Electromagnetic Simulation
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can someone help me to access IEEE papers? I need Kane S. Yee
Numerical solution of initial boundary value problems involvin maxwells equations in isotrpic media IEEE Trans. Antennas and Propagation vol.14,1966 pp 302-307
its table of contents is
1 Notations and Mathematical Preliminaries 1
1.1 Notations and Abbreviations 1
1.2 Mathematical Preliminaries 2
1.2.1 Functions and Integration 2
1.2.2 The Fourier Transform 4
1.2.3 Regularity 4
1.2.4 Linear Spaces 7
1.2.5 Functional Spaces 8
1.2.6 Sobolev Spaces 10
1.2.7 Bases in Hilbert Space H 11
1.2.8 Linear Operators 12
Bibliography 14
2 Intuitive Introduction to Wavelets 15
2.1 Technical History and Background 15
2.1.1 Historical Development 15
2.1.2 When Do Wavelets Work? 16
2.1.3 A Wave Is a Wave but What Is a Wavelet? 17
2.2 What Can Wavelets Do in Electromagnetics and
Device Modeling? 18
2.2.1 Potential Benefits of Using Wavelets 18
2.2.2 Limitations and Future Direction of Wavelets 19
2.3 The Haar Wavelets and Multiresolution Analysis 20
2.4 How Do Wavelets Work? 23
Bibliography 28
3 Basic Orthogonal Wavelet Theory 30
3.1 Multiresolution Analysis 30
3.2 Construction of Scalets ϕ(τ) 32
3.2.1 Franklin Scalet 32
3.2.2 Battle–Lemarie Scalets 39
3.2.3 Preliminary Properties of Scalets 40
3.3 Wavelet ψ(τ) 42
3.4 Franklin Wavelet 48
3.5 Properties of Scalets ϕˆ(ω) 51
3.6 Daubechies Wavelets 56
3.7 Coifman Wavelets (Coiflets) 64
3.8 Constructing Wavelets by Recursion and Iteration 69
3.8.1 Construction of Scalets 69
3.8.2 Construction of Wavelets 74
3.9 Meyer Wavelets 75
3.9.1 Basic Properties of Meyer Wavelets 75
3.9.2 Meyer Wavelet Family 83
3.9.3 Other Examples of Meyer Wavelets 92
3.10 Mallat’s Decomposition and Reconstruction 92
3.10.1 Reconstruction 92
3.10.2 Decomposition 93
3.11 Problems 95
3.11.1 Exercise 1 95
3.11.2 Exercise 2 95
3.11.3 Exercise 3 97
3.11.4 Exercise 4 97
Bibliography 98
4 Wavelets in Boundary Integral Equations 100
4.1 Wavelets in Electromagnetics 100
4.2 Linear Operators 102
4.3 Method of Moments (MoM) 103
4.4 Functional Expansion of a Given Function 107
4.5 Operator Expansion: Nonstandard Form 110
4.5.1 Operator Expansion in Haar Wavelets 111
4.5.2 Operator Expansion in General Wavelet Systems 113
4.5.3 Numerical Example 114
4.6 Periodic Wavelets 120
4.6.1 Construction of Periodic Wavelets 120
4.6.2 Properties of Periodic Wavelets 123
4.6.3 Expansion of a Function in Periodic Wavelets 127
4.7 Application of Periodic Wavelets: 2D Scattering 128
4.8 Fast Wavelet Transform (FWT) 133
4.8.1 Discretization of Operation Equations 133
4.8.2 Fast Algorithm 134
4.8.3 Matrix Sparsification Using FWT 135
4.9 Applications of the FWT 140
4.9.1 Formulation 140
4.9.2 Circuit Parameters 141
4.9.3 Integral Equations and Wavelet Expansion 143
4.9.4 Numerical Results 144
4.10 Intervallic Coifman Wavelets 144
4.10.1 Intervallic Scalets 145
4.10.2 Intervallic Wavelets on [0, 1] 154
4.11 Lifting Scheme and Lazy Wavelets 156
4.11.1 Lazy Wavelets 156
4.11.2 Lifting Scheme Algorithm 157
4.11.3 Cascade Algorithm 159
4.12 Green’s Scalets and Sampling Series 159
4.12.1 Ordinary Differential Equations (ODEs) 160
4.12.2 Partial Differential Equations (PDEs) 166
4.13 Appendix: Derivation of Intervallic Wavelets on [0, 1] 172
4.14 Problems 185
4.14.1 Exercise 5 185
4.14.2 Exercise 6 185
4.14.3 Exercise 7 185
4.14.4 Exercise 8 186
4.14.5 Project 1 187
Bibliography 187
5 Sampling Biorthogonal Time Domain Method (SBTD) 189
5.1 Basis FDTD Formulation 189
5.2 Stability Analysis for the FDTD 194
5.3 FDTD as Maxwell’s Equations with Haar Expansion 198
5.4 FDTD with Battle–Lemarie Wavelets 201
5.5 Positive Sampling and Biorthogonal Testing Functions 205
5.6 Sampling Biorthogonal Time Domain Method 215
5.6.1 SBTD versus MRTD 215
5.6.2 Formulation 215
5.7 Stability Conditions for Wavelet-Based Methods 219
5.7.1 Dispersion Relation and Stability Analysis 219
5.7.2 Stability Analysis for the SBTD 222
5.8 Convergence Analysis and Numerical Dispersion 223
5.8.1 Numerical Dispersion 223
5.8.2 Convergence Analysis 225
5.9 Numerical Examples 228
5.10 Appendix: Operator Form of the MRTD 233
5.11 Problems 236
5.11.1 Exercise 9 236
5.11.2 Exercise 10 237
5.11.3 Project 2 237
Bibliography 238
6 Canonical Multiwavelets 240
6.1 Vector-Matrix Dilation Equation 240
6.2 Time Domain Approach 242
6.3 Construction of Multiscalets 245
6.4 Orthogonal Multiwavelets ￠ ψ(t) 255
6.5 Intervallic Multiwavelets ψ(t) 258
6.6 Multiwavelet Expansion 261
6.7 Intervallic Dual Multiwavelets ˜ ψ(t ) 264
6.8 Working Examples 269
6.9 Multiscalet-Based 1D Finite Element Method (FEM) 276
6.10 Multiscalet-Based Edge Element Method 280
6.11 Spurious Modes 285
6.12 Appendix 287
6.13 Problems 296
6.13.1 Exercise 11 296
Bibliography 297
7 Wavelets in Scattering and Radiation 299
7.1 Scattering from a 2D Groove 299
7.1.1 Method of Moments (MoM) Formulation 300
7.1.2 Coiflet-Based MoM 304
7.1.3 Bi-CGSTAB Algorithm 305
7.1.4 Numerical Results 305
7.2 2D and 3D Scattering Using Intervallic Coiflets 309
7.2.1 Intervallic Scalets on [0, 1] 309
7.2.2 Expansion in Coifman IntervallicWavelets 312
7.2.3 Numerical Integration and Error Estimate 313
7.2.4 Fast Construction of Impedance Matrix 317
7.2.5 Conducting Cylinders, TM Case 319
7.2.6 Conducting Cylinders with Thin Magnetic Coating 322
7.2.7 Perfect Electrically Conducting (PEC) Spheroids 324
7.3 Scattering and Radiation of Curved Thin Wires 329
7.3.1 Integral Equation for Curved Thin-Wire Scatterers
and Antennae 330
7.3.2 Numerical Examples 331
7.4 Smooth Local Cosine (SLC) Method 340
7.4.1 Construction of Smooth Local Cosine Basis 341
7.4.2 Formulation of 2D Scattering Problems 344
7.4.3 SLC-Based Galerkin Procedure and Numerical Results 347
7.4.4 Application of the SLC to Thin-Wire Scatterers
and Antennas 355
7.5 Microstrip Antenna Arrays 357
7.5.1 Impedance Matched Source 358
7.5.2 Far-Zone Fields and Antenna Patterns 360
Bibliography 363
8 Wavelets in Rough Surface Scattering 366
8.1 Scattering of EM Waves from Randomly Rough Surfaces 366
8.2 Generation of Random Surfaces 368
8.2.1 Autocorrelation Method 370
8.2.2 Spectral Domain Method 373
8.3 2D Rough Surface Scattering 376
8.3.1 Moment Method Formulation of 2D Scattering 376
8.3.2 Wavelet-Based Galerkin Method for 2D Scattering 380
8.3.3 Numerical Results of 2D Scattering 381
8.4 3D Rough Surface Scattering 387
8.4.1 Tapered Wave of Incidence 388
8.4.2 Formulation of 3D Rough Surface Scattering
Using Wavelets 391
8.4.3 Numerical Results of 3D Scattering 394
Bibliography 399
9 Wavelets in Packaging, Interconnects, and EMC 401
9.1 Quasi-static Spatial Formulation 402
9.1.1 What Is Quasi-static? 402
9.1.2 Formulation 403
9.1.3 Orthogonal Wavelets in L2([0, 1]) 406
9.1.4 Boundary Element Method and Wavelet Expansion 408
9.1.5 Numerical Examples 412
9.2 Spatial Domain Layered Green’s Functions 415
9.2.1 Formulation 417
9.2.2 Prony’s Method 423
9.2.3 Implementation of the Coifman Wavelets 424
9.2.4 Numerical Examples 426
9.3 Skin-Effect Resistance and Total Inductance 429
9.3.1 Formulation 431
9.3.2 Moment Method Solution of Coupled Integral Equations 433
9.3.3 Circuit Parameter Extraction 435
9.3.4 Wavelet Implementation 437
9.3.5 Measurement and Simulation Results 438
9.4 Spectral Domain Green’s Function-Based Full-Wave Analysis 440
9.4.1 Basic Formulation 440
9.4.2 Wavelet Expansion and Matrix Equation 444
9.4.3 Evaluation of Sommerfeld-Type Integrals 447
9.4.4 Numerical Results and Sparsity of Impedance Matrix 451
9.4.5 Further Improvements 455
9.5 Full-Wave Edge Element Method for 3D Lossy Structures 455
9.5.1 Formulation of Asymmetric Functionals with Truncation
Conditions 456
9.5.2 Edge Element Procedure 460
9.5.3 Excess Capacitance and Inductance 464
9.5.4 Numerical Examples 466
Bibliography 469
10 Wavelets in Nonlinear Semiconductor Devices 474
10.1 Physical Models and Computational Efforts 474
10.2 An Interpolating Subdivision Scheme 476
10.3 The Sparse Point Representation (SPR) 478
10.4 Interpolation Wavelets in the FDM 479
10.4.1 1D Example of the SPR Application 480
10.4.2 2D Example of the SPR Application 481
10.5 The Drift-Diffusion Model 484
10.5.1 Scaling 486
10.5.2 Discretization 487
10.5.3 Transient Solution 489
10.5.4 Grid Adaptation and InterpolatingWavelets 490
10.5.5 Numerical Results 492
10.6 Multiwavelet Based Drift-Diffusion Model 498
10.6.1 Precision and Stability versus Reynolds 499
10.6.2 MWFEM-Based 1D Simulation 502
10.7 The Boltzmann Transport Equation (BTE) Model 504
10.7.1 Why BTE? 505
10.7.2 Spherical Harmonic Expansion of the BTE 505
10.7.3 Arbitrary Order Expansion and Galerkin’s Procedure 509
10.7.4 The Coupled Boltzmann–Poisson System 515
10.7.5 Numerical Results 517
Bibliography 524
Index 527
Preface
Applied mathematics has made considerable progress in wavelets. In recent years
interest in wavelets has grown at a steady rate, and applications of wavelets are expanding rapidly. A virtual flood of engineers, with little mathematical sophistication, is about to enter the field of wavelets. Although more than 100 books on wavelets have been published since 1992, there is still a large gap between the mathematician’s rigor and the engineer’s interest. The present book is intended to bridge this gap between mathematical theory and engineering applications.
