Wavelets in Electromagnetics and Device Modeling

✍ Scribed by George W. Pan

• Publisher: Wiley-IEEE Press
• Year: 2003
• Tongue: English
• Leaves: 553
• Series: Wiley Series in Microwave and Optical Engineering
• Category: Library

✦ Synopsis

Wavelet theory is new to mathematics and has wide applications in science engineering. Because it has the potential to become an important tool in electronic applications such as packaging, interconnections, antenna theory, and wireless communications, engineers are preparing to enter the field in a virtual flood.

While wavelets have been extensively covered from a mathematician's point of view, this timely text bridges the gap between mathematical theory and engineering applications to help engineers exploit the advantages of wavelets.

Equally valuable as a beginning engineer's guide or as a reference for experienced engineers and scientists, Wavelets in Electromagnetics and Device Modeling offers a quick introduction to the basics of wavelets and then, without overly complex or abstract mathematics, outlines applications of wavelets in real-world engineering problems. Aspects of wavelet theory covered include:
* Basic orthogonal wavelet theory, biorthogonal wavelets, weighted wavelets, interpolating wavelets, Green's wavelets, and multiwavelets
* Special treatment of edges including the periodic wavelets, intervallic wavelets, and Malvar wavelets for the method of moments (MoM)
* Derivation of positive sampling functions and their biorthogonal counterparts employing Daubechies wavelets
* Using the sampling biorthogonal time domain (SBTD) method to improve the finite difference time domain (FDTD) scheme
* Applications in the edge-based finite element method (EEM)
* Advanced topics such as scattering and radiation, 3-D rough surface scattering, packaging, and interconnects
* Semiconductor device modeling using wavelets

Other valuable features of the book include detailed discussions of numerical procedures to help engineers develop their own algorithms and computer codes. Providing physical insight rather than rigorous mathematics, Wavelets in Electromagnetics and Device Modeling will launch engineers into the emerging new field of wavelets and their exciting new applications.

• The first book on the subject.
• Written by an acknowledged expert in the field.
• The techniques discussed have important applications to wireless engineering.
• An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.  

✦ Table of Contents

Wavelets in
Electromagnetics
and Device Modeling......Page 4
Copyright......Page 5
Contents......Page 8
Preface......Page 16
ACKNOWLEDGMENTS......Page 17
1.1 NOTATIONS AND ABBREVIATIONS......Page 20
1.2.1 Functions and Integration......Page 21
1.2.3 Regularity......Page 23
1.2.4 Linear Spaces......Page 26
1.2.5 Functional Spaces......Page 27
1.2.6 Sobolev Spaces......Page 29
1.2.7 Bases in Hilbert Space H......Page 30
1.2.8 Linear Operators......Page 31
BIBLIOGRAPHY......Page 33
2.1.1 Historical Development......Page 34
2.1.2 When Do Wavelets Work?......Page 35
2.1.3 A Wave Is a Wave but What Is a Wavelet?......Page 36
2.2.1 Potential Bene . ts of Using Wavelets......Page 37
2.2.2 Limitations and Future Direction of Wavelets......Page 38
2.3 THE HAAR WAVELETS AND MULTIRESOLUTION ANALYSIS......Page 39
2.4 HOW DO WAVELETS WORK?......Page 42
BIBLIOGRAPHY......Page 47
3.1 MULTIRESOLUTION ANALYSIS......Page 49
3.2.1 Franklin Scalet......Page 51
3.2.2 Battle ¨C Lemarie Scalets......Page 58
3.2.3 Preliminary Properties of Scalets......Page 59
3.3 WAVELET ¦×( ¦Ó)......Page 61
3.4 FRANKLIN WAVELET......Page 67
3.5 PROPERTIES OF SCALETS .( . ¦Ø)......Page 70
3.6 DAUBECHIES WAVELETS......Page 75
3.7 COIFMAN WAVELETS ( COIFLETS)......Page 83
3.8.1 Construction of Scalets......Page 88
3.8.2 Construction of Wavelets......Page 93
3.9.1 Basic Properties of Meyer Wavelets......Page 94
3.9.2 Meyer Wavelet Family......Page 102
3.10.1 Reconstruction......Page 111
3.10.2 Decomposition......Page 112
3.11.2 Exercise 2......Page 114
3.11.4 Exercise 4......Page 116
BIBLIOGRAPHY......Page 117
4.1 WAVELETS IN ELECTROMAGNETICS......Page 119
4.2 LINEAR OPERATORS......Page 121
4.3 METHOD OF MOMENTS ( MoM)......Page 122
4.4 FUNCTIONAL EXPANSION OF A GIVEN FUNCTION......Page 126
4.5 OPERATOR EXPANSION: NONSTANDARD FORM......Page 129
4.5.1 Operator Expansion in Haar Wavelets......Page 130
4.5.2 Operator Expansion in General Wavelet Systems......Page 132
4.5.3 Numerical Example......Page 133
4.6.1 Construction of Periodic Wavelets......Page 139
4.6.2 Properties of Periodic Wavelets......Page 142
4.6.3 Expansion of a Function in Periodic Wavelets......Page 146
4.7 APPLICATION OF PERIODIC WAVELETS: 2D SCATTERING......Page 147
4.8.1 Discretization of Operation Equations......Page 152
4.8.2 Fast Algorithm......Page 153
4.8.3 Matrix Sparsi . cation Using FWT......Page 154
4.9.1 Formulation......Page 159
4.9.2 Circuit Parameters......Page 160
4.9.3 Integral Equations and Wavelet Expansion......Page 162
4.10 INTERVALLIC COIFMAN WAVELETS......Page 163
4.10.1 Intervallic Scalets......Page 164
4.10.2 Intervallic Wavelets on [ 0, 1]......Page 173
4.11.1 Lazy Wavelets......Page 175
4.11.2 Lifting Scheme Algorithm......Page 176
4.12 GREEN¡¯S SCALETS AND SAMPLING SERIES......Page 178
4.12.1 Ordinary Differential Equations ( ODEs)......Page 179
4.12.2 Partial Differential Equations ( PDEs)......Page 185
4.13 APPENDIX: DERIVATION OF INTERVALLIC WAVELETS ON [ 0, 1]......Page 191
4.14.3 Exercise 7......Page 204
4.14.4 Exercise 8......Page 205
BIBLIOGRAPHY......Page 206
5.1 BASIS FDTD FORMULATION......Page 208
5.2 STABILITY ANALYSIS FOR THE FDTD......Page 213
5.3 FDTD AS MAXWELL¡¯S EQUATIONS WITH HAAR EXPANSION......Page 217
5.4 FDTD WITH BATTLE ¨C LEMARIE WAVELETS......Page 220
5.5 POSITIVE SAMPLING AND BIORTHOGONAL TESTING FUