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The Finite Difference Time Domain Method for Electromagnetics With MATLAB Simulation
封面在附件：book_cover.jpg

本帖最后由 huangfeihong88 于 2009-11-26 20:16 编辑

Description

The scope of the book is the fundamental techniques in the FDTD method. The book consists of 12 chapters, each chapter built on the concepts provided in the previous chapters. In each chapter the details of the concepts are discussed at a graduate student level. Using this book, students will be able to construct a program with sufficient functionally to solve some basic problems. The construction of final equations is presented with a detailed step-by-step approach. In most cases the full-set of equations are provided.

While constructing the equations, the reader needs to visualize the positioning and orientation of field components in a three dimensional space. This is very difficult and usually requires extensive experience to be able to imagine the 3D space. Therefore, the book presents the construction of equations accompanied by a nice set of 3D illustrations. The figures greatly facilitate the understanding of the concepts.

While the concepts are being presented, it has been kept in mind that the outcome of the book will be a software package that will be sufficient to solve several types of basic electromagnetic problems. In each chapter the transformation of the concepts into programming is explained. Therefore the chapters are presented in such a way that, by adding/developing a new part of the code, chapter by chapter, at the end a well developed FDTD simulation package will be constructed.


Table of Contents


1 Introduction to FDTD

1.1 FDTD Basic Equations

1.2 Approximation of Derivatives by Finite Differences

1.3 FDTD 3D

1.4 FDTD 2D

1.5 FDTD 1D

1.6 Exercises


2 Numerical Stability and Dispersion

2.1 Numerical Stability

2.2 Numerical Dispersion

2.3 Exercises


3 Building Objects in The Yee Grid

3.1 Code: Definition of Objects

3.1.1 Defining The Problem Space Parameters

3.1.2 Defining The Objects in The Problem Space


3.2 Material Approximations

3.3 Subcell Averaging Schemes

3.4 Objects in The Yee Grid

3.5 Code: Creation of Material Grid

3.6 Improved Eight-Subcell Averaging

3.7 Exercises


4 Active and Passive Lumped Elements

4.1 Voltage Source Updating Equation

4.2 Hard Voltage Source

4.3 Current Source

4.4 Resistor

4.5 Capacitor

4.6 Inductor

4.7 Distributed Lumped Elements

4.8 Diode

4.9 Summary

4.10 Simulation of Lumped Elements

4.10.1 Definition of Lumped Elements

4.10.2 FDTD parameters and Field Arrays

4.10.3 Initialization of Lumped Element Components

4.10.4 Initialization of Updating Coefficients

4.10.5 Sampling Electric and Magnetic Fields, Voltages and Currents

4.10.6 Definition and Initialization of Output Parameters

4.10.7 Running an FDTD Simulation: The Time Marching Loop

4.10.8 Displaying FDTD Simulation Results


4.11 Simulation Examples

4.11.1 A Resistor Excited by a Sinusoidal Voltage Source

4.11.2 A Diode Excited by a Sinusoidal Voltage Source

4.11.3 A Capacitor Excited by a Unit-Step Voltage Source


4.12 Exercises


5 Source Waveforms

5.1 Common Source Waveforms

5.1.1 Sinusoidal Waveform

5.1.2 Gaussian Waveform

5.1.3 Normalized Derivative of a Gaussian Waveform

5.1.4 Cosine Modulated Gaussian Waveform


5.2 Initialization of Source Waveforms

5.3 Code: Time to Frequency Domain Transformation

5.4 Simulation Examples

5.4.1 Recovering a Time Waveform from its Fourier Transform

5.4.2 An RLC Circuit


5.5 Exercises


6 S-Parameters

6.1 S-parameter Definition

6.2 S-Parameters Calculation

6.3 Exercises


7 Perfectly Matched Layer

7.1 Theory of PML

7.1.1 Theory of PML at vacuum-PML interface

7.1.2 Theory of PML at PML-PML interface


7.2 PML 3D

7.3 PML Loss Functions

7.4 PML Updating Equations

7.4.1 PML Updating Equations - 2D TEz

7.4.2 PML Updating Equations - 2D TMz

7.4.3 MATLAB Implementation of 2D FDTD with PML


7.5 Simulation Example

7.6 Exercises


8 CPML

8.1 Formulation of CPML

8.1.1 PML in Stretched Coordinates

8.1.2 Complex Stretching Variables in CFS-PML

8.1.3 The Matching Conditions at The PML-PML Interface

8.1.4 Equations in Time Domain

8.1.5 Discrete Convolution

8.1.6 The Recursive Convolution Method


8.2 The CPML Algorithm

8.2.1 Updating Equations for CPML

8.2.2 Addition of Auxiliary CPML Terms at Respective Regions


8.3 Parameter Distribution

8.4 MATLAB Implementation of CPML in 3D FDTD

8.4.1 Definition of CPML

8.4.2 Initialization of CPML

8.4.3 Application of CPML in FDTD Loop


8.5 Simulation Examples

8.5.1 Microstrip Low-Pass Filter

8.5.2 Microstrip Branch Line Coupler

8.5.3 Characteristic Impedance of a Microstrip Line


8.6 Exercises


9 Near-Field to Far-Field Transformation

9.1 Implementation of Surface Equivalence Theorem

9.1.1 Surface equivalence theorem

9.1.2 Equivalent surface currents

9.1.3 Antenna on infinite ground plane


9.2 Near Field to Far Field Transformation

9.2.1 Time domain to frequency domain transformation

9.2.2 Vector potential approach

9.2.3 Polarization of radiation field

9.2.4 Radiation efficiency


9.3 MATLAB Implementation of NF-FF Transformation

9.3.1 Definition of NF-FF Parameters

9.3.2 Initialization of NF-FF Parameters

9.3.3 NF-FF DFT

9.3.4 Postprocessing for Farfield Calculation


9.4 Simulation Examples

9.4.1 Inverted-F Antenna

9.4.2 Strip-Fed Rectangular Dielectric Resonator Antenna


9.5 Exercises


10 Thin Wire Modeling

10.1 Thin Wire Formulation

10.2 MATLAB Implementation of Thin Wire Formulation

10.3 Simulation Examples

10.3.1 Thin Wire Dipole Antenna


10.4 Exercises


11 Scattered Field Formulation

11.1 The Scattered Field Formulation

11.2 The Scattered Field Updating Equations

11.3 Incident Plane Waves

11.4 MATLAB Implementation of Scattered Field Formulation

11.4.1 Definition of Incident Plane Wave

11.4.2 Initialization of The Incident Fields

11.4.3 Initialization of The Updating Coefficients

11.4.4 Calculation of The Scattered Fields

11.4.5 Post-processing and Simulation Results


11.5 Simulation Examples

11.5.1 Scattering From a Dielectric Sphere

11.5.2 Scattering From a Dielectric Cube


11.6 Exercises


12 GPU Acceleration of FDTD

12.1 Graphical Processors and General Math

12.2 Introduction To Brook

12.3 Sample 2D Implementation Using Brook

12.4 Extension Into 3D

12.5 Exercises


A One-Dimensional FDTD Code

B CPML Regions and Associated Field Updates for a 3D Domain

B.1 3D CPML Ex

B.2 3D CPML Ey

B.3 3D CPML Ez

B.4 3D CPML Hx

B.5 3D CPML Hy

B.6 3D CPML Hz


C Matlab Code for Plotting Farfield Patterns

Index

Bibliography


About the Authors

Atef Elsherbeni is a full Professor of Electrical Engineering at the University of Mississippi and Director of the School of Engineering CAD Lab. He is Editor-in-Chief and Managing Editor of the Applied Computational Electromagnetics Society (ACES) Journal, Editor of the Journal Of Electromagnetic Waves and Applications, Associate Editor of The Radio Science Journal, and coauthor of the book MATLAB Simulations for Radar Systems Analysis. Dr. Elsherbeni earned Bachelors degrees in both EE and Applied Physics, as well as his Masters degree in EE, at Cairo University. He earned his doctorate and was a post-doctoral Fellow at the University of Manitoba.

Veysel Demir received his Bachelor of Science degree in electrical engineering from the Middle East Technical University, Ankara, Turkey, in 1997. He received both the Master of Science and Doctor of Philosophy degrees in Electrical Engineering from Syracuse University, Syracuse, New York, in 2002 and 2004, respectively. He joined the Department of Electrical Engineering at Northern Illinois University as an Assistant Professor in August 2007. His research interests include numerical analysis techniques (FDTD, FDFD, and MoM), as well as microwave and RF circuit analysis and design. Dr. Demir is a member of the IEEE and ACES, and he has coauthored more than 20 technical journal and conference papers. He serves as a reviewer for both the Applied Computational Electromagnetics (ACES) Journal and the Transactions on Microwave Theory and Techniques (MTT) Journal.

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