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E-raamat: Finite-Difference Time-Domain Method for Electromagnetics with MATLAB(R) Simulations

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(Colorado School of Mines, Electrical Engineering and Computer Science Department, USA), (Northern Illinois University, Department of Electrical Engineering, USA)
  • Formaat: PDF+DRM
  • Sari: Electromagnetic Waves
  • Ilmumisaeg: 03-Mar-2016
  • Kirjastus: SciTech Publishing Inc
  • Keel: eng
  • ISBN-13: 9781613531792
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Finite-Difference Time-Domain Method for Electromagnetics with MATLAB(R) SimulationsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Electromagnetic Waves
  • Ilmumisaeg: 03-Mar-2016
  • Kirjastus: SciTech Publishing Inc
  • Keel: eng
  • ISBN-13: 9781613531792
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This book introduces the powerful Finite-Difference Time-Domain method to students and interested researchers and readers. An effective introduction is accomplished using a step-by-step process that builds competence and confidence in developing complete working codes for the design and analysis of various antennas and microwave devices. This book will serve graduate students, researchers, and those in industry and government who are using other electromagnetics tools and methods for the sake of performing independent numerical confirmation. No previous experience with finite-difference methods is assumed of readers.



Key features







Presents the fundamental techniques of the FDTD method at a graduate level, taking readers from conceptual understanding to actual program development. Full derivations are provided for final equations. Includes 3D illustrations to aid in visualization of field components and fully functional MATLAB® code examples. Completely revised and updated for this second edition, including expansion into advanced techniques such as total field/scattered field formulation, dispersive material modeling, analysis of periodic structures, non-uniform grid, and graphics processing unit acceleration of finite-difference time-domain method.
List of figures xv
List of tables xxiv
Preface xxv
Acknowledgements xxviii
1 Introduction to FDTD 1(32)
1.1 The finite-difference time-domain method basic equations
2(2)
1.2 Approximation of derivatives by finite differences
4(9)
1.3 FDTD updating equations for three-dimensional problems
13(10)
1.4 FDTD updating equations for two-dimensional problems
23(4)
1.5 FDTD updating equations for one-dimensional problems
27(5)
1.6 Exercises
32(1)
2 Numerical stability and dispersion 33(10)
2.1 Numerical stability
33(4)
2.1.1 Stability in time-domain algorithm
33(2)
2.1.2 CFL condition for the FDTD method
35(2)
2.2 Numerical dispersion
37(4)
2.3 Exercises
41(2)
3 Building objects in the Yee grid 43(28)
3.1 Definition of objects
43(7)
3.1.1 Defining the problem space parameters
45(3)
3.1.2 Defining the objects in the problem space
48(2)
3.2 Material approximations
50(2)
3.3 Subcell averaging schemes for tangential and normal components
52(3)
3.4 Defining objects snapped to the Yee grid
55(3)
3.4.1 Defining zero-thickness PEC objects
57(1)
3.5 Creation of the material grid
58(8)
3.6 Improved eight-subcell averaging
66(1)
3.7 Exercises
66(5)
4 Active and passive lumped elements 71(72)
4.1 FDTD updating equations for lumped elements
71(15)
4.1.1 Voltage source
72(2)
4.1.2 Hard voltage source
74(1)
4.1.3 Current source
75(1)
4.1.4 Resistor
76(1)
4.1.5 Capacitor
77(1)
4.1.6 Inductor
78(1)
4.1.7 Lumped elements distributed over a surface or within a volume
79(2)
4.1.8 Diode
81(4)
4.1.9 Summary
85(1)
