Samala Rathan
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
Teaching Interests
- Calculus
- Numerical Methods
- Linear Algebra & Differential Equations
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, Grade-I, Indian Institute of Petroleum and Energy, Visakhapatnam, Jan-2022 to till date.
- Assistant Professor, Grade-II, Indian Institute of Petroleum and Energy, Visakhapatnam, July-2019 to Jan-2022.
- 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)
- 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
2024:
- 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).
- 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).
- 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).
- 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).
2022:
- 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).
2021:
- 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).
2020:
- 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).
- 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).
- 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).
- 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).
2018:
- 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).
- 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).
- 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).
2017:
- 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).
- 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).
Conference Publications
- A. Arun G Neelan, S. Rathan, Triplet Order Adaptive Seventh-Order WENO Scheme for Compressible Flows, 5th International Conference on Recent Advancement in Physics Sciences, IoP Publishing, Accepted, 2024.
Conference Presentations:
- Samala Rathan, Rakesh Kumar: A contributed talk on '"A high-resolution third-order hybrid WENO scheme for solving hyperbolic conservation laws" at the "Latest Advances in Computational and Applied Mathematics (LACAM-24)" will be held at IISER Thiruvananthapuram, Kerala, India. (February 21 -24, 2024)
- Lavanya V Salian, Samala Rathan, Debojyoti Ghosh: A contributed talk on '"A new central compact finite difference scheme with high spectral resolution for dispersive equations" at the "Latest Advances in Computational and Applied Mathematics (LACAM-24)" will be held at IISER Thiruvananthapuram, Kerala, India. (February 21 -24, 2024) [Best presentation award to Lavanya V Salian]
- Jan Friedrich, Sanjibanee Sudha, Samala Rathan:A contributed talk on “Numerical methods for non-local conservation laws" to present at 89th Annual Conference of Indian Mathematical Society (IMS) organized by the Department of Mathematics, BITS PILANI, Hyderabad (Dec 22-27, 2023)
Lavanya V. Salian, Samala Rathan: A contributed talk on " "A fifth-order WENO scheme with exponential basis for solving dispersive equations" to present at the "International Conference on Applied Mathematics and Mechanics (ICAMM 2023)" organized by Department of Mathematics, IIT Indore (October 18-20, 2023)
- Lavanya V. Salian, Samala Rathan: A contributed talk on " "Weighted essentially non-oscillatory scheme for dispersion equations with exponential approximation space" to present at the "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi (June 15-17, 2023)
- Arun Govind Neelan, Samala Rathan: A contributed talk on "Numerical stability analysis using deep neural network" to present at the "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi(June 15-17, 2023)
- Sudipta Sahu, Samala Rathan: A contributed talk on "Improved upwind scheme for advection equation with exponential approximation space" to present at the "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi (June 15-17, 2023)
- Jan Friedrich, Sanjibanee Sudha, Samala Rathan: A contributed talk on “Finite-volume schemes for a class of non-local conservation laws" to present at the "International Conference on Differential Equations and Control Problems (ICDECP23)'" organized by the Department of Mathematics & Statistics, IIT Mandi (June 15-17, 2023)
- Sudipta Sahu, Samala Rathan: Selected an abstract titled "Improved upwind scheme for advection equation with exponential approximation space" as a contributed talk at the 'Second International Conference on Mathematical Analysis and Computing (ICMAC-2022)' held at SSN College of Engineering, Tamilnadu (Dec 22-23, 2022)
- Samala Rathan, G Naga Raju: 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.
- Samala Rathan, G Naga Raju: 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.
Research Projects
Current:
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 (Dec, 2021 to Dec, 2024)
Cost of the Project: Rs. 16,20,400.00/-
2. Title of the project:Design and Analysis of Numerical Techniques for Hyperbolic Systems of Conservation Laws
Sponsoring agency: IRG, IIPE Visakhapatnam
Project duration: 3 years (June, 2021 to June, 2024)
Cost of the Project: Rs. 5,85,000.00/-
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.
- All India rank 144, IIT-JAM 2011.
- Mandal level third topper in S.S.C., 2006.
Administrative Responsibilities:
Current:
- Dean's council coordinator-Faculty Affairs, from August 23rd, 2023 to till date
- PIC-Admissions committee, from Jan 5th, 2021 to till date
- Member, EAA-Activities committee, from Mar 7th 2022 to till date
- In-charge, H&S departmental website design and maintenance committee, June 17th, 2022 to till date
- Member, Scholarship committee, from Jan 5th 2021 to Mar 6th 2022.
- Member, EAA-Sports Events committee, from Jan 5th 2021 to Mar 6th 2022.
- Member, EAA-News letter and Magazine committee, from Jan 5th 2021 to Mar 6th 2022.
- Member, EAA-Class committee, from Jan 5th 2021 to Mar 6th 2022.
- Member, Library committee, from Jan 5th 2021 to Mar 6th 2022.
- Member, EAA-Sports Events committee, from March 5th 2020 to Jan 4th 2021.
- Member, EAA-Class committee, from March 5th 2020 to Jan 4th 2021.
- Member, Library committee, from August 6th 2019 to Jan 4th 2021.
- Member, EAA-Cultural Events committee, from August 6th 2019 to March 4th 2020.
- Member, EAA-Technical Events committee, from August 6th 2019 to March 4th 2020.
- Member, EAA-Scholarship and Awards committee, from August 6th 2019 to March 4th 2020.
- 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 "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.
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)