Partial Differential Equations : From Theory to Computation (2019)

 

  Convener(s)
Name: Dr. Rajendra K Ray Dr. Prasanth P. Jose
Mailing Address: Associate Professor
School of Basic Sciences
Indian Institute of Technology Mandi		 Assistant Professor
School of Basic Sciences
Indian Institute of Technology Mandi
Email: rajendra at iitmandi.ac.in prasanth at iitmandi.ac.in

The applicants are expected to make their own travel arrangements.

Dates: 

Monday, June 3, 2019 - 09:30 to Saturday, June 15, 2019 - 18:30

Venue: 

Venue Address: 

Indian Institute of Technology (IIT) Mandi,
Prashar Road, Tehsil Sadar, Near Kataula, Kamand
Himachal Pradesh 175005

Venue State: 

Venue City: 

PIN: 

175005

Chrono Order: 

321

Syllabus: 

Many physical phenomena and engineering problems are governed by Partial Differential Equations(PDEs). It is therefore important to understand the mathematical aspects of PDEs and their solution process. The theory of PDEs mainly deals with the existence and uniqueness of the solution and itsstability and regularity. The solution process includes methodologies to find solutions, either in closed form or by an approximation. Proposed instructional school aims to provide the participants a taste of classical theory of second order PDEs and to introduce them the advanced PDEs through variational approach. Furthermore, the school aims to demonstrate numerical techniques to solve the PDEs, in particular, finite difference methods and finite element methods. The topics in the school are designed in such way that the participants get exposure to topics in both classical and modern approaches in the theory and computation of PDEs, which are also part of the curriculum in the universities and post graduate colleges.

Syllabus:


Name of the Speaker with affiliation

 No. of Lectures

Detailed Syllabus

 

K. Sreenadh, IIT Delhi

6

Classical PDEs: Laplace equation: Harmonic functions, maximum principle, fundamental solution, Green’s function and the solvability of Dirichlet problem.

Heat equation: Weak and strong maximum principles for the heat equation, fundamental solution, existence and uniqueness for the initial value problem.

T. Muthukumar,

IIT Kanpur

 

6

Variational Approach for PDEs: Quick review of distributions, mainly the concept of weak derivative, Fourier transform and convolution.

Sobolev spaces, mainly H^1 space and important inequalities, imbedding and Trace theorems.

Variational approach to elliptic PDEs, existence, uniqueness, regularity results and eigenvalue problem.

 

Rajendra K. Ray, IIT Mandi

6

 

Finite Difference Methods: Analysis (consistency, convergence, stability and error estimate) of finite difference schemes for

 Heat equation (1D and 2D)

 Wave equation (1D and 2D)

Laplace equation(1D and 2D)

Some nonlinear equations like semi-linear heat, Burgers will also be discussed

Highlighting new phenomenon discovered through numerics.

 

Saumya Bajpai, IIT Goa

6

Finite Element Methods: Introduction to finite element methods, construction of finite element spaces, Interpolation theory, applications to elliptic and parabolic PDEs. Error analysis. implementation aspects.

 

References:
1. L.C. Evans, Partial Differential Equations, AMS.
2. J.C. Strikwerda, Finite difference schemes and PDEs, SIAM
3. J.N. Reddy, An introduction to Finite Element Method, McGraw Hill.
4. S. Larsson and V. Thomee. Partial differential equations with numerical methods, Springer.

 

 

 

 

Time Table: 

Day

Date

Lecture 1

(9.30
to
11.00)

Tea

(11.05 to
11.25)

Lecture 2

(11.30
to
1.00)

Lunch

(1.05
to
2.25)

Tutorial

(2.30
to
3.30)

Tea

(3.35 to
3.55)

Tutorial

(4.00
to
5.00)

Snacks

(5.05
to
5.30)

 

 

(name of the speaker)

 

(name of the speaker)

 

(name of the speaker + tutors)

 

(name of the speaker + tutors)

 

Mon

03/06/2019

KS

 

KS

 

KS, RR, AK

 

TM, RR, SJ

 

