-2025).
  • Presented an invited talk titled "Hybrid WENO for solving hyperbolic conservation laws" at Institut für Geometrie und Praktische Mathematik, RWTH Aachen University, Germany(14-07-2025)
  • Presented an invited talk titled "A high-resolution third-order hybrid weighted essentially nonoscillatory scheme for hyperbolic conservation laws" in the International Conference on Connecting Theory and Practice in Mathematics, Statistics and Data Science (ICMSD-2025) during 15-17, March 2025  organized by the Department of Mathematics, School of Advanced Sciences, VIT-AP University and Department of Mathematics and Statistics, The University of the West Indies, Trinidad and Tobago.
  • Presented an invited talk titled "Numerical methods for scalar hyperbolic conservation laws" in the workshop on  'Recent Advances in Differential Equations and Applications' organized by the Department of Mathematics, School of Advanced Sciences, VIT AP University, Andhra Pradesh, India, 27th October 2023.
  • Presented an invited talk titled "High-Resolution Shock Capturing High-order WENO schemes for Hyperbolic Conservation Laws" on 12-10-2018 at IIT Bombay.
  • Presented an invited talk titled "High-order WENO schemes with variant nonlinear weights for hyperbolic conservation laws" on 25-07-2018 at TIFR CAM, Bangalore.

Conference Presentations:

  •  A contributed talk on '"A high-resolution third-order hybrid WENO scheme for hyperbolic conservation laws" at the conference HYP2024, Shanghai, China (July 01 -05, 2024)
  • A contributed talk on “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.
  • A contributed talk on “Investigation of weighted essentially non-oscillatory scheme at critical points and near discontinuities” in the conference on Computational PDE at TIFR-CAM, Bengaluru, 2015.

Workshops:

  • Speaker in NCM ATM workshop on "Numerical Methods for Partial Differential Equations" during December 16-27, 2024,  held at IIPE, Visakhapatnam, India.

Reviewer

  •  Mathematical Reviews, American Mathematical Society
  •  zbMath Open
  • Journal of Computational Physics (Elsevier)
  • Journal of Computational and Applied Mathematics (Elsevier)
  • Applied Numerical Mathematics (Elsevier)
  • Computers and Mathematics with Applications (Elsevier)
  • Computers & Fluids (Elsevier)
  • Acta Mechanica Sinica (Elsevier)
  • European Journal of Mechanics/B Fluids (Elsevier)
  • Communications in Nonlinear Science and Numerical Simulation (Elsevier)
  • International Journal for Numerical Methods in Fluids (Wiley)
  • Computational & Applied Mathematics (Springer)
  • International Journal of Computational Fluid Dynamics (Taylor & Francis)
  • International Journal of Computer Mathematics (Taylor & Francis)
  • International Journal for Computational Methods in Engineering Science & Mechanics (Taylor & Francis)
  • Journal of Applied Mathematics (Hindawi)
  • Indian Journal of Pure and Applied Mathematics (Springer)


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