4.2 Definition, initialization, and simulation of lumped elements
86(46)
4.2.1 Definition of lumped elements
86(3)
4.2.2 Initialization of FDTD parameters and arrays
89(1)
4.2.3 Initialization of lumped element components
90(7)
4.2.4 Initialization of updating coefficients
97(11)
4.2.5 Sampling electric and magnetic fields, voltages, and currents
108(3)
4.2.6 Definition and initialization of output parameters
111(8)
4.2.7 Running an FDTD simulation: The time-marching loop
119(10)
4.2.8 Displaying FDTD simulation results
129(3)
4.3 Simulation examples
132(9)
4.3.1 A resistor excited by a sinusoidal voltage source
132(3)
4.3.2 A diode excited by a sinusoidal voltage source
135(2)
4.3.3 A capacitor excited by a unit-step voltage source
137(4)
4.4 Exercises
141(2)
5 Source waveforms and time to frequency domain transformation 143(26)
5.1 Common source waveforms for FDTD simulations
143(8)
5.1.1 Sinusoidal waveform
144(1)
5.1.2 Gaussian waveform
145(3)
5.1.3 Normalized derivative of a Gaussian waveform
148(3)
5.1.4 Cosine-modulated Gaussian waveform
151(1)
5.2 Definition and initialization of source waveforms for FDTD simulations
151(4)
5.3 Transformation from time domain to frequency domain
155(3)
5.4 Simulation examples
158(9)
5.4.1 Recovering a time waveform from its Fourier transform
160(2)
5.4.2 An RLC circuit excited by a cosine-modulated Gaussian waveform
162(5)
5.5 Exercises
167(2)
6 S-Parameters 169(16)
6.1 Scattering parameters
169(1)
6.2 S-Parameter calculations
170(9)
6.3 Simulation examples
179(5)
6.3.1 Quarter-wave transformer
179(5)
6.4 Exercises
184(1)
7 Perfectly matched layer absorbing boundary 185(44)
7.1 Theory of PML
185(6)
7.1.1 Theory of PML at the vacuum—PML interface
185(3)
7.1.2 Theory of PML at the PML—PML interface
188(3)
7.2 PML equations for three-dimensional problem space
191(1)
7.3 PML loss functions
192(2)
7.4 FDTD updating equations for PML and MATLAB® implementation
194(21)
7.4.1 PML updating equations — two-dimensional TEz case
194(3)
7.4.2 PML updating equations — two-dimensional TMz case
197(2)
7.4.3 MATLAB® implementation of the two-dimensional FDTD method with PML
199(16)
7.5 Simulation examples
215(12)
7.5.1 Validation of PML performance
215(5)
7.5.2 Electric field distribution
220(5)
7.5.3 Electric field distribution using DFT
225(2)
7.6 Exercises
227(2)
8 Advanced PML formulations 229(50)
8.1 Formulation of CPML
229(5)
8.1.1 PML in stretched coordinates
229(1)
8.1.2 Complex stretching variables in CFS-PML
230(1)
8.1.3 The matching conditions at the PML—PML interface
231(1)
8.1.4 Equations in the time domain
231(1)
8.1.5 Discrete convolution
231(1)
8.1.6 The recursive convolution method
232(2)
8.2 The CPML algorithm
234(3)
8.2.1 Updating equations for CPML
235(1)
8.2.2 Addition of auxiliary CPML terms at respective regions
236(1)
8.3 CPML parameter distribution
237(1)
8.4 MATLAB® implementation of CPML in the three-dimensional FDTD method
238(11)
8.4.1 Definition of CPML
239(1)
8.4.2 Initialization of CPML
240(6)
8.4.3 Application of CPML in the FDTD time-marching loop
246(3)
8.5 Simulation examples
249(15)
8.5.1 Microstrip low-pass filter
249(1)
8.5.2 Microstrip branch line coupler
250(8)
8.5.3 Characteristic impedance of a microstrip line
258(6)
8.6 CPML in the two-dimensional FDTD method
264(3)
8.7 MATLAB® implementation of CPML in the two-dimensional FDTD method
267(6)
8.7.1 Definition of CPML
268(1)
8.7.2 Initialization of CPML
268(1)
8.7.3 Application of CPML in the FDTD time-marching loop
269(2)
8.7.4 Validation of CPML performance
271(2)
8.8 Auxiliary differential equation PML
273(2)
8.8.1 Derivation of the ADE-PML formulation
273(2)
8.8.2 MATLAB® implementation of the ADE-PML formulation
275(1)