Tues

04/06/2019

KS

 

KS

 

KS, RR, AK

 

TM, RR, SJ

 

Wed

05/06/2019

KS

 

TM

 

KS, RR, AK

 

TM, RR, SJ

 

Thu

06/06/2019

KS

 

TM

 

KS, RR, AK

 

TM, RR, SJ

 

Fri

07/06/2019

TM

 

TM

 

TM, RR, SJ

 

TM, RR, AK

 

Sat

08/06/2019

TM

 

TM

 

TM, RR, SJ

 

TM, RR, AK

 

SUNDAY : OFF

Mon

10/06/2019

RR

 

RR

 

RR, AK, SJ

 

RR, AK, SJ

 

Tues

11/06/2019

RR

 

RR

 

RR, AK, SJ

 

RR, AK, SJ

 

Wed

12/06/2019

SB

 

RR

 

SB, TM, AK

 

SB, TM, AK

 

Thu

13/06/2019

SB

 

RR

 

SB, RR, SJ

 

SB, RR, SJ

 

Fri

14/06/2019

SB

 

SB

 

SB, RR, AK

 

SB, RR, AK

 

Sat

15/06/2019

SB

 

SB

 

SB, RR, SJ

 

SB, RR, SJ

  

KS: K. Sreenadh
TM: T. Muthukumar
RR: Rajendra K. Ray
SB: Saumya Bajpai
SB: Subit K Jain
AK: Atendra Kumar

 

 

 

 

 

 

 

Selected Applicants: 

 

