EE813 - Finite Elements for Electromagnetics

Fall 2003

MWF 1:30-2:20pm

Place: CL 139

Instructor: Fernando L. Teixeira (teixeira.5@osu.edu)

Office hours: After class

Basic Outline:

1. Introduction

1.1 Maxwell’s equations and boundary conditions

1.2 Classification of PDEs.

2. Finite differences (FD) for PDEs

2.1 Discretization of partial derivatives.

2.2 Matrix solution methods

3. Finite-difference time-domain (FDTD) method

3.1 1-D case

3.2 Truncation error and dispersion analysis

3.3 Stability analysis

3.4 Lossy materials

3.5 Dispersive materials

3.6 3-D FDTD

3.7 Absorbing boundary conditions

3.8 FDTD in curvilinear coordinate systems and irregular grids

4. Finite element method

4.1 1-D case

4.2 2-D case

4.3 Solution methods for sparse linear systems

4.4 Spurious modes and 3-D vector finite elements

4.5 Paraxial approximation and propagation algorithms

4.5 Time-domain finite-element (TDFE)

4.6 Grid generation

5. Topics in discrete electromagnetic theory

5.1 Motivation: Irregular grids and compatible discretizations

5.1 Electromagnetic fields as differential forms

5.2 Vector finite elements and Whitney forms

5.3 de Rham diagram

5.4 Hodge star operators

Main references:

1. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2^nd Edition, Artech House.
2. J. Jin, The Finite Element Method in Electromagnetics, 2^nd Edition, Wiley.

Course grading: Based on homework sets and projects.

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