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.
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.
A thorough understanding of Maxwell’s equations, boundary conditions, radiation, electromagnetic theorems and effective boundary conditions, and Green’s functions as covered in 5105 and 5106. In addition, computer programming in a scientific language, preferably FORTRAN, is required background for this course.
Percentage of Course
|Basic equations review||2%|
|Linear operator concepts||3%|
|Green’s functions and integral equations||5%|
|Waveguide iris problem||5%|
|Green’s function approach|
|Method of moments||5%|
|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%|