PEI333 COMPUTATIONAL
ELECTROMAGNETIC |
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Prerequisite(s): |
Overview: Background
: The Heritage of the 1980's , The Rise of Partial Differential Equation
Methods , Interdisciplinary Impact of Emerging Time-Domain PDE Solvers, History of Space-Grid Time-Domain
Techniques for Maxwell's Equations , General Characteristics of Space-Grid
Time-Domain Approaches : Classes of FD-TD and FV-TD Algorithms ,
Predictive Dynamic Range , Scaling to Very Large Problem Sizes : Algorithm
Scaling Factors , Computer Architecture Scaling Factors , Defense Applications,
Dual-Use Electromagnetics Technology.
One-Dimensional Scalar Wave Equation: Propagating-Wave Solutions , Finite
Differences , Finite-Difference Approximation of the Scalar Wave Equation ,
Dispersion Relations for the One-Dimensional Wave Equation , Numerical Phase
Velocity, Numerical Group Velocity, Numerical Stability: The Time Eigenvalue Problem,
The Space Eigenvalue Problem, Enforcement of
Stability .
Introduction to Maxwell’s' Equations and the Yee Algorithm: Maxwell's Equations in Three Dimensions ,
Reduction to Two Dimensions : TM Mode, TE Mode , Reduction
to One Dimension : TM Mode , TE Mode, Equivalence to the
Wave Equation in One Dimension , Yee Algorithm.
Numerical Stability: Basic-Stability Analysis Procedure, TM Mode, Time Eigenvalue Problem, Space Eigenvalue
Problem, Enforcement of Stability, Extension to the Full
Three-Dimensional Yee Algorithm, Generalized Stability Problem: Boundary
Conditions, Variable and Unstructured Meshing, Lossy,
Dispersive, Nonlinear, and Gain Materials
Numerical Dispersion: Basic Procedure, Substitution of Traveling-Wave Trial
Solution, Extension to the Full Three-Dimensional Yee Algorithm, Comparison
with the Ideal Dispersion Case, Reduction to the Ideal Dispersion Case for
Special Grid Conditions, Dispersion-Optimized Basic Yee Algorithm,
Dispersion-Optimized Yee Algorithm with Fourth-Order Accurate Spatial Central
Differences: Formulation, Example, Pros and Cons
Recommended Books
1.
Taflove, A. and Hagness, S.C., Computational Electrodynamics, Artech House (2006).
Sullivan, D.M., Electromagnetic Simulation Using the FDTD Method, IEEE Computer Society Press (2000).