8.9 Exercises
275(4)
9 Near-field to far-field transformation 279(44)
9.1 Implementation of the surface equivalence theorem
281(4)
9.1.1 Surface equivalence theorem
281(1)
9.1.2 Equivalent surface currents in FDTD simulation
282(3)
9.1.3 Antenna on infinite ground plane
285(1)
9.2 Frequency domain near-field to far-field transformation
285(4)
9.2.1 Time-domain to frequency-domain transformation
285(1)
9.2.2 Vector potential approach
286(1)
9.2.3 Polarization of radiation field
287(2)
9.2.4 Radiation efficiency
289(1)
9.3 MATLAB® implementation of near-field to far-field transformation
289(20)
9.3.1 Definition of NF—FF parameters
289(1)
9.3.2 Initialization of NF—FF parameters
290(3)
9.3.3 NF—FF DFT during time-marching loop
293(4)
9.3.4 Postprocessing for far-field calculation
297(12)
9.4 Simulation examples
309(11)
9.4.1 Inverted-F antenna
309(6)
9.4.2 Strip-fed rectangular dielectric resonator antenna
315(5)
9.5 Exercises
320(3)
10 Thin-wire modeling 323(22)
10.1 Thin-wire formulation
323(4)
10.2 MATLAB® implementation of the thin-wire formulation
327(3)
10.3 Simulation examples
330(5)
10.3.1 Thin-wire dipole antenna
330(5)
10.4 An improved thin-wire model
335(4)
10.5 MATLAB® implementation of the improved thin-wire formulation
339(1)
10.6 Simulation example
339(2)
10.7 Exercises
341(4)
11 Scattered field formulation 345(36)
11.1 Scattered field basic equations
345(1)
11.2 The scattered field updating equations
346(4)
11.3 Expressions for the incident plane waves
350(4)
11.4 MATLAB® implementation of the scattered field formulation
354(11)
11.4.1 Definition of the incident plane wave
354(1)
11.4.2 Initialization of the incident fields
355(3)
11.4.3 Initialization of the updating coefficients
358(1)
11.4.4 Calculation of the scattered fields
359(2)
11.4.5 Postprocessing and simulation results
361(4)
11.5 Simulation examples
365(15)
11.5.1 Scattering from a dielectric sphere
365(5)
11.5.2 Scattering from a dielectric cube
370(6)
11.5.3 Reflection and transmission coefficients of a dielectric slab
376(4)
11.6 Exercises
380(1)
12 Total field/scattered field formulation 381(16)
12.1 Introduction
381(5)
12.2 MATLAB® implementation of the TF/SF formulation
386(7)
12.2.1 Definition and initialization of incident fields
386(3)
12.2.2 Updating incident fields
389(1)
12.2.3 Updating fields on both sides of the TF/SF boundary
390(3)
12.3 Simulation examples
393(3)
12.3.1 Fields in an empty problem space
394(1)
12.3.2 Scattering from a dielectric sphere
395(1)
12.4 Exercises
396(1)
13 Dispersive material modeling 397(16)
13.1 Modeling dispersive media using ADE technique
398(4)
13.1.1 Modeling Debye medium using ADE technique
398(2)
13.1.2 Modeling Lorentz medium using ADE technique
400(1)
13.1.3 Modeling Drude medium using ADE technique
401(1)
13.2 MATLAB® implementation of ADE algorithm for Lorentz medium
402(8)
13.2.1 Definition of Lorentz material parameters
402(1)
13.2.2 Material grid construction for Lorentz objects
403(3)
13.2.3 Initialization of updating coefficients
406(2)
13.2.4 Field updates in time-marching loop
408(2)
13.3 Simulation examples
410(2)
13.3.1 Scattering from a dispersive sphere
410(2)
13.4 Exercises
412(1)
14 Analysis of periodic structures 413(34)
14.1 Periodic boundary conditions
413(4)
14.2 Constant horizontal wavenumber method
417(5)
14.3 Source excitation
422(2)
14.4 Reflection and transmission coefficients
424(5)
14.4.1 TE mode reflection and transmission coefficients
425(2)
14.4.2 TM mode reflection and transmission coefficients
427(1)
14.4.3 TEM mode reflection and transmission coefficients
428(1)
14.5 MATLAB® implementation of PBC FDTD algorithm
429(13)
14.5.1 Definition of a PBC simulation
429(2)
