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Computational Electrodynamics The Finite-Difference Time-Domain Method

ISBN-10: 1580538320
ISBN-13: 9781580538329
Edition: 3rd 2005
List price: $159.00 Buy it from $152.32
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Description: In the third edition of this text, the authors have updated the book's discussions of FDTD theory and applications, as well as enhancing the educational content of the text, both from a fundamental theoretical perspective and from the perspective of  More...

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Book details

List price: $159.00
Edition: 3rd
Copyright year: 2005
Publisher: Artech House
Binding: Hardcover
Pages: 1006
Size: 7.25" wide x 10.00" long x 2.25" tall
Weight: 4.246
Language: English

In the third edition of this text, the authors have updated the book's discussions of FDTD theory and applications, as well as enhancing the educational content of the text, both from a fundamental theoretical perspective and from the perspective of ease of use for course instructors.

Allen Taflove is a professor of electrical and computer engineering at Northwestern University, Evanston, IL. He is also the author of Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House 1995).

Preface to the Second Edition
Preface to the First Edition
Electrodynamics Entering the 21st Century
Introduction
The Heritage of Military Defense Applications
Frequency-Domain Solution Techniques
Rise of Finite-Difference Time-Domain Methods
History of FDTD Techniques for Maxwell's Equations
Characteristics of FDTD and Related Space-Grid Time-Domain Techniques
Classes of Algorithms
Predictive Dynamic Range
Scaling to Very Large Problem Sizes
Examples of Applications (including Color Plate Section, pages 9-16)
Radar-Guided Missile
High-Speed Computer Circuit-Board Module
Power-Distribution System for a High-Speed Computer Multichip Module
Microwave Amplifier
Cellular Telephone
Optical Microdisk Resonator
Photonic Bandgap Microcavity Laser
Colliding Spatial Solitons
Conclusions
References
The One-Dimensional Scalar Wave Equation
Introduction
Propagating-Wave Solutions
Dispersion Relation
Finite Differences
Finite-Difference Approximation of the Scalar Wave Equation
Numerical Dispersion Relation
Case 1: Very Fine Sampling in Time and Space ([Delta]t [right arrow] 0, [Delta]x [right arrow] 0)
Case 2: Magic Time-Step (c[Delta]t = [Delta]x)
Case 3: Dispersive Wave Propagation
Example of Calculation of Numerical Phase Velocity and Attenuation
Examples of Calculations of Pulse Propagation
Numerical Stability
Complex-Frequency Analysis
Examples of Calculations Involving Numerical Instability
Summary
Order of Accuracy
Lax-Richtmyer Equivalence Theorem
Limitations
References
Bibliography on Stability of Finite-Difference Methods
Problems
Introduction to Maxwell's Equations and the Yee Algorithm
Introduction
Maxwell's Equations in Three Dimensions
Reduction to Two Dimensions
TM[subscript z] Mode
TE[subscript z] Mode
Reduction to One Dimension
x-Directed, z-Polarized TEM Mode
x-Directed, y-Polarized TEM Mode
Equivalence to the Wave Equation in One Dimension
The Yee Algorithm
Basic Ideas
Finite Differences and Notation
Finite-Difference Expressions for Maxwell's Equations 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[subscript z] and TE[subscript z] Modes
Interpretation as Faraday's and Ampere's Laws in Integral Form
Divergence-Free Nature
Alternative Finite-Difference Grids
Cartesian Grids
Hexagonal Girds
Tetradecahedron/Dual-Tetrahedron Mesh in Three Dimensions
Summary
References
Problems
Numerical Dispersion and Stability
Introduction
Derivation of the Numerical Dispersion Relation for Two-Dimensional Wave Propagation
Extension to Three Dimensions
Comparison With the Ideal Dispersion Case
Anisotropy of the Numerical Phase Velocity
Sample Values of Numerical Phase Velocity
Intrinsic Grid Velocity Anisotropy
Complex-Valued Numerical Wavenumbers
Case 1: Numerical Wave Propagation Along the Principal Lattice Axes
Case 2: Numerical Wave Propagation Along a Grid Diagonal
Example of Calculation of Numerical Phase Velocity and Attenuation
Example of Calculation of Wave Propagation
Numerical Stability
Complex-Frequency Analysis
Example of a Numerically Unstable Two-Dimensional FDTD Model
Generalized Stability Problem
Boundary Conditions
Variable and Unstructured Meshing
Lossy, Dispersive, Nonlinear, and Gain Materials
Modified Yee-Based Algorithms for Improved Numerical Dispersion
Strategy 1: Center a Specific Numerical Phase-Velocity Curve About c
Strategy 2: Use Fourth-Order-Accurate Spatial Differences
Strategy 3: Use Hexagonal Grids
Strategy 4: Use Discrete Fourier Transforms to Calculate the Spatial Derivatives
Alternating-Direction-Implicit Time-Stepping Algorithm for Operation Beyond the Courant Limit
Numerical Formulation of the Zheng/Chen/Zhang Algorithm
Numerical Stability
Numerical Dispersion
Discussion
Summary
References
Problems
Projects
Incident Wave Source Conditions
Introduction
Pointwise E and H Hard Sources in One Dimension
Pointwise E and H Hard Sources in Two Dimensions
Green's Function for the Scalar Wave Equation in Two Dimensions
Obtaining Comparative FDTD Data
Results for Effective Action Radius of a Hard-Sourced Field Component
J and M Current Sources in Three Dimensions
Sources and Charging
Sinusoidal Sources
Transient (Pulse) Sources
Intrinsic Lattice Capacitance
Intrinsic Lattice Inductance
Impact Upon FDTD Simulations of Lumped-Element Capacitors and Inductors
The Plane-Wave Source Condition
The Total-Field/Scattered-Field Technique: Ideas and One-Dimensional Formulation
Ideas
One-Dimensional Formulation
Two-Dimensional Formulation of the TF/SF Technique
Consistency Conditions
Calculation of the Incident Field
Illustrative Example
Three-Dimensional Formulation of the TF/SF Technique
Consistency Conditions
Calculation of the Incident Field
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 Modal Hard Source
Total-Field/Reflected-Field Modal Formulation
Resistive Source and Load Conditions
Summary
References
Problems
Projects
Analytical Absorbing Boundary Conditions
Introduction
Bayliss-Turkel Radiation 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 Radiation Operators
Formulation
First Two Higdon Operators
Discussion
Liao Extrapolation in Space and Time
Formulation
Discussion
Ramahi Complementary Operators
Basic Idea
Complementary Operators
Effect of Multiple Wave Reflections
Basis of the Concurrent Complementary Operator Method
Illustrative FDTD Modeling Results Obtained Using the C-COM
Summary
References
Problems
Perfectly Matched Layer Absorbing Boundary Conditions
Introduction
Plane Wave Incident Upon a Lossy Half-Space
Plane Wave Incident Upon Berenger's PML Medium
Two-Dimensional TE[subscript z] Case
Two-Dimensional TM[subscript z] Case
Three-Dimensional Case
Stretched-Coordinate Formulation of Berenger's PML
An Anisotropic PML Absorbing Medium
Perfectly Matched Uniaxial Medium
Relationship to Berenger's Split-Field PML
A Generalized Three-Dimensional Formulation
Inhomogeneous Media
Theoretical Performance of the PML
The Continuous Space
The Discrete Space
Efficient Implementation of UPML in FDTD
Derivation of the Finite-Difference Expressions
Computer Implementation of the UPML
Numerical Experiments With Berenger's Split-Field PML
Outgoing Cylindrical Wave in a Two-Dimensional Open-Region Grid
Outgoing Spherical Wave in a Three-Dimensional Open-Region Lattice
Dispersive Wave Propagation in Metal Waveguides
Dispersive and Multimode Wave Propagation in Dielectric Waveguides
Numerical Experiments With UPML
Current Source Radiating in an Unbounded Two-Dimensional Region
Highly Elongated Domains
