Course Syllabus

Fall 1998

Professor C. D. Cantrell, UT-Dallas

Textbooks:

Required: Computational Electrodynamics, Second Edition, by Professor Allen Taflove (editor) and Susan C. Hagness. Published by Artech House (ISBN 1580530761).

Recommended: Electromagnetic Simulation Using the FDTD Method, by Dennis M. Sullivan. Published by IEEE (ISBN 0780347471).

Syllabus:

1. 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
• RCS Modeling of Entire Aircraft to 1 GHz
• Desirable Additional Modeling Capabilities for Defense Applications
• Dual-Use Electromagnetics Technology
• Antenna Design
• Bioelectromagnetic Systems 1: Hyperthermia Treatment of Cancer
• Bioelectromagnetic Systems 2: Physics of Human Vision
• Digital Circuit Packaging and Interconnects
• Incorporation of Models of Active Circuit Devices
• Subpicosecond Photonic Devices

2. The 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
• Case 1: Very Fine Mesh
• Case 2: Magic Time Step
• Case 3: Dispersive Wave Propagation
• Numerical Group Velocity
• Case 1: Very Fine Mesh
• Case 2: Magic Time Step
• Numerical Stability
• The Time Eigenvalue Problem
• The Space Eigenvalue Problem
• Enforcement of Stability

3. 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
• Basic Ideas
• Finite Differences and Notation
• Finite-Difference Expressions for Maxwell's Equation in Three Dimensions
• Space Region with a Continuous Variation of Material Properties
• Space Region with a Finite Number of Distinct Media
• Space Region with Nonpermeable Media
• Reduction to the Two-Dimensional TM and TE Modes
• Interpretation as Faraday's and Ampere's Laws in Integral Form
• Divergence-Free Nature
• Exponential Time-Stepping

4. 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

5. 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

6. Incident Wave Source Conditions for Free Space and Waveguides

• Requirements for the Plane Wave Source Condition
• Insertion of the Incident Wave As an Initial Condition
• The Hard Source
• Total-Field/Scattered-Field Formulation
• Ideas
• One-Dimensional Example
• Two-Dimensional Example
• Calculation of the Incident Field to Implement the Connecting Condition
• Extension to Three Dimensions
• Pure Scattered-Field Formulation
• Application to PEC Structures
• Application to Lossy Dielectric Structures
• Choice of Incident Plane Wave Formulation
• Waveguide Source Conditions
• Pulsed Electric Field Hard Source
• Total-Field/Reflected-Field Formulations
• Resistive Source and Load Conditions

7. Absorbing Boundary Conditions for Free Space and Waveguides

• Bayliss-Turkel Scattered-Wave Annihilating Operators
• Spherical Coordinates
• Cylindrical Coordinates
• Engquist-Majda One-Way Wave Equations
• One-Term and Two-Term Taylor Series Approximations
• Mur Finite-Difference Scheme
• Trefethen-Halpern Generalized and Higher-Order ABCs
• Theoretical Reflection Coefficient Analysis
• Numerical Experiments
• Higdon Operator
• Liao Extrapolation
• Mei-Fang Superabsorption
• Berenger Perfectly Matched Layer
• Theory, Two-Dimensional TE Case
• Theory, Two-Dimensional TM Case
• Theory, Full-Vector Three-Dimensional Case
• Numerical Experiments Verifying the Effectiveness of PML ABC
• Absorbing Boundary Conditions for Waveguides

8.Near-to-Far-Field Transformation

• Two-Dimensional Transformation, Phasor Domain
• Application of Green's Theorem
• Far-Field Limit
• Reduction to Standard Form
• Obtaining Phasor Quantities Via Discrete Fourier Transformation
• Surface Equivalence Theorem
• Extension to Three Dimensions, Phasor Domain
• Time-Domain Near-to-Far-Field Transformation

9. Dispersive, Nonlinear, and Gain Materials

• Recursive Convolution Method, Linear Isotropic Case
• Total-Field Formulation
• Scattered-Field Formulation
• Recursive Convolution Method, Linear Gyrotropic Case
• Time-Domain Susceptibility Functions
• Time-Stepping Algorithm
• Discussion
• Auxiliary Differential Equation Method, Linear Isotropic Case
• Introduction: The Single-Relaxation Dispersion, Initial Formulation
• Multiple Lorentzian Relaxations, Refined Formulation
• Comparison with the Recursive Convolution Method
• Auxiliary Differential Equation Method, Nonlinear Lorentz Media (Nonlinear Optics)
• Governing Equations
• Equivalent System of Ordinary Differential Equations
• Algorithm
• Results for Temporal Solitons
• Results for Spatial Solitons
• Auxiliary Differential Equation Method, Lorentz Gain Media (Active Lasing Materials)
• Theory and Numerical Implementation
• Generic Validations
• Discussion

10. Local Subcell Models of Fine Geometrical Features

• Basis of Contour-Path FD-TD Modeling
• The Simplest Contour-Path Subcell Models
• Diagonal Split-Cell Model for PEC Surfaces
• Average Properties Model for Material Surfaces
• The Contour-Path Model of the Narrow Slot
• The Thin Wire
• Conformal Modeling of Curved Surfaces
• Two-Dimensional PEC Structures, TE Case
• Two-Dimensional PEC Structures, TM Case
• Illustrative Results, Aluminum Winglike Object
• Three-Dimensional PEC Structures
• Two-Dimensional Material Structures
• The Thin Material Sheet
• Basis
• Illustrative Results
• Dispersive Surface Impedance
• Maloney-Smith Method
• Beggs et al. Method
• Lee et al. Method
• Relativistic Motion of PEC Boundaries
• Basis
• Illustrative Results
• Numerical Stability

11. Explicit Time-Domain Solution of Maxwell's Equations Using Nonorthogonal and Unstructured Grids

• Nonuniform Orthogonal Grids
• Locally Conformal Grids, Globally Orthogonal
• Global Curvilinear Coordinates
• Nonorthogonal Curvilinear FD-TD Algorithm
• Stability Criterion
• Irregular Nonorthogonal Structured Grids
• Irregular Nonorthogonal Unstructured Grids
• Generalized Yee Algorithm
• Inhomogeneous Media
• Practical Implementation of the Generalized Yee Algorithm
• A Planar Generalized Yee Algorithm
• Time-Stepping Expressions
• Projection Operators
• Efficient Time-Stepping Implemenation
• Analysis of Printed Circuit Devices Using the Planar Generalized Yee Algorithm

12. The Body of Revolution FD-TD Algorithm

• Field Expansion
• Difference Equations for Off-Axis Cells
• The e_r Patch Integral
• The e_f Patch Integral
• The e_z Patch Integral
• Difference Equations
• Surface-Conforming Patch Integrals
• Difference Equation for On-Axis Cells
• The e_z Patch Integral Near the Axis
• The e_f Patch Integral Near the Axis
• The h_r Patch Integral Near the Axis
• Numerical Stability
• PML Absorbing Boundary Condition
• BOR FD-TD Background
• Extension of PML to the BOR Waveguide Case
• Application to Partial Accelerator Physics

13. Modeling of Electromagnetic Fields in High-Speed Electronic Circuits

• Basic Circuit Parameter
• Transmission Line Parameters
• Impedance
• S-Parameters
• Differential Capacitance Calculation
• Differential Inductance Calculation
• Lumped Inductance Due to a Discontinuity
• Flux/Current Definition
• Fitting Z(w) or S_mn(w) to an Equivalent Circuit
• Parallel Coplanar Microstrips
• Multilayered Interconnect Modeling Examples
• Digital Signal Processing and Spectrum Estimation Techniques
• Prony's Method
• Autoregressive Models
• System Identification
• Modeling of Lumped Circuit Elements
• FD-TD Formulation Extended to Circuit Elements
• The Resistor
• The Resistive Voltage Source
• The Capacitor
• The Inductor
• The Diode
• The Bipolar Junction Transistor
• Direct Linking of FD-TD and SPICE

14. FD-TD and Antenna Analysis

• Antenna Characteristics
• Antenna Fields and Radiation Patterns
• Antenna Impedance
• Motivation for Using FD-TD in Antenna Design
• The Monopole Over a PEC Ground Plane
• Modeling Considerations
• Results
• Waveguide and Horn Antennas
• Two-Dimensional Horn Antenna
• Three-Dimensional Waveguide Radiator
• The Vivaldi Slotline Array
• Background
• The Planar Element
• The Two-Element Vivaldi Pair
• The Quad Element
• The Linear Phased Array
• Active Impedance of the Phased Array
• Linear Superposition

15. Electromagnetic Wave Scattering, Penetration and Coupling for Complex Structures

• Scattering and Radar Cross Section
• Small PEC Cube, Broadside Incidence
• Nine-Wavelength T-Shaped Conducting Target
• Generic Curved-Surface Targets, Conformally Modeled
• Full-Scale Military Fighter Aircraft
• Penetration and Coupling
• Empty Cylindrical PEC Cavity
• Loaded Missile Guidance Section
• Spatial Decomposition via a Schelkunoff Equivalence Principle
• Cylindrical PEC Cavity Loaded by a Wire Bundle
• Biological Tissue Structures
• The First FD-TD Biological Tissue Model: The Human Eye
• Patient-Specific Electromagnetic Hyperthermia Models Derived for Computed Tomography Imaging and Analysis
• Visible Light Interactions with the Vertebrate Retinal Rod
• Microlaser Cavities

16. Efficient FD-TD Algorithms for Vector and Multiprocessor Computers

• Pipelined RISC and Vector Processors
• Multiprocessor Computers
• Introduction to Parallelism
• Parallel FD-TD Algorithm
• Numerical Benchmarks
• Parallel Nonorthogonal FD-TD Algorithms
• Parallel Planar Generalized Yee Algorithm
• The Parallel Algorithm
• Spatial Decomposition Algorithms
• Porting FDTD3D to the Cray T3D
• Cray T3D architecture
• T3D Programming Models
• Program Design Issues
• Single-Processor Optimization
• Performance