1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 8 H. O. #13 3 July 2008
Our subject for this Lecture is by and large well covered in Chapter 5 of the textbook, Taove and Hagness, Computational Electrodynamics. We thus provide only abbrevia
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 9 H. O. #14 24 June 2008
9.1
TOTAL-FIELD/SCATTERED-FIELD FORMULATION IN THREE DIMENSIONS
The total-eld/scattered eld formulation was described in Lecture #8 for the two-dimensional case, requ
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 11 H. O. #17 08 July 2008
11.1
RADIATION OPERATORS AS ABSORBING BOUNDARY CONDITIONS
The use of various so-called radiation operators as the basis for Absorbing Boundary Conditions for FDTD ca
1 EE256 Numerical Electromagnetics Marshall Summer 2008 H. O. #18 08 July 2008
LECTURE 12
12.1
OBLIQUE INCIDENCE ON LOSSY MEDIUM
The Perfectly Matched Layer (PML) method for absorbing waves incident on the boundaries of an FDTD grid is based on reection/r
1 EE256 Numerical Electromagnetics Marshall Summer 2008 H. O. #19 08 July 2008
LECTURE 13
13.1
PERFECTLY MATCHED LAYER (PML) BOUNDARY CONDITION
The Berenger PML method for absorbing waves incident on the boundaries of an FDTD grid is based on reection/ref
1
EE256 Numerical Electromagnetics Marshall Summer 2008
H. O. #20 08 July 2008
Homework #1 Solutions
1
PROBLEM 1
Given the rst-order Euler Method (aka FOEM): y n+1 = y n f (y n , tn )t It can be applied to the differential equation y y + =0 t We start wit
1 EE256 Numerical Electromagnetics Marshall Summer 2008 H. O. #21 15 July 2008
LECTURE 14
14.1
PERFECTLY MATCHED UNIAXIAL MEDIUM
We mentioned in Lecture 13 that the important property of the Berenger PML medium was that it hosted different conductivities
1 EE256 Numerical Electromagnetics Marshall Summer 2008 HOMEWORK ASSIGNMENT #3 (due Tuesday, July 29th) H.O. #22 17 July 2008
1. One dimensional wave incident on a dielectric slab. Consider the propagation of a one dimensional electromagnetic wave in a me
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 10 H. O. #15 24 June 2008
10.1
ABSORBING BOUNDARY CONDITIONS
The necessarily nite nature of any FDTD spatial grid is a most important limitation in problems for which the FDTD algorithm must
1 EE256 Numerical Electromagnetics Inan Spring 2007 LECTURE 7 H. O. #10 16 April 2007
7.1
NUMERICAL DISPERSION AND DISSIPATION (DIFFUSION)
The von Neumann stability condition is widely applicable and enables the assessment of the stability of any nite dif
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 7 H. O. #6 24 June 2008
7.1
NUMERICAL DISPERSION AND DISSIPATION (DIFFUSION)
The von Neumann stability condition is widely applicable and enables the assessment of the stability of any nite d
EE256-Numerical Electromagnetics Marshall Summer 2008 SCHEDULE DATE 24 June (T) 26 June (Th) 01 July (T) 03 July (Th) 08 July (T) 10 July (Th) 15 July (T) TOPIC Introduction & Review of Electromagnetics Partial Differential Equations and Physical Systems
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE1 1 H. O. #3 24 June 2008
1.1
INTRODUCTION
Our purpose in this course is to provide an introduction to numerical electromagnetics, more commonly referred to as computational electromagnetics (
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 2 H. O. #4 24 June 2008
2.1
PARTIAL DIFFERENTIAL EQUATIONS AND PHYSICAL SYSTEMS
Most physical systems are described by one or more partial differential equations, which can be derived by dire
1 EE256 Numerical Electromagnetics Marshall Summer 2008 HOMEWORK ASSIGNMENT #1 (due Tuesday, July 8th) H.O. #5 24 June 2008
1. First-order Euler method for an ODE. Consider using the rst-order Euler method for the solution of equation [2.31] of the Lectur
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 3 H. O. #6 24 June 2008
3.1
FINITE DIFFERENCE SOLUTIONS OF THE CONVECTION EQUATION
As the simplest example of a PDE, we consider nite difference solutions of the convection equation [2.20]. A
1 EE256 Numerical Electromagnetics Marshall Summer 2008 H. O. #6 24 June 2008
LECTURE 4
4.1
THE FDTD GRID AND THE YEE ALGORITHM
After a brief exposure to different nite difference algorithms and methods, we now focus our attention on the so-called FDTD al
1 EE256 Numerical Electromagnetics Marshall Summer 2008 LECTURE 5 H. O. #6 24 June 2008
5.1
FDTD EXPRESSIONS IN THREE DIMENSIONS
The FDTD expressions for Maxwells Equations in three dimensions are given in Section 3.6.3 of the textbook, Computational Elec
1 EE256 Numerical Electromagnetics Marshall Summer 2008 H. O. #6 24 June 2008
LECTURE 6
6.1
NUMERICAL STABILITY OF FINITE DIFFERENCE METHODS
The most commonly used procedure for assessing the stability of a nite difference scheme is the so-called1 von Neu
A 3-D Perfectly Matched Medium from Modi ed Maxwell's Equations with Stretched Coordinatesy
Weng Cho Chew and William H. Weedon Electromagnetics Laboratory Department of Electrical and Computer Engineering University of Illinois, Urbana, IL 61801
Key Term