Convener(s)
| Name: | Dr. Chamakuri Nagaiah | G.D. Veerappa Gowda |
| Mailing Address: | Assistant Professor School of Mathematics IISER Thiruvananthapuram, Kerala, 695551, India. |
Raja Ramanna Fellow TIFR Centre for Applicable Mathematics Sharadanagar, Chikkabommasandra Yelahanka New Town, Bangalore - 65. |
| Email: | nagaiah.chamakuri at iisertvm.ac.in | gowda at tifrbng.res.in |
Partial Differential Equations(PDEs) play an important role in science and engineering applications, such as the propagation of heat or sound, fluid flow, finite elasticity, electrodynamics, cancer modeling, etc. In general, the solution of PDEs can be very challenging, depending on the type of equation, the number of independent variables, the boundary and initial conditions, and nonlinearities. Even if we know the theoretical existence and the uniqueness of the solution, it may not be possible to obtain analytical solutions. The only way to get approximate solutions is by using numerical techniques. This workshop offers an introduction to some important numerical methods for linear and non-linear ordinary and partial differential equations, and various numerical discretization techniques for their solution, namely finite difference (FDM), finite volume methods (FVM),finite element methods (FEM), and discontinuous Galerkin methods (DGM). It also includes an introduction to Machine Learning, Deep Learning, and Physics Informed Neural Networks (PINNs).This workshop is intended for Ph.Ds and Postdocs so that they can learn these techniques and use them in their research.
Dates:
Venue:
Venue Address:
Indian Institute of Science Education and Research Thiruvananthapuram,
Maruthamala PO, Vithura, Thiruvananthapuram 695551, Kerala.
Venue State:
Venue City:
PIN:
Chrono Order:
Syllabus:
| Name of the Speaker with affiliation | No.of Lectures | Detailed Syllabus |
| Veerappa Gowda G. D., Raja Ramanna Fellow, TIFR Centre for Ap- plicable Mathematics, Bengaluru | 4 lectures of 1 and half hours each |
Non-linear hyperbolic conservation laws: Con- cept of weak solutions, entropy condition and uniqueness of the solution. Construction of Godunov, Lax-Friedrichs, Engquist-Osher and Lax-Wendroff schemes. Lax-Wendroff theorem for convergence of the numerical solution. Fi- nite volume schemes. Monotone schemes: L∞ stability, total variation diminishing property and their convergence to the entropy solution. Higher order schemes. Finite volume schemes in higher dimensions. |
| Praveen Chandrashekar, Associate Professor, TIFR-Centre for Ap- plicable Mathematics, Bengaluru |
4 lectures of 1 and half hours each |
Discontinuous Galerkin method for hyperbolic PDE: The lectures will provide an introduction to DG methods starting with 1-D problems. The topics covered include: numerical flux, semi- discrete stability, basis functions, implementa- tion details, limiters and TVD property, and, Fourier stability analysis. Then we will discuss DG for hyperbolic systems, multi-dimensional scheme, modal and nodal versions, special ver- sions like flux reconstruction, etc. The lectures will be complemented with examples of com- puter codes implementing these methods. |
| Sashi Kumar Ganesan, Associate Professor, Com- putational Data Science, IISc Bengaluru |
4 lectures of 1 and half hours each |
Introduction to Computational Science, Banach and Hilbert spaces, Weak derivatives, Sobolev spaces, A general elliptic problem of second or- der and its weak solution, Standard Galerkin method, Abstract error estimate. Implementa- tion of the finite element method: Mesh han- dling and data structure, Numerical integration, Sparse matrix storage, Assembling of system matrices and load vectors, Inclusion of bound- ary conditions. Introduction to Machine Learn- ing, Deep Learning. Introduction to Physics In- formed Neural Networks (PINNs). |
| K.R.Arun, Assistant Professor, School of Mathematics, IISER Thiruvananthapuram |
