Numerical Methods for Partial Differential Equations (2022)

Venue: IISER,  Thiruvananthapuram, Kerala
Date:  19th, Sep 2022 to 24th, Sep 2022

 

School 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.

 

List of the actual speakers:

Name of the speaker

Position

Affiliation and address
Sudarshan Kumar K Assistant Professor IISER Thiruvananthapuram
 K.R. Arun Assistant Professor IISER Thiruvananthapuram
G D Veerappa Gowda Professor TIFR-CAM, Bangalore
 Praveen Chandrashekar Associate Professor TIFR-CAM, Bangalore
Sashi Kumar Ganesan Associate Professor IISc Bengaluru

List of the actual tutors:

Name of the tutor

Position

Affiliation and address
Rakesh Kumar Postdoc IISER Thiruvananthapuram
Thivin Anandh SRF  IISc Bengaluru
 Aswin V.S Postdoc  IISER Thiruvananthapuram

 

 Syllabus:  

Actual syllabus covered by each speaker:

Name of the Speaker

:

Detailed Syllabus
Prof. Veerappa Gowda (GDVG),
Raja Ramanna Fellow, TIFR-CAM, Bengaluru		   Non-linear hyperbolic conservation laws: Concept 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 nu-
merical solution. Finite volume schemes. Monotone schemes: L∞ stability, total varia-
tion diminishing property and their convergence to the entropy solution. Higher order
schemes.
Dr. Praveen Chandrashekar,
Associate Professor, TIFR-CAM, Bengaluru		   Discontinuous Galerkin method for hyperbolic PDE: The lectures will provide an in-
troduction to DG methods starting with 1-D problems. The topics covered include:
numerical flux, semidiscrete stability, basis functions, implementation details, limiters
and TVD property, and, Fourier stability analysis. Then we will discuss DG for hyper-
bolic systems, multi-dimensional scheme, modal and nodal versions, special versions like flux reconstruction, etc. The lectures will be complemented with examples of computer codes implementing these methods.
Dr. Sashi Kumar Ganesan, Associate Professor, Computational Data Science,
IISc Bengaluru		    Introduction to Computational Science, Banach and Hilbert spaces, Weak derivatives,
Sobolev spaces, A general elliptic problem of second order and its weak solution, Stan-
dard Galerkin method, Abstract error estimate. Implementation of the finite element
method: Mesh handling and data structure, Numerical integration, Sparse matrix stor-
age, Assembling of system matrices and load vectors, Inclusion of boundary conditions.
Introduction to Machine Learning, Deep Learning. Introduction to Physics Informed
Neural Networks (PINNs).
 Dr. K.R.Arun, Assistant Professor, School of Mathematics, IISER Thiruvanan-
thapuram		    IVP for ODEs: One step methods: consistency and convergence; Runge-Kutta methods;
Linear-Multistep methods: zero stability and consistency; Stiff equations and absolute
stability.
Dr. Sudarshan Kumar K, Assistant Professor, School of Mathematics, IISER
Thiruvananthapuram		   Linear PDEs: Linear advection equation: finite difference scheme, consistency and stabil-
ity; Heat equation: finite difference schemes, theta methods, stability; Poisson equation:
finite difference scheme; Wave equation in 1D: L2 stability.

 

 

 

 Time Table

Actual time-table that was followed during the programme:

 

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) SKG GDV T(PCR+RKR)
      (one hour)     (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:

SKK: Sudarshan Kumar K

KRA: K.R. Arun

GDV: G D Veerappa Gowda

PCR: Praveen Chandrashekar

SKG: Sashi Kumar Ganesan

RKR: Rakesh Kumar

TAH: Thivin Anandh

AVS: Aswin V.S

 

List of actual Participants

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 sss Male IIT Guwahati Utkal University 2020
2 41555 Ms. Shailee Sharma s Female Dr. B. R. Ambedkar National Institute of technology Jalandhar Dr. Bhimrao Ambedkar University, Agra 2019
3 41579 Ms. Anjaly Anand s Female National Institute of Technology Calicut M.Sc(Tech) in Mathematics and Scientific Computing 2013
4 41679 Mr. Rajesh Yadav s Male Rajiv Gandhi Institute of Petroleum Technology National Institute of Technology, Rourkela 2019
5 41686 Ms. Maria Robert s Female National Institute of Technology, Calicut Cochin University of Science and Technology 2019
6 41730 Mr. Md Hasanuzzaman s Male National Institute of Technology Silchar Jamia Millia Islamia 2020
7 41755 Mr. Raghunath Bandha s Male Indian Institute of Technology Guwahati Indian Institute of Technology Kharagpur 2020
8 41768 Mr. Rupam Shankar Nath s Male Gauhati University IIT GUWAHATI 2018
9 41789 Mr. Ajeet Singh s Male IIT Roorkee IIT ROORKEE 2020
10 41820 Mr. Jitendra Nath Naik s Male IIT Goa Utkal University 2018
11 41828 Ms. Dona Alex s Female NIT Tiruchirappalli Pondicherry University 2019
12 41920 Ms. Deepika Parmar s Female Defence Institute of Advanced Technology IIT Gandhinagar 2018
13 41959 Ms. Archana Yadav s Female University of Delhi NIT Calicut Kerala 2021
14 42021 Mr. Ayush Agrawal s Male IIT Roorkee IIT Gandhinagar 2019
15 42032 Ms Poojitha S s Female National Institute of Technology Calicut Govt. College Kasaragod 2020
16 42125 Mr. Aniruddha Kumar Sharma s Male Indian Institute of Technology Roorkee Chhatrapati Sahu Ji Maharaj University Kanpur, M.Sc. 2019
17 42160 Mr. Uzair Ahmed s Male Jamia Millia Islamia Indian Institute of Technology Kanpur 2020
18 42223 Mr. Ravi Mahla s Male National Institute of Technology, Warangal National Institute of Technology, Warangal 2020
19 42351 Ms. Jyoti . s Female University of Delhi University of Delhi 2016
20 42433 Mr. Arnab Pal s 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 s Male Indian Institute of Technology Ropar Indian Institute of Technology, Guwahati 2020
23 42805 Mr. Sarabindu Dolui s Male National Institute of Technology, Andhra Pradesh B.H.U. 2018
24 42733 Mr Harish Mallesham Nagula s Male Institute of Chemical Technology Indian Oil Campus Bhubaneshwar M.Sc 2018
25 42182 Ms Deepalakshmi P s Female SRM Institute of Science and Technology, Shrimathi Indira Gandhi College of Arts and Science, Trichy, TamilNaadu. 2021
26 42552 Mr. Niranjan . s Male SOUTH ASIAN UNIVERSITY NEW DELHI SOUTH ASIAN UNIVERSITY, NEW DELHI 2020
27 42577 Ms Varshini Sandrasekaran s Female PSG COLLEGE OF ARTS & SCIENCE PSG COLLEGE OF ARTS & SCIENCE 2018
28 41692 Ms Aswathy Satheesh s Female National Institute of Technology, Calicut M G University 2015
29 42747 Ms. Tanya Rastogi s 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 s Female IISER IISER Trivandrum  
2 42393 Ms Tooba Shaikh s Female Indian Institute of Science Education and Research Indian Institute of Science education and Research 2022
3 42015 Mr. Sangram Satpathi s Male IISER TVM IISER TVM  
4 42140 Ms Manika Bag s Female IISER-TVM IISER-TVM 2022
5 41048 Dr Manimaran J s Male IISER Thiruvandapuram Bharathiar University 2012
6 41995 Mr. Nishant Ranwan s Male IISER TVM Indian Institute Of Technology, Patna 2021
7 42438 Mr. Nikhil Manoj s Male IISER Thiruvananthapuram Cochin University of Science and Technology 2020
8 42129 Mr. Subham Nayak s Male IISER-Thiruvananthapuram Pondicherry University 2019
9 42512 Mr. Ritabrata Jana s Male IISER Thiruvananthapuram Banaras Hindu University 2019

 

 

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