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Courses » Computational Electromagnetics & Applications

Computational Electromagnetics & Applications

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.  

1601 students have enrolled already!!

ABOUT THE INSTRUCTOR



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

Name: Bharat Bhushan Bhatt
Department: Metallurgical  Engineering and Materials Science
Qualification: M.Tech
Contact no: +91 7738706971
Email: iitd.bharat@gmail.com

TEACHING ASSISTANT 2
Name: Mayur Darak
Department: Centre for Research in Nanotechnology & Science (CRNTS) 
Qualification: M. S
Contact: +91 8087285905
Email: darak.mayur@gmail.com
    

COURSE CONTENT

Week 1: Finite Difference Method (FDM) - I
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 4: Accuracy, Dispersion
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


Week 3: FDM - III
Lecture 6: Maxwell PDE System
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

Week 4: Boundary Conditions (BCs)
Lecture 9:  Introduction
Lecture 10:  Absorbing Boundary Conditions (ABCs)

Exercise 9: Scattering of electromagnetic waves
Lab Tour - 2
Summary


Week 5: Variational Method (VM)
Lecture 11:  Background, Calculus of Variations
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

Week 7: FEM - II
Lecture 18:  FETD, Examples 

Exercise 15:
Exercise 16
Exercise 17
Summary


Week 8: Method of Moments (MoM)
Lecture 19: Galerkin Method Integral Equation, Integral Equation to Matrix Form
Lecture 20: Pocklington Integral
Lecture 21: Hallen Integral Convergence Comparison
Lecture 22: Antenna Example 

Exercise 18
Exercise 19
Lab Tour - 3
Summary

Week 9: Finite Volume Method (FVM) - I
Lecture 23: Motivation and Background
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

Week 10: FVM - II 
Lecture 28: Domain Truncation Techniques
Lecture 29: Applications - I
Lecture 30: Applications - II
Lecture 31: Challenges

Exercise 21
Lab Tour - 4
Summary


Week 11: Algebraic Topological Method (ATM) - I
Lecture 32: Introduction, Motivation, Theoretical Background
Lecture 33: Cochains
Lecture 34: Boundary Operator 

Summary

Week 12: ATM - II & Mimetic Method 
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

SUGGESTED BOOKS FOR COMPUTATIONAL ELECTROMAGNETICS

IF YOU WANT TO REVISE ELECTROMAGNETICS BASICS

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