2 lectures of 1 and half hours each |
IVP for ODEs : One step methods: consis- tency and convergence; Runge-Kutta methods; Linear- Multistep methods: zero stability and consistency; Stiff equations and absolute stabil- ity |
| Sudarshan Kumar K, Assistant Professor, School of Mathematics, IISER Thiruvananthapuram |
2 lectures of 1 and half hours each |
Linear PDEs: Linear advection equation: fi- nite difference scheme, consistency and stability; Heat equation: finite difference schemes, theta methods, stability; Poisson equation: finite dif- ference scheme; Wave equation in 1D: L2 stabil- ity. |
Time Table:
| Time/Day | 19-09-2022 | 20-09-2022 | 21-09-2022 | 22-09-2022 | 23-09-2022 | 24-09-2022 |
| 09:00-10:30 | KRA | GDV | PCR | SKG | SKG | PCR |
| 10:30-11:00 | Tea | Tea | Tea | Tea | Tea | Tea |
| 11:00-12:30 | SKK | SKK | SKG | PCR | PCR | GDV |
| 12:30-14:00 | Lunch | Lunch | Lunch | Lunch | Lunch | Lunch |
| 14:00-15:30 | KRA | GDV | T(SKG+TAH) (one hour) |
SKG | GDV | T(PCR+RKR) |
| (one hour) | ||||||
| 15:30-16:00 | Tea | Tea | Tea | Tea | Tea | Tea |
| 16:00-17:00 | T(SKK+AVS) | T(GDV+AVS) | T(SKG+TAH) | T(PCR+RKR) |
• Full forms for the abbreviations of speakers and tutors:
• Speakers
– SKK: Sudarshan Kumar K (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)
– KRA: K.R. Arun (Assistant Professor, School of Mathaematics, IISER Thiruvananthapuram)
– GDV: G D Veerappa Gowda (Professor, TIFR-CAM, Bangalore)
– PCR: Praveen Chandrashekar (Associate Professor, TIFR-CAM, Bangalore)
– SKG: Sashi Kumar Ganesan (Associate Professor, Computational Data Science, IISc Bengaluru)
• Tutors
– RKR: Rakesh Kumar (Postdoc, School of Mathaematics, IISER Thiruvananthapuram)
– TAH: Thivin Anandh (SRF, Computational Data Science, IISc Bengaluru)
– AVS: Aswin V.S (Postdoc, School of Mathaematics, IISER Thiruvananthapuram)
• References
– E. Süli & David F. Mayers, An Introduction to Numerical Analysis, Cambridge University Press(2003).
– J.C. Strikwerda, Finite difference schemes and Partial differential equations, Wordsworth and Brooks(1989).
– E. Godlewski and P.A. Raviart, Hyperbolic Systems of Conservation Laws, Ellipses(1991).
– Sashikumaar Ganesan & Lutz Tobiska, Finite elements: Theory and Algorithms, Cambridge University Press(2017).
– P.G. Ciarlet, The finite element method for elliptic problems, North-Holland(1978)
Selected Applicants:
| Outsation Participants | ||||||
| Serial | SID | Full Name | Gender | Affiliation | University/ Institute M.Sc./ M.A. | Year of Passing M.Sc./ M.A |
| 1 | 41137 | Mr. Achyuta Ranjan Dutta Mohapatra | Male | IIT Guwahati | Utkal University | 2020 |
| 2 | 41555 | Ms. Shailee Sharma | Female | Dr. B. R. Ambedkar National Institute of technology Jalandhar | Dr. Bhimrao Ambedkar University, Agra | 2019 |
| 3 | 41579 | Ms. Anjaly Anand | Female | National Institute of Technology Calicut | M.Sc(Tech) in Mathematics and Scientific Computing | 2013 |
| 4 | 41679 | Mr. Rajesh Yadav | Male | Rajiv Gandhi Institute of Petroleum Technology | National Institute of Technology, Rourkela | 2019 |
| 5 | 41686 | Ms. Maria Robert | Female | National Institute of Technology, Calicut | Cochin University of Science and Technology | 2019 |
| 6 | 41730 | Mr. Md Hasanuzzaman | Male | National Institute of Technology Silchar | Jamia Millia Islamia | 2020 |
| 7 | 41755 | Mr. Raghunath Bandha | Male | Indian Institute of Technology Guwahati | Indian Institute of Technology Kharagpur | 2020 |
| 8 | 41768 | Mr. Rupam Shankar Nath | Male | Gauhati University | IIT GUWAHATI | 2018 |
| 9 | 41789 | Mr. Ajeet Singh | Male | IIT Roorkee | IIT ROORKEE | 2020 |
| 10 | 41820 | Mr. Jitendra Nath Naik | Male | IIT Goa | Utkal University | 2018 |
| 11 | 41828 | Ms. Dona Alex | Female | NIT Tiruchirappalli | Pondicherry University | 2019 |
| 12 | 41920 | Ms. Deepika Parmar | Female | Defence Institute of Advanced Technology | IIT Gandhinagar | 2018 |