14.5.2 Initialization of PBC
431(3)
14.5.3 PBC updates in time-marching loop
434(8)
14.6 Simulation examples
442(5)
14.6.1 Reflection and transmission coefficients of a dielectric slab
442(1)
14.6.2 Reflection and transmission coefficients of a dipole FSS
443(1)
14.6.3 Reflection and transmission coefficients of a Jarusalem-cross FSS
444(3)
15 Nonuniform grid 447(24)
15.1 Introduction
447(1)
15.2 Transition between fine and coarse grid subregions
447(5)
15.3 FDTD updating equations for the nonuniform grids
452(2)
15.4 Active and passive lumped elements
454(3)
15.5 Defining objects snapped to the electric field grid
457(1)
15.6 MATLAB® implementation of nonuniform grids
458(8)
15.6.1 Definition of subregions
459(1)
15.6.2 Initialization of subregions
460(4)
15.6.3 Initialization of updating coefficients
464(2)
15.6.4 Initialization of time step duration
466(1)
15.7 Simulation examples
466(5)
15.7.1 Microstrip patch antenna
466(1)
15.7.2 Three-pole microstrip low-pass filter
467(4)
16 Graphics processing unit acceleration of finite-difference time-domain method 471(20)
16.1 GPU programming using CUDA
472(5)
16.1.1 Host and device
472(2)
16.1.2 Thread hierarchy
474(2)
16.1.3 Memory hierarchy
476(1)
16.1.4 Performance optimization in CUDA
477(1)
16.1.5 Achieving parallelism
477(1)
16.2 CUDA implementation of two-dimensional FDTD
477(10)
16.2.1 Coalesced global memory access
479(2)
16.2.2 Thread to cell mapping
481(5)
16.2.3 Use of shared memory
486(1)
16.2.4 Optimization of number of threads
487(1)
16.3 Performance of two-dimensional FDTD on CUDA
487(4)
Appendix A One-dimensional FDTD code 491(4)
Appendix B Convolutional perfectly-matched layer regions and associated field updates for three-dimensional domain 495(10)
Appendix C MATLAB® code for plotting far-field patterns 505(4)
Appendix D MATLAB® GUI for project template 509(2)
References 511(8)
About the authors 519(4)
Index 523
Atef Z. Elsherbeni is a distinguished chair professor and interim department head of the Electrical Engineering and Computer Science Department at Colorado School of Mines. His research interests include the scattering and diffraction of EM waves, finite-difference time-domain analysis of antennas and microwave devices, field visualization and software development for EM education, interactions of electromagnetic waves with the human body, RFID and sensor integrated FRID systems, reflector and printed antennas and antenna arrays, and measurement of antenna characteristics and material properties. Dr Elsherbeni is a Fellow of IEEE and ACES, and Editor-in-Chief for ACES Journal. He was the General Chair for the 2014 APS-URSI Symposium and was the President of ACES Society from 2013 to 2015.



Veysel Demir is an Associate Professor at the Department of Electrical Engineering at Northern Illinois University. His main field of research is electromagnetics and microwaves, and he is especially experienced in applied computational electromagnetics. He heavily participated in the development of time-domain and frequency-domain numerical analysis tools for new applications and contributed to research on improving the accuracy and speed of the algorithms being developed. He is experienced in designing RF/microwave circuits and antennas for the related technologies, and performing experimental characterizations of these devices. Dr Demir is a member of IEEE, ACES, and SigmaXi, has co-authored more than 50 technical journal and conference papers, and served as a technical program co-chair for the 2014 IEEE International Symposium on Antennas and Propagation and USNC-URSI Radio Science Meeting and for the ACES 2015 conference.
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