In an attempt to exploit the advantages of wavelets, the book covers basic wavelet
principles from an engineer’s point of view. With a minimum number of theorems
and proofs, the book focuses on providing physical insight rather than rigorous mathematical presentations. As a result the subject matter is developed and presented in a more basic and familiar way for engineers with a background in electromagnetics, including linear algebra, Fourier analysis, sampling function of sin πx/πx, Dirac δ function, Green’s functions, and so on. The multiresolution analysis (MRA) is naturally delivered in Chapter 2 as a basic introduction that shows a signal decomposed into several resolution levels. Each level can be processed according to the requirement of the application. The application of MRA lies within the Mallat decomposition and reconstruction algorithm. MRA is further explained in a fast wavelet transform section with an example of frequency-dependent transmission lines. Mathematically elegant proofs and derivations are presented in a smaller font if their content is beyond the engineering requirement. Readers with no time or interest in this depth of mathematics may always skip the paragraphs or sections written in smaller font without jeopardizing their understanding of the main subjects.
The main body of the book came from conference presentations, including the
IEEE Microwave Theory and Techniques Symposium (IEEE-MTT), IEEE Antennas
and Propagation (IEEE-AP), Radio Science (URSI), IEEE Magnetics, Progress in
Electromagnetic Research Symposium (PIERS), Electromagnetic and Light Scattering (ELS), COMPUMAG, Conference on Electromagnetic Field Computation
(CEFC), Association for Computational Electromagnetic Society (ACES), International Conference on Microwave and Millimeter Wave Technology (ICMTT), and International Conference on Computational Electromagnetics and its Applications (ICCEA). The book has evolved from curricula taught at the graduate level in the Department of Electronic Engineering at Canterbury University (Christchurch, New Zealand) and Arizona State University. The material was taught as short courses at MoscowState University, CSIRO(Sydney, Australia), IEEE Microwave Theory and Techniques Symposium, Beijing University, Aerospace 207 Institute, and the 3rd Institute of China. The participants in these courses were electrical engineering and computer science students as well as practicing engineers in industry. These people had little or no prior knowledge of wavelets. The book may serve as a reference book for engineers, practicing scientists, and other professionals. Real-world state-of-the-art issues are extensively discussed, including full-wave modeling of coupled lossy and dispersive transmission lines, scattering of electromagnetic waves from 2D/3D bodies and from randomly rough surfaces, radiation from linear and patch antennas, and modeling of 2D semiconductor devices. The book can also be used as a textbook, as it contains questions, working examples, and 11 exercise assignments with a solution manual. It has been used several times in teaching a one-semester graduate course in electrical engineering.
The book consists of 10 chapters. The first six chapters are dedicated to basic
theory and training, followed by four chapters in real-world applications. Chapter
1 summarizes mathematical preliminaries, which may be skipped on the first
reading. Chapter 2 provides some background and theoretical insights. Chapter 3
covers the basic orthogonal wavelet theory. Other wavelet topics are discussed in
Chapters 4 through 10, including biorthogonal wavelets, weighted wavelets, interpolating wavelets, Green’s wavelets, and multiwavelets. Chapter 4 presents applications of wavelets in solving integral equations. Special treatments of edges are discussed here, including periodic wavelets and intervallic wavelets. Chapter 5 derives the positive sampling functions and their biorthogonal counterparts using Daubechies wavelets. Many advantages derive from the use of the sampling biorthogonal time domain (SBTD) method to replace the finite difference time domain (FDTD) scheme. Chapter 6 studies multiwavelet theory, including biorthogonal and orthogonal multiwavelets with applications in the edge-based finite element method (EEM).
Advanced topics are presented in Chapter 7, 8, and 9, respectively, for scattering and radiation, 3D rough surface scattering, packaging and interconnects. Chapter 10 is devoted to semiconductor device modeling using the aforementioned knowledge of wavelets. Numerical procedures are fully detailed so as to help interested readers develop their own algorithms and computer codes.
