Course Objectives: To understand the concepts of computational electromagnetics, to enable analysis of numerical stability and dispersion

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

Course Outcomes:After the completion of this course the student will be able to:

• understand the fundaments and overview of Partial Differential Equation and Time-Domain Methods

• understand one-dimensional scalar wave equation

• understand the concept ofMaxwell’s' Equations and Yee Algorithm

• understand the Numerical StabilitySchemes

• understand the Numerical Dispersion

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).