The BRADLEY DEPARTMENT of ELECTRICAL and COMPUTER ENGINEERING

# ECE 6124 Advanced Numerical Electromagnetics | ECE | Virginia Tech

### Course Information

#### Description

A thorough coverage of numerical methods for electromagnetics, including topics on the foundations of function theory, Green's functions, mode-matching, and numerical expansion techniques in both the time and frequency domains. Emphasis will be placed on the method of moments and the finite element method, with development of the theoretical foundations of these methods.

#### Why take this course?

Current state-of-the-art work in electromagnetics requires extensive computation of the fields in an electromagnetic system. This computation is generally done in an approximate manner using either analytical approximations or numerical processes. In practice, a combination of the two is required. This course offers the foundation and theoretical basis for many of the current numerical techniques in use. The emphasis is on the foundations of the techniques, rather than simply how to run a computer program. These foundations are necessary for the future development of computer tools in the electromagnetics area. The primary emphasis will be specifically on the moment method and the finite-element method of computation which are at the forefront of current computational techniques.

### Learning Objectives

• Develop appropriate computer solutions for electromagnetics problems from fundamental principles of numerical methods for EM
• Recognize the limitations on such solutions and method
• Compare the attributes of various numerical techniques.

### Course Topics

#### Percentage of Course

Basic equations review 2%
Linear operator concepts 3%
Green’s functions and integral equations 5%
Waveguide iris problem 5%
Mode matching
Green’s function approach
Method of moments 5%
Wire antennas 15%
Equivalent sources
Singular integrals
Source modeling
Transient Wire Analysis 8%
Time domain solution
Stability and poles
(singularity expansion method-SEM) (singularity expansion method-SEM)
Surfaces and volumes - basic concepts 10%
Coated bodies/surface impedance 3%
Finite Differences (FD) 2-d LaPlace 10%
Generalized FD and Finite Difference-Time Domain,FD-TD, in 2-d 3%
Sparse Matrix methods and gridding concepts 5%
Finite Element Method (FEM) 20%
Application to LaPlace’s equation
Principles for dynamics, particularly guided waves
Review of other methods: Unimoment, extended boundary condition, parabolic wave equation, etc. 3%
Basic Sommerfeld theory for wires (if time permits) 3%