Numerical solution of initial boundary value problems involvin maxwells equations in isotrpic media IEEE Trans. Antennas and Propagation vol.14,1966 pp 302-307
Numerical solution of inital boundary value problems involving maxwell's equations in isotropic media
do you know that some authors now use the wavelet in electromagnetic? see this book title:
Wavelets in Electromagnetics and Device Modeling
GEORGE W. PAN
Arizona State University
Tempe, Arizona
A JOHN WILEY & SONS PUBLICATION
Copyright c 2003 by John Wiley & Sons, Inc. All rights reserved.
you can download it from www.4shared.com
its front cover is shown below:
its table of contents is
1 Notations and Mathematical Preliminaries 1
1.1 Notations and Abbreviations 1
1.2 Mathematical Preliminaries 2
1.2.1 Functions and Integration 2
1.2.2 The Fourier Transform 4
1.2.3 Regularity 4
1.2.4 Linear Spaces 7
1.2.5 Functional Spaces 8
1.2.6 Sobolev Spaces 10
1.2.7 Bases in Hilbert Space H 11
1.2.8 Linear Operators 12
Bibliography 14
2 Intuitive Introduction to Wavelets 15
2.1 Technical History and Background 15
2.1.1 Historical Development 15
2.1.2 When Do Wavelets Work? 16
2.1.3 A Wave Is a Wave but What Is a Wavelet? 17
2.2 What Can Wavelets Do in Electromagnetics and
Device Modeling? 18
2.2.1 Potential Benefits of Using Wavelets 18
2.2.2 Limitations and Future Direction of Wavelets 19
2.3 The Haar Wavelets and Multiresolution Analysis 20
2.4 How Do Wavelets Work? 23
Bibliography 28
3 Basic Orthogonal Wavelet Theory 30
3.1 Multiresolution Analysis 30
3.2 Construction of Scalets ϕ(τ) 32
3.2.1 Franklin Scalet 32
3.2.2 Battle–Lemarie Scalets 39
3.2.3 Preliminary Properties of Scalets 40
3.3 Wavelet ψ(τ) 42
3.4 Franklin Wavelet 48
3.5 Properties of Scalets ϕˆ(ω) 51
3.6 Daubechies Wavelets 56
3.7 Coifman Wavelets (Coiflets) 64
3.8 Constructing Wavelets by Recursion and Iteration 69
3.8.1 Construction of Scalets 69
3.8.2 Construction of Wavelets 74
3.9 Meyer Wavelets 75
3.9.1 Basic Properties of Meyer Wavelets 75
3.9.2 Meyer Wavelet Family 83
3.9.3 Other Examples of Meyer Wavelets 92
3.10 Mallat’s Decomposition and Reconstruction 92
3.10.1 Reconstruction 92
3.10.2 Decomposition 93
3.11 Problems 95
3.11.1 Exercise 1 95
3.11.2 Exercise 2 95
3.11.3 Exercise 3 97
3.11.4 Exercise 4 97
Bibliography 98
4 Wavelets in Boundary Integral Equations 100
4.1 Wavelets in Electromagnetics 100
4.2 Linear Operators 102
4.3 Method of Moments (MoM) 103
4.4 Functional Expansion of a Given Function 107
4.5 Operator Expansion: Nonstandard Form 110
4.5.1 Operator Expansion in Haar Wavelets 111
4.5.2 Operator Expansion in General Wavelet Systems 113
4.5.3 Numerical Example 114
4.6 Periodic Wavelets 120
4.6.1 Construction of Periodic Wavelets 120
4.6.2 Properties of Periodic Wavelets 123
4.6.3 Expansion of a Function in Periodic Wavelets 127
4.7 Application of Periodic Wavelets: 2D Scattering 128
4.8 Fast Wavelet Transform (FWT) 133
4.8.1 Discretization of Operation Equations 133
4.8.2 Fast Algorithm 134
4.8.3 Matrix Sparsification Using FWT 135
4.9 Applications of the FWT 140
4.9.1 Formulation 140
4.9.2 Circuit Parameters 141
4.9.3 Integral Equations and Wavelet Expansion 143
4.9.4 Numerical Results 144
4.10 Intervallic Coifman Wavelets 144
