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 TimeDomain PDE Solvers, History of SpaceGrid TimeDomain Techniques for Maxwell's Equations , General Characteristics of SpaceGrid TimeDomain Approaches : Classes of FDTD and FVTD Algorithms , Predictive Dynamic Range , Scaling to Very Large Problem Sizes : Algorithm Scaling Factors , Computer Architecture Scaling Factors , Defense Applications, DualUse Electromagnetics Technology.

One-Dimensional Scalar Wave Equation: PropagatingWave Solutions, Finite Differences, FiniteDifference Approximation of the Scalar Wave Equation, Dispersion Relations for the OneDimensional 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: BasicStability Analysis Procedure, TM Mode, Time Eigenvalue Problem, Space Eigenvalue Problem, Enforcement of Stability, Extension to the Full ThreeDimensional Yee Algorithm, Generalized Stability Problem: Boundary Conditions, Variable and Unstructured Meshing, Lossy, Dispersive, Nonlinear, and Gain Materials

Numerical Dispersion: Basic Procedure, Substitution of TravelingWave Trial Solution, Extension to the Full ThreeDimensional Yee Algorithm, Comparison with the Ideal Dispersion Case, Reduction to the Ideal Dispersion Case for Special Grid Conditions, DispersionOptimized Basic Yee Algorithm, DispersionOptimized Yee Algorithm with FourthOrder Accurate Spatial Central Differences: Formulation, Example, Pros and Cons


Course Learning Outcomes (CLO):

After the completion of the course the students will be able to 

1.       Apply partial differential equation and timedomain methods for analysis.

2.      Use onedimensional scalar wave equation

3.      Handle the concept   of maxwell’s' equations and yee algorithm

4.      Apply the numerical stability schemes

5.      Apply the numerical dispersion techniques.

Recommended Books:

1.      Taflove, A.  and Hagness, S.C., Computational Electrodynamics, Artech House (2006).

2.      Sullivan, D.M., Electromagnetic Simulation Using the FDTD Method, IEEE Computer Society Press (2000).