Microstrip Transmission Line
UPML Termination for Conductive Media
Theory
Numerical Example: Termination of a Conductive Half-Space Medium
UPML Termination for Dispersive Media
Theory
Numerical Example: Reflection by a Lorentz Medium
Summary and Conclusions
References
Projects
Near-to-Far-Field Transformation
Introduction
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
Summary
References
Project
Dispersive and Nonlinear Materials
Introduction
Types of Dispersions Considered
Debye Media
Lorentz Media
Piecewise-Linear Recursive Convolution Method, Linear Material Case
General Formulation of the Method
Application to Debye Media
Application to Lorentz Media
Numerical Results
Piecewise-Linear Recursive Convolution Method, Nonlinear Dispersive Material Case
Governing Equations
General Formulation of the Method
FDTD Realization in One Dimension
Numerical Results
Auxiliary Differential Equation Method, Linear Material Case
Formulation for Multiple Debye Poles
Formulation for Multiple Lorentz Pole Pairs
Numerical Results
Auxiliary Differential Equation Method, Nonlinear Dispersive Material Case
Formulation for Multiple Lorentz Pole Pairs, TM[subscript Z] Case
Numerical Results for Temporal Solitons
Numerical Results for Spatial Solitons
Summary and Conclusions
References
Problems
Projects
Local Subcell Models of Fine Geometrical Features
Introduction
Basis of Contour-Path FDTD 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 Contour-Path Model of the Thin Wire
Locally Conformal Models of Curved Surfaces
Dey-Mittra Technique for PEC Structures
Illustrative Results for PEC Structures
Dey-Mittra Technique for Material Structures
Maloney-Smith Technique for Thin Material Sheets
Basis
Illustrative Results
Dispersive Surface Impedance
Maloney-Smith Method
Beggs Method
Lee Method
Relativistic Motion of PEC Boundaries
Basis
Illustrative Results
Summary and Discussion
References
Bibliography
Projects
Nonorthogonal and Unstructured Grids
Introduction
Nonuniform Orthogonal Grids
Locally Conformal Grids, Globally Orthogonal
Global Curvilinear Coordinates
Nonorthogonal Curvilinear FDTD 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 Implementation
Examples of Passive-Circuit Modeling Using the Planar Generalized Yee Algorithm
32-GHz Wilkinson Power Divider
32-GHz Gysel Power Divider
Signal Lines in an IBM Thermal Conduction Module
Summary and Conclusions
References
Problems
Projects
Bodies of Revolution
Introduction
Field Expansion
Difference Equations for Off-Axis Cells
Ampere's Law Contour Path Integral to Calculate e[subscript r]
Ampere's Law Contour Path Integral to Calculate e[subscript phi]
Ampere's Law Contour Path Integral to Calculate e[subscript z]
Difference Equations
Surface-Conforming Contour Path Integrals
Difference Equations for On-Axis Cells
Ampere's Law Contour Path Integral to Calculate e[subscript z] on the z-Axis
Ampere's Law Contour Path Integral to Calculate e[subscript phi] on the z-Axis
Faraday's Law Calculation of h[subscript r] on the z-Axis
Numerical Stability
PML Absorbing Boundary Condition
BOR-FDTD Background
Extension of PML to the General BOR Case
Examples
Application to Particle Accelerator Physics
Definitions and Concepts
Examples
Summary
References
Problems
Projects
Analysis of Periodic Structures
Introduction
Review of Scattering From Periodic Structures
Direct Field Methods
Normal Incidence Case
Multiple Unit Cells for Oblique Incidence
Sine-Cosine Method
Angled-Update Method
Introduction to the Field-Transformation Technique
Multiple-Grid Approach
Formulation
Numerical Stability Analysis
Numerical Dispersion Analysis
Lossy Materials
Lossy Screen Example
Split-Field Method, Two Dimensions
Formulation
Numerical Stability Analysis
Numerical Dispersion Analysis
Lossy Materials
Lossy Screen Example
Split-Field Method, Three Dimensions
Formulation
Numerical Stability Analysis