4.10.1 Intervallic Scalets 145
4.10.2 Intervallic Wavelets on [0, 1] 154
4.11 Lifting Scheme and Lazy Wavelets 156
4.11.1 Lazy Wavelets 156
4.11.2 Lifting Scheme Algorithm 157
4.11.3 Cascade Algorithm 159
4.12 Green’s Scalets and Sampling Series 159
4.12.1 Ordinary Differential Equations (ODEs) 160
4.12.2 Partial Differential Equations (PDEs) 166
4.13 Appendix: Derivation of Intervallic Wavelets on [0, 1] 172
4.14 Problems 185
4.14.1 Exercise 5 185
4.14.2 Exercise 6 185
4.14.3 Exercise 7 185
4.14.4 Exercise 8 186
4.14.5 Project 1 187
Bibliography 187
5 Sampling Biorthogonal Time Domain Method (SBTD) 189
5.1 Basis FDTD Formulation 189
5.2 Stability Analysis for the FDTD 194
5.3 FDTD as Maxwell’s Equations with Haar Expansion 198
5.4 FDTD with Battle–Lemarie Wavelets 201
5.5 Positive Sampling and Biorthogonal Testing Functions 205
5.6 Sampling Biorthogonal Time Domain Method 215
5.6.1 SBTD versus MRTD 215
5.6.2 Formulation 215
5.7 Stability Conditions for Wavelet-Based Methods 219
5.7.1 Dispersion Relation and Stability Analysis 219
5.7.2 Stability Analysis for the SBTD 222
5.8 Convergence Analysis and Numerical Dispersion 223
5.8.1 Numerical Dispersion 223
5.8.2 Convergence Analysis 225
5.9 Numerical Examples 228
5.10 Appendix: Operator Form of the MRTD 233
5.11 Problems 236
5.11.1 Exercise 9 236
5.11.2 Exercise 10 237
5.11.3 Project 2 237
Bibliography 238
6 Canonical Multiwavelets 240
6.1 Vector-Matrix Dilation Equation 240
6.2 Time Domain Approach 242
6.3 Construction of Multiscalets 245
6.4 Orthogonal Multiwavelets ￠ ψ(t) 255
6.5 Intervallic Multiwavelets ψ(t) 258
6.6 Multiwavelet Expansion 261
6.7 Intervallic Dual Multiwavelets ˜ ψ(t ) 264
6.8 Working Examples 269
6.9 Multiscalet-Based 1D Finite Element Method (FEM) 276
6.10 Multiscalet-Based Edge Element Method 280
6.11 Spurious Modes 285
6.12 Appendix 287
6.13 Problems 296
6.13.1 Exercise 11 296
Bibliography 297
7 Wavelets in Scattering and Radiation 299
7.1 Scattering from a 2D Groove 299
7.1.1 Method of Moments (MoM) Formulation 300
7.1.2 Coiflet-Based MoM 304
7.1.3 Bi-CGSTAB Algorithm 305
7.1.4 Numerical Results 305
7.2 2D and 3D Scattering Using Intervallic Coiflets 309
7.2.1 Intervallic Scalets on [0, 1] 309
7.2.2 Expansion in Coifman IntervallicWavelets 312
7.2.3 Numerical Integration and Error Estimate 313
7.2.4 Fast Construction of Impedance Matrix 317
7.2.5 Conducting Cylinders, TM Case 319
7.2.6 Conducting Cylinders with Thin Magnetic Coating 322
7.2.7 Perfect Electrically Conducting (PEC) Spheroids 324
7.3 Scattering and Radiation of Curved Thin Wires 329
7.3.1 Integral Equation for Curved Thin-Wire Scatterers
and Antennae 330
7.3.2 Numerical Examples 331
7.4 Smooth Local Cosine (SLC) Method 340
7.4.1 Construction of Smooth Local Cosine Basis 341
7.4.2 Formulation of 2D Scattering Problems 344
7.4.3 SLC-Based Galerkin Procedure and Numerical Results 347
7.4.4 Application of the SLC to Thin-Wire Scatterers
and Antennas 355
7.5 Microstrip Antenna Arrays 357
7.5.1 Impedance Matched Source 358
7.5.2 Far-Zone Fields and Antenna Patterns 360
Bibliography 363
8 Wavelets in Rough Surface Scattering 366
8.1 Scattering of EM Waves from Randomly Rough Surfaces 366
8.2 Generation of Random Surfaces 368
