**COURSE INTRODUCTION**

Accurately predicting the behaviour of electromagnetic
systems is a key element in developing novel applications. Computational
electromagnetics is an interesting domain bridging theory and experiment. This
course is for people who are interested in deepening their knowledge about
modelling electromagnetic systems and who wanted to build a strong foundation
in the underlying physics. In this course, in addition to important modelling techniques widely
used for electromagnetic applications, we will also introduce algebraic
topology based modelling method which is not widely known to engineering
community.

The course is targeted at students and researchers from science, engineering and applied mathematics background who wanted to understand the dynamics of electromagnetic systems. People working in R&D in industries will also benefit from this course. We also use simulations to explain some of the underlying physics and mathematics.

INTENDED AUDIENCE

Elective courses for Electrical Engineering, Applied Mathematics, Engineering Physics, Graduate, Postgraduate, and Research Students (B.E, M.E, M.S, B.Sc., M.Sc., Ph.D.)

**PREREQUISITES**

Vector Calculus, Partial Differential Equations, Linear Algebra, Basic Electromagnetics

**INDUSTRIES & RESEARCH INSTITUTIONS WHICH WILL BENEFIT FROM THIS COURSE**

Defence Labs - DRDO, NPL, Atomic Research Institutions - BARC, IGCAR, Applied Electromagnetics Research Labs - SAMEER, IITs, IISC. Electrical and Electronics Industries, Public and Private Universities.

The course is targeted at students and researchers from science, engineering and applied mathematics background who wanted to understand the dynamics of electromagnetic systems. People working in R&D in industries will also benefit from this course. We also use simulations to explain some of the underlying physics and mathematics.

INTENDED AUDIENCE

Elective courses for Electrical Engineering, Applied Mathematics, Engineering Physics, Graduate, Postgraduate, and Research Students (B.E, M.E, M.S, B.Sc., M.Sc., Ph.D.)

Vector Calculus, Partial Differential Equations, Linear Algebra, Basic Electromagnetics

Prof. Dr. Krish Sankaran is the Founder-CEO of Prajñālaya, a Swiss-based R&D venture working in the domain terahertz, high energy density storage and water desalination technologies. He is visiting Indian Institute of Technology - IIT Bombay as an Associate Professor in the department of electrical engineering and he is also a guest Professor at the Swiss Federal Institute of Technology, ETH Zurich, Switzerland. He splits in time between India and Switzerland. He has worked in all three sectors - government, civil and private - including the European Commission, World Economic Forum, ABB, Alstom. Past industrial engagements include senior management roles in business development and operations (50-60 Million EUR revenue) with profit and loss responsibilities in 8 countries and 3 continents. During 2011-2014, he was the Head of the Business Sector and Knowledge Partnerships at the World Economic Forum (WEF) and he was also selected as a Global Leadership Fellow. At the WEF, he advised governments on various public policy and governance challenges in energy and infrastructure sectors. He has developed unique insights into policy development processes. He has deviced policy simulation frameworks which are very helpful to plan scenarios for leaders in governments, businesses and civil societies. In Fall 2012, he was invited as an adjunct professor in Columbia University, New York city. He received doctorate degree in engineering science from the Swiss Federal Institute of Technology ETH Zurich, Switzerland, an executive master degree in organizational leadership jointly from the Wharton School, Columbia University, INSEAD, and London Business School in collaboration with the World Economic Forum. He has several years of training in Vedanta philosophy. Further information: www.linkedin.com/in/drksankaran

TEACHING ASSISTANT 1

Department: Metallurgical Engineering and Materials Science

Qualification: M.Tech

Contact no: +91 7738706971

Email: iitd.bharat@gmail.com

Name: Mayur Darak

Department: Centre for Research in Nanotechnology & Science (CRNTS)

