Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing
Author(s): Stephen D. Gedney
Edition: 1
Publisher: Morgan & Claypool
Year: 2011
Language: English
Pages: 250
A Brief History of the FDTD Method......Page 15
Limitations of the FDTD Method......Page 18
Alternate Solution Methods......Page 22
Outline to the Remainder of the Text......Page 23
References......Page 25
The Transmission Line Equations......Page 35
Explicit Time Update Solution......Page 36
Numerical Dispersion......Page 39
Stability......Page 42
Sources and Loads......Page 45
Problems......Page 49
References......Page 50
Maxwell's Equations......Page 53
The Yee-Algorithm......Page 55
Gauss's Laws......Page 60
Finite Integration Technique CH3.BIB5......Page 61
Stability......Page 62
Numerical Dispersion and Group Delay......Page 66
Material and Boundaries......Page 72
Lossy Media......Page 78
Dispersive Media......Page 79
Non-Uniform Gridding......Page 82
Problems......Page 85
References......Page 86
The Gaussian Pulse......Page 89
The Differentiated Pulse......Page 90
The Modulated Pulse......Page 92
Volume Current Density......Page 93
Surface Current Density......Page 95
Discrete Voltage Source......Page 97
Discrete Thévenin Source......Page 98
Lumped Loads......Page 101
The Total-Field Scattered Field Formulation......Page 103
General Description of a Uniform Plane Wave......Page 108
Computing the Discrete Incident Field Vector......Page 110
Numerical Dispersion......Page 111
Problems......Page 112
References......Page 113
Introduction......Page 115
The First-Order Sommerfeld ABC......Page 116
The Higdon ABC......Page 119
The Betz-Mittra ABC......Page 122
References......Page 123
Introduction......Page 127
The Anisotropic PML......Page 128
Stretched Coordinate Form of the PML......Page 132
The Ideal PML......Page 134
PML Parameter Scaling......Page 135
Reflection Error......Page 137
The Complex Frequency Shifted (CFS) PML......Page 138
An ADE form of the CFS-PML......Page 139
Yee-Algorithm for the CFS-PML......Page 141
Example of the CFS-PML......Page 145
References......Page 147
The Basic Thin-Wire Subcell Model......Page 151
Curvature Correction......Page 153
Modeling the End-Cap......Page 156
Delta-Gap Source......Page 160
A Transmission Line Feed......Page 164
Conformal FDTD Methods for Conducting boundaries......Page 166
Dey-Mittra (DM) Conformal FDTD Method for Conducting Boundaries......Page 167
Yu-Mittra (YM) Conformal FDTD Method for Conducting Boundaries......Page 171
BCK Conformal FDTD Method for Conducting Boundaries......Page 172
Narrow Slots......Page 173
Conformal FDTD Methods for Material Boundaries......Page 176
Thin Material Sheets......Page 179
Problems......Page 183
References......Page 184
Discrete Network Port Parameterization......Page 187
Admittance-Parameters......Page 191
Scattering Parameters......Page 192
Near-Field to Far-Field (NF-FF) Transformations......Page 199
Huygen Surface......Page 200
Frequency Domain NF-FF Transform......Page 202
Antenna Gain......Page 207
Scattering Cross Section......Page 208
Problems......Page 209
References......Page 211
Translating the Discrete FDTD Equations to a High-Level Programming Language......Page 213
Top-Level Design......Page 221
Array Indexing the 3D-FDTD......Page 224
Lossy and Inhomogeneous Media......Page 229
Implementing the CFS-CPML......Page 230
Edge Length Normalization......Page 241
General FDTD Update Equations......Page 242
Author's Biography......Page 245
Index......Page 247