8.2.1 Autocorrelation Method 370
8.2.2 Spectral Domain Method 373
8.3 2D Rough Surface Scattering 376
8.3.1 Moment Method Formulation of 2D Scattering 376
8.3.2 Wavelet-Based Galerkin Method for 2D Scattering 380
8.3.3 Numerical Results of 2D Scattering 381
8.4 3D Rough Surface Scattering 387
8.4.1 Tapered Wave of Incidence 388
8.4.2 Formulation of 3D Rough Surface Scattering
Using Wavelets 391
8.4.3 Numerical Results of 3D Scattering 394
Bibliography 399
9 Wavelets in Packaging, Interconnects, and EMC 401
9.1 Quasi-static Spatial Formulation 402
9.1.1 What Is Quasi-static? 402
9.1.2 Formulation 403
9.1.3 Orthogonal Wavelets in L2([0, 1]) 406
9.1.4 Boundary Element Method and Wavelet Expansion 408
9.1.5 Numerical Examples 412
9.2 Spatial Domain Layered Green’s Functions 415
9.2.1 Formulation 417
9.2.2 Prony’s Method 423
9.2.3 Implementation of the Coifman Wavelets 424
9.2.4 Numerical Examples 426
9.3 Skin-Effect Resistance and Total Inductance 429
9.3.1 Formulation 431
9.3.2 Moment Method Solution of Coupled Integral Equations 433
9.3.3 Circuit Parameter Extraction 435
9.3.4 Wavelet Implementation 437
9.3.5 Measurement and Simulation Results 438
9.4 Spectral Domain Green’s Function-Based Full-Wave Analysis 440
9.4.1 Basic Formulation 440
9.4.2 Wavelet Expansion and Matrix Equation 444
9.4.3 Evaluation of Sommerfeld-Type Integrals 447
9.4.4 Numerical Results and Sparsity of Impedance Matrix 451
9.4.5 Further Improvements 455
9.5 Full-Wave Edge Element Method for 3D Lossy Structures 455
9.5.1 Formulation of Asymmetric Functionals with Truncation
Conditions 456
9.5.2 Edge Element Procedure 460
9.5.3 Excess Capacitance and Inductance 464
9.5.4 Numerical Examples 466
Bibliography 469
10 Wavelets in Nonlinear Semiconductor Devices 474
10.1 Physical Models and Computational Efforts 474
10.2 An Interpolating Subdivision Scheme 476
10.3 The Sparse Point Representation (SPR) 478
10.4 Interpolation Wavelets in the FDM 479
10.4.1 1D Example of the SPR Application 480
10.4.2 2D Example of the SPR Application 481
10.5 The Drift-Diffusion Model 484
10.5.1 Scaling 486
10.5.2 Discretization 487
10.5.3 Transient Solution 489
10.5.4 Grid Adaptation and InterpolatingWavelets 490
10.5.5 Numerical Results 492
10.6 Multiwavelet Based Drift-Diffusion Model 498
10.6.1 Precision and Stability versus Reynolds 499
10.6.2 MWFEM-Based 1D Simulation 502
10.7 The Boltzmann Transport Equation (BTE) Model 504
10.7.1 Why BTE? 505
10.7.2 Spherical Harmonic Expansion of the BTE 505
10.7.3 Arbitrary Order Expansion and Galerkin’s Procedure 509
10.7.4 The Coupled Boltzmann–Poisson System 515
10.7.5 Numerical Results 517
Bibliography 524
Index 527
Preface
Applied mathematics has made considerable progress in wavelets. In recent years
interest in wavelets has grown at a steady rate, and applications of wavelets are expanding rapidly. A virtual flood of engineers, with little mathematical sophistication, is about to enter the field of wavelets. Although more than 100 books on wavelets have been published since 1992, there is still a large gap between the mathematician’s rigor and the engineer’s interest. The present book is intended to bridge this gap between mathematical theory and engineering applications.