| 13 | 41959 | Ms. Archana Yadav | Female | University of Delhi | NIT Calicut Kerala | 2021 |
| 14 | 42021 | Mr. Ayush Agrawal | Male | IIT Roorkee | IIT Gandhinagar | 2019 |
| 15 | 42032 | Ms Poojitha S | Female | National Institute of Technology Calicut | Govt. College Kasaragod | 2020 |
| 16 | 42125 | Mr. Aniruddha Kumar Sharma | Male | Indian Institute of Technology Roorkee | Chhatrapati Sahu Ji Maharaj University Kanpur, M.Sc. | 2019 |
| 17 | 42160 | Mr. Uzair Ahmed | Male | Jamia Millia Islamia | Indian Institute of Technology Kanpur | 2020 |
| 18 | 42223 | Mr. Ravi Mahla | Male | National Institute of Technology, Warangal | National Institute of Technology, Warangal | 2020 |
| 19 | 42351 | Ms. Jyoti . | Female | University of Delhi | University of Delhi | 2016 |
| 20 | 42433 | Mr. Arnab Pal | Male | INDIAN INSTITUTE OF SCIENCE BANGALORE | INDIAN INSTITUTE OF TECHNOLOGY GUWAHATI M.Sc. | 2020 |
| 21 | 42784 | Ms. Anita Devi | Female | SLIET Longowal,Sangrur,Punjab | Central university of himachal pradesh, dharamshala, kangra, himachal pradesh | 2016 |
| 22 | 42803 | Mr. Vishal Tiwari | Male | Indian Institute of Technology Ropar | Indian Institute of Technology, Guwahati | 2020 |
| 23 | 42805 | Mr. Sarabindu Dolui | Male | National Institute of Technology, Andhra Pradesh | B.H.U. | 2018 |
| 24 | 42733 | Mr Harish Mallesham Nagula | Male | Institute of Chemical Technology Indian Oil Campus Bhubaneshwar | M.Sc | 2018 |
| 25 | 42182 | Ms Deepalakshmi P | Female | SRM Institute of Science and Technology, | Shrimathi Indira Gandhi College of Arts and Science, Trichy, TamilNaadu. | 2021 |
| 26 | 42552 | Mr. Niranjan . | Male | SOUTH ASIAN UNIVERSITY NEW DELHI | SOUTH ASIAN UNIVERSITY, NEW DELHI | 2020 |
| 27 | 42577 | Ms Varshini Sandrasekaran | Female | PSG COLLEGE OF ARTS & SCIENCE | PSG COLLEGE OF ARTS & SCIENCE | 2018 |
| 28 | 41692 | Ms Aswathy Satheesh | Female | National Institute of Technology, Calicut | M G University | 2015 |
| 29 | 42747 | Ms. Tanya Rastogi | Female | Malaviya National Institute of Technology Jaipur | Motilal Nehru National Institute of Technology Allahabad, Prayagraj | 2020 |
| 30 | 42145 | Ms. Jaismitha B | Female | SRM Institute of Science and Technology | SRM Institute of Science and Technology Kattankulathur | 2021 |
| 31 | 42146 | Ms Vaidehi P | Female | SRM Institute of Science and Technology, | SRM Institute of Science and Technology - Kattankulathur | 2021 |
| 32 | 41134 | Mrs. Lavanya V Salian | Female | Indian Institute of Petroleum and Energy (IIPE) | Mangalore University | 2015 |
| 33 | 42576 | Mrs Nasira Banu.A | Female | PSG COLLEGE OF ARTS AND SCIENCE | PSG college of arts and Science,Coimbatore | 2004 |
| 34 | 42844 | Ms.Ambalika Halder | Female | NIT Andhra | Jadavpur university | 2019 |
| 35 | 42828 | Mr Vivek R | Male | Sri Ramakrishna Mission Vidyalaya College of Arts and Science | Sri Ramakrishna Mission Vidyalaya College of Arts and Science | 2020 |
| local Participants | ||||||
| 1 | 41593 | Ms Soundarya S | Female | IISER | IISER Trivandrum | |
| 2 | 42393 | Ms Tooba Shaikh | Female | Indian Institute of Science Education and Research | Indian Institute of Science education and Research | 2022 |
| 3 | 42015 | Mr. Sangram Satpathi | Male | IISER TVM | IISER TVM | |
| 4 | 42140 | Ms Manika Bag | Female | IISER-TVM | IISER-TVM | 2022 |
| 5 | 41048 | Dr Manimaran J | Male | IISER Thiruvandapuram | Bharathiar University | 2012 |
| 6 | 41995 | Mr. Nishant Ranwan | Male | IISER TVM | Indian Institute Of Technology, Patna | 2021 |
| 7 | 42438 | Mr. Nikhil Manoj | Male | IISER Thiruvananthapuram | Cochin University of Science and Technology | 2020 |
| 8 | 42129 | Mr. Subham Nayak | Male | IISER-Thiruvananthapuram | Pondicherry University | 2019 |
| 9 | 42512 | Mr. Ritabrata Jana | Male | IISER Thiruvananthapuram | Banaras Hindu University | 2019 |
How to Reach:
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