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Computational Electromagnetics :

The 2D Vector Finite Element Method

Uday Khankhoje

Electrical Engineering, IIT Madras

1

Topics in this module

1 Shape functions

2 Equation Setup, Converting to weak form, Boundary conditions

3 Choosing Variables

4 Putting it together

1

Table of Contents

1 Shape functions

2 Equation Setup, Converting to weak form, Boundary conditions

3 Choosing Variables

4 Putting it together

2

2D scalar Shape functions

3

2D vector Shape functions

3

Table of Contents

1 Shape functions

2 Equation Setup, Converting to weak form, Boundary conditions

3 Choosing Variables

4 Putting it together

4

Vector Wave Equation → Weak Form

5

Radiation Boundary Condition

5

Table of Contents

1 Shape functions

2 Equation Setup, Converting to weak form, Boundary conditions

3 Choosing Variables

4 Putting it together

6

Total field formulation

7

Scattered field formulation

8

Comparing Total & Scattered field formulation

8

Table of Contents

1 Shape functions

2 Equation Setup, Converting to weak form, Boundary conditions

3 Choosing Variables

4 Putting it together

9

Assembling the system of equations

10

Computing the far-field

11

Numerical aspects in computing matrix elements

12

Summary of FEM procedure

12

Topics that were covered in this module

1 Shape functions

2 Equation Setup, Converting to weak form, Boundary conditions

3 Choosing Variables

4 Putting it together

References: Ch 4 of FEM for Electromagnetics; Volakis, Chatterjee, Kempel; IEEE

Press

Instructor notes on 2D edge based FEM:

http://www.ee.iitm.ac.in/uday/notes/fem2dprimer.pdf