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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.

 

Week

Topics

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

2.

 FDM - II

Lecture 4: Accuracy, Dispersion
Lecture 5: Stability, Example

Exercise 4
Exercise 5
Exercise 6

Summary

3.

FDM - III

Lecture 6: Maxwell PDE System
Lecture 7: Maxwell FDTD System
Lecture 8: Maxwell FDFD System

Exercise 7
Exercise 8
Summary

4.

Boundary Conditions (BCs)

Lecture 9: Introduction
Lecture 10: Absorbing Boundary Conditions (ABCs)

Exercise 9
Lab Tour - 2
Summary

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
Exercise 11
Summary

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
Exercise 13
Exercise 14
Summary

7.

FEM - II

Lecture 18: FETD, Examples

Exercise 15
Exercise 16
Exercise 17
Lab Tour - 3
Summary

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
Summary

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

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

11.

Algebraic Topological Method (ATM) - I

Lecture 32: Introduction, Motivation, Theoretical Background
Lecture 33: Cochains
Lecture 34: Boundary Operator

Summary

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

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




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