Qualification: M. S

Contact: +91 8087285905

Email: darak.mayur@gmail.com

**COURSE
CONTENT
**

Lecture 1: Motivation & Background

Lecture 2: Finite Differencing – 1

Lecture 3: Finite Differencing – 2

Exercise 1: Laplace Equation

Exercise 2: Poisson Equation

Exercise 3: Heat Diffusion Equation

Lab Tour - 1

Summary

Week 2: FDM - II

Lecture 5: Stability, Example

Exercise 4: Helmholtz Equation

Exercise 5: Capacitance of a pair of coaxial rectangles

Exercise 6: Square-wave test to solve advection equation

Summary

Lecture 7: Maxwell FDTD System

Lecture 8: Maxwell FDFD System

Exercise 7: Plotting E & H fields for various profiles of constitutive parameters of two different media

Exercise 8: Single and double slit diffraction

Summary

Lecture 10: Absorbing Boundary Conditions (ABCs)

Exercise 9: Scattering of electromagnetic waves

Lab Tour - 2

Summary

Week 5: Variational Method (VM)

Lecture 12: Rayleigh-Ritz Method

Lecture 13: Method of Weighted Residuals

Lecture 14: Galerkin Method, Functional from PDE

Exercise 10: Poisson Equation using Rayleigh-Ritz method

Exercise 11: Potential profile of a capacitor

Summary

**Week 6: Finite Element Method (FEM) - I
**Lecture 15: Background, FEM from Weighted Residuals

Lecture 16: Formulation (Basis Function, Mapping)

Lecture 17: Poisson Equation, Time Domain FEM (FETD)

Exercise 12: Capacitance between concentric conductors and plotting voltage profile-part 1

Exercise 13: Capacitance between concentric conductors and plotting voltage profile-part 2

Exercise 14: Capacitance between concentric conductors and plotting voltage profile-part 3

Summary

Exercise 15:

Exercise 16

Exercise 17

Summary

Lecture 20: Pocklington Integral

Lecture 21: Hallen Integral Convergence Comparison

Lecture 22: Antenna Example

Exercise 18

Exercise 19

Lab Tour - 3

Summary

Lecture 24: Background Derivation of Eigenvalue Equation

Lecture 25: Discretization Maxwell Equation

Lecture 26: Flux Calculation: Gudnov, MUSCL, Central Flux, Truly Upwind Scheme

Lecture 27: Truly Upwind Scheme, Geometrical Reconstruction

Exercise 20

Summary

Lecture 29: Applications - I

Lecture 30: Applications - II

Lecture 31: Challenges

Exercise 21

Lab Tour - 4

Summary

Lecture 33: Cochains

Lecture 34: Boundary Operator

Summary

Lecture 35: Coboundary Operator

Lecture 36: Space Orientation

Lecture 37: Time Orientation

Exercise 22

Lecture 38: Introduction to Mimetic Method

Lecture 39: Formulation

Lecture 40: Comparison to Other Methods (ATM, FDM)

Summary

Grand Summary

- Bondeson, A., Rylander, T., Ingelström, P.,
*Computational Electromagnetics*, Springer, 2005. - Sadiku, M. N. O,
*Numerical Techniques in Electromagnetics*, CRC Press, 1992. (be careful with this edition: has a lot of typos) - Sankaran,
K.
*Accurate Domain Truncation Techniques for Time-Domain Conformal Methods*, ETH Zurich, 2007. Weblink: https://www.researchgate.net/publication/282120723_Accurate_domain_truncation_techniques_for_time-domain_conformal_methods

**IF YOU WANT TO REVISE ELECTROMAGNETICS BASICS**

- Richard Feynman, Feynman Lectures in Physics,Volume 2, Addison–Wesley, 1964. Weblink: http://www.feynmanlectures.caltech.edu/II_toc.html
- Arnold Sommerfeld, Electrodynamics (Lectures on Theoretical Physics), Volume 3, Academic Press, 1964.
- Sergei A. Schelkunoff, Electromagnetic Fields, Blaisdell Publishing Company, 1963.