UPML Absorbing Boundary Condition
Application of the Periodic FDTD Method
Photonic Bandgap Structures
Frequency-Selective Surfaces
Antenna Arrays
Summary and Conclusions
Acknowledgments
References
Projects
Modeling of Antennas
Introduction
Formulation of the Antenna Problem
Transmitting Antenna
Receiving Antenna
Symmetry
Excitation
Antenna Feed Models
Detailed Modeling of the Feed
Simple Gap Feed Model for a Monopole Antenna
Improved Simple Feed Model
Near-to-Far-Field Transformations
Use of Symmetry
Time-Domain Near-to-Far-Field Transformation
Frequency-Domain Near-Field to Far-Field Transformation
Plane-Wave Source
Effect of an Incremental Displacement of the Surface Currents
Effect of an Incremental Time Shift
Relation to Total-Field/Scattered-Field Lattice Zoning
Case Study I: The Standard-Gain Horn
Case Study II: The Vivaldi Slotline Array
Background
The Planar Element
The Vivaldi Pair
The Vivaldi Quad
The Linear Phased Array
Phased-Array Radiation Characteristics Indicated by the FDTD Modeling
Active Impedance of the Phased Array
Near-Field Simulations
Generic 900-MHz Cellphone Handset in Free Space
900-MHz Dipole Antenna Near a Layered Bone-Brain Half-Space
840-MHz Dipole Antenna Near a Rectangular Brain Phantom
900-MHz Infinitesimal Dipole Antenna Near a Spherical Brain Phantom
1,900-MHz Half-Wavelength Dipole Near a Spherical Brain Phantom
Selected Recent Applications
Use of Photonic-Bandgap Materials
Ground-Penetrating Radar
Antenna-Radome Interaction
Personal Wireless Communications Devices
Biomedical Applications of Antennas
Summary and Conclusions
References
Projects
High-Speed Electronic Circuits With Active and Nonlinear Components
Introduction
Basic Circuit Parameters
Transmission Line Parameters
Impedance
S Parameters
Differential Capacitance Calculation
Differential Inductance Calculation
Lumped Inductance Due to a Discontinuity
Flux / Current Definition
Fitting Z([omega]) or S([omega]) to an Equivalent Circuit
Discussion: Choice of Methods
Inductance of Complex Power-Distribution Systems
Method Description
Example: Multiplane Meshed Printed-Circuit Board
Discussion
Parallel Coplanar Microstrips
Multilayered Interconnect Modeling Example
Digital Signal Processing and Spectrum Estimation
Prony's Method
Autoregressive Models
Pade Approximation
Modeling of Lumped Circuit Elements
FDTD Formulation Extended to Circuit Elements
The Resistor
The Resistive Voltage Source
The Capacitor
The Inductor
The Diode
The Bipolar Junction Transistor
Direct Linking of FDTD and SPICE
Basic Idea
Norton Equivalent Circuit "Looking Into" the FDTD Space Lattice
Thevenin Equivalent Circuit "Looking Into" the FDTD Space Lattice
Case Study: A 6-GHz MESFET Amplifier Model
Large-Signal Model
Amplifier Configuration
Analysis of the Circuit Without the Packaging Structure
Analysis of the Circuit With the Packaging Structure
Summary and Conclusions
Acknowledgements
References
Additional Bibliography
Projects
Microcavity Optical Resonators
Introduction
Issues Related to FDTD Modeling of Optical Structures
Optical Waveguides
Material Dispersion and Nonlinearities
Macroscopic Modeling of Optical Gain Media
Theory
Validation Studies
Application to Vertical-Cavity Surface-Emitting Lasers
Passive Studies
Active Studies
Microcavities Based on Photonic Bandgap Structures, Quasi One-Dimensional Case
Microcavities Based on Photonic Bandgap Structures, Two-Dimensional Case
Microcavity Ring Resonators
FDTD Modeling Considerations
Coupling to Straight Waveguides
Coupling to Curved Waveguides
Elongated Ring Designs
Resonances
Microcavity Disk Resonators
Resonance Behavior
Suppression of Higher Order Radial Whispering-Gallery Modes
Additional FDTD Modeling Studies
Summary and Conclusions
References
Additional Bibliography
Projects
Acronyms
About the Authors
Index

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