In an attempt to exploit the advantages of wavelets, the book covers basic wavelet
principles from an engineer’s point of view. With a minimum number of theorems
and proofs, the book focuses on providing physical insight rather than rigorous mathematical presentations. As a result the subject matter is developed and presented in a more basic and familiar way for engineers with a background in electromagnetics, including linear algebra, Fourier analysis, sampling function of sin πx/πx, Dirac δ function, Green’s functions, and so on. The multiresolution analysis (MRA) is naturally delivered in Chapter 2 as a basic introduction that shows a signal decomposed into several resolution levels. Each level can be processed according to the requirement of the application. The application of MRA lies within the Mallat decomposition and reconstruction algorithm. MRA is further explained in a fast wavelet transform section with an example of frequency-dependent transmission lines. Mathematically elegant proofs and derivations are presented in a smaller font if their content is beyond the engineering requirement. Readers with no time or interest in this depth of mathematics may always skip the paragraphs or sections written in smaller font without jeopardizing their understanding of the main subjects.
The main body of the book came from conference presentations, including the
IEEE Microwave Theory and Techniques Symposium (IEEE-MTT), IEEE Antennas
and Propagation (IEEE-AP), Radio Science (URSI), IEEE Magnetics, Progress in
Electromagnetic Research Symposium (PIERS), Electromagnetic and Light Scattering (ELS), COMPUMAG, Conference on Electromagnetic Field Computation
(CEFC), Association for Computational Electromagnetic Society (ACES), International Conference on Microwave and Millimeter Wave Technology (ICMTT), and International Conference on Computational Electromagnetics and its Applications (ICCEA). The book has evolved from curricula taught at the graduate level in the Department of Electronic Engineering at Canterbury University (Christchurch, New Zealand) and Arizona State University. The material was taught as short courses at MoscowState University, CSIRO(Sydney, Australia), IEEE Microwave Theory and Techniques Symposium, Beijing University, Aerospace 207 Institute, and the 3rd Institute of China. The participants in these courses were electrical engineering and computer science students as well as practicing engineers in industry. These people had little or no prior knowledge of wavelets. The book may serve as a reference book for engineers, practicing scientists, and other professionals. Real-world state-of-the-art issues are extensively discussed, including full-wave modeling of coupled lossy and dispersive transmission lines, scattering of electromagnetic waves from 2D/3D bodies and from randomly rough surfaces, radiation from linear and patch antennas, and modeling of 2D semiconductor devices. The book can also be used as a textbook, as it contains questions, working examples, and 11 exercise assignments with a solution manual. It has been used several times in teaching a one-semester graduate course in electrical engineering.
The book consists of 10 chapters. The first six chapters are dedicated to basic
theory and training, followed by four chapters in real-world applications. Chapter
1 summarizes mathematical preliminaries, which may be skipped on the first
reading. Chapter 2 provides some background and theoretical insights. Chapter 3
covers the basic orthogonal wavelet theory. Other wavelet topics are discussed in
Chapters 4 through 10, including biorthogonal wavelets, weighted wavelets, interpolating wavelets, Green’s wavelets, and multiwavelets. Chapter 4 presents applications of wavelets in solving integral equations. Special treatments of edges are discussed here, including periodic wavelets and intervallic wavelets. Chapter 5 derives the positive sampling functions and their biorthogonal counterparts using Daubechies wavelets. Many advantages derive from the use of the sampling biorthogonal time domain (SBTD) method to replace the finite difference time domain (FDTD) scheme. Chapter 6 studies multiwavelet theory, including biorthogonal and orthogonal multiwavelets with applications in the edge-based finite element method (EEM).
Advanced topics are presented in Chapter 7, 8, and 9, respectively, for scattering and radiation, 3D rough surface scattering, packaging and interconnects. Chapter 10 is devoted to semiconductor device modeling using the aforementioned knowledge of wavelets. Numerical procedures are fully detailed so as to help interested readers develop their own algorithms and computer codes.