Sr. SID Full Name Gender Affiliation Position in College/ University University/Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 24493 Ms Sarojini Sowmiya Manohar Female Bharathidasan University PhD Central University of Tamil Nadu 2016  
2 24581 Mr Akmal Raza Male Jamia Millia Islamia PhD (student) Jamia Millia Islamia 2014  
3 24660 Mr Kumar Rajeev Ranjan Male NIT Patna Ph.D IIT Roorkee 2012  
4 24682 Ms. Aakansha Chauhan Female IIT(BHU) Varanasi PhD Banasthali University, Rajasthan 2015  
5 24699 Mr. Sachin Kumar Male Ujjain Engg. College Ujjain Assistant Professor NIT trichy 2016  
6 24848 Mr. Yuvaraj P Male Bharthiyar University Asst.Professor Bharthiyar University 2011  
7 24862 Mr. Sachin Kumar Male Guru Ghasidas University Assistant Professor Pondicherry University 2018  
8 24881 Mr. Prodip Roy Male Mahadevananda Mahavidyalaya Assistant Professor University of Kalyani 2000  
9 24901 Mr. Akshay Kumar Male University of Hyderabad Ph.D Banaras Hindu University 2017  
10 24996 Dr. Krishna Pada Das Male Mahadevananda Mahavidyalaya Assistant Professor University of Calcutta 2006 21/9/2011
11 25185 Dr. Madhuri Jain Female banasthali vidyapith assistant professor AGra University 2005 30/12/2010
12 25200 Dr. Jitender Singh Male Guru Nanak Dev University Amritsar Assisatnt Professor Panjab University Chandigarh 2002 7/4/2008
13 25312 Dr. Deepti Kaur Female Maitreyi College, University of Delhi Assistant Professor M.Sc. Mathematics 2009 15/5/2018
14 25322 Mr. Saurabh Kumar Male The LNM Institute of Information Techonolgy Research Scholor C.C.S University Meerut 2016  
15 25613 Mrs Sherin Jose T Female St.Joseph's College Irinjalakuda, Thrissur, Kerala Assistant Professor St. Joseph's College Irinjalakuda 2004  
16 26004 Mr. Sandeep Kumar Kumar Male IIT BHU Research scholar ph.d University of Allahabad 2015  
17 26344 Mr. Bhimanand Pandurang Gajbhare Male Vaidyanath College parli Vaijnath Dist. Beed. Assistant Professor Swami Ramanand Teerth Marathwada University Nanded 2005  
18 26399 Mr. Guru Prasad N S Male National Institute Of Engineering, Mysuru Assistant Professor Mysore University/ M.Sc. 2015  
19 26748 Ms. Pratima Tiwari Female IIT BHU Research scholar NIT Jamshedpur 2017  
20 26806 Ms. Swati Yadav Female IIT (BHU), Varanasi PhD university of Luchnow 2015  
21 26889 Mr. S.Shankar Narayan Male CMR Institute of Technology Asst.Professor Bangalore University 2016  
22 26959 Ms Nandhini Rajendran Female PSG College of Arts & Science Assistant Professor PSG College of Arts & Science, M.Sc 2016  
23 26979 Ms Anu Rani Female Bennett university PhD SLIET, Longowal(M.Sc.) 2017  
24 27068 Mr. Mahesh Udupa Male Dayananda Sagar University Junior Research Fellow St. Joseph's College 2018  
25 27082 Mr. Tamil Selvan T Male PSG College of Arts & Science Assistant Professor PSG College of Arts & Science 2016  
26 27163 Mr. Soura Sana Male IIT Bhubaneswar phD The University of Burdwan 2015  
27 27169 Dr. Apu Kumar Saha Male National Institute Of Technology Agartala Associate Professor Tripura University 1998 9/4/2012
28 27199 Dr. Subburayan Veerasamy Male SRM Institute of Science and Technology, Assistant Professor M.Sc. 2009 25/11/2013
29 27205 Mr. Runu Dhar Male Maharaja Bir Bikram University Associate Professor Tripura University 1998 9/10/2012
30 27336 Dr. Rajendra Kumar Bairwa Male Department of Mathematics, University of Rajasthan , Jaipur Assistant Professor University of Rajasthan, Jaipur 2007 10/11/2016
31 27350 Ms S Yaazhini Female Anna University PhD scholar Central University Of Tamilnadu 2016  
32 27360 Mr. Biswajit Pandit Male IIT Patna PhD Scholar IIT Guwahati 2016  
33 27468 Dr Gunvant Achutrao Birajdar Male Tata Institute Of Social Sciences Assistant Professor Dr B A M University Aurangabad 2008 18/1/2014
34 27541 Ms Pavithra Kumar Female Anna University, CEG Campus PH.D RIASM University Of Madras 2014  
35 27570 Ms Soumyarani Mishra Female S'O'A University PhD STUDENT CET, BBSR 2017  
36 27613 Mrs Sonali Mandar Narsale Female Modern education society's college of engineering,pune01 Assistant Professor Pune 2006  
37 27647 Mr. Aniruddha Palit Male Surya Sen Mahavidyalaya Assistant Professor University Of North Bengal 2004 14/11/2017
38 27686 Mr. Divay Divay Male IIT Delhi PhD Student IIT Madras 2017  
39 27691 Ms. Manisha Chowdhury Female Indian Institute of Technology Kanpur, Kanpur PhD IIT Kanpur 2014  
40 27751 Ms. Sangita Dey Female IIT Kanpur PHD IIT Madras 2013  
41 27755 Dr. Tarul Garg Female The Northcap University Assistant Professor IIT Roorkee 2013 6/9/2018
42 27757 Ms Megha P Female National Institute of Technology Karnataka PhD Mahatma Gandhi College Iritty, Kannur. 2016  
43 27830 Dr Halle Dattu Male Rajiv Gandhi University of Knowledge Technologies Asst prof Pondicherry University 2009 12/12/2016
44 27850 Ms. Tanvi Wadhawan Female IIT Delhi PhD. IIT Roorkee 2018 27/12/2018
45 27864 Prof. Vijay Jayantibhai Solanki Male Government Engineering college,Bharuch Asst. Prof. The M.S.University of Baroda,Vadodara. 2009  
46 27987 Dr Deepak Grover Male Lovely Professional University Phagwara Assistant professor Guru Jambheshwar University Hisar 2006 28/3/2014

 

 

How to Reach: 

Click here

School Short Name: 

pdeftc

Last Date Application: 

Thursday, February 7, 2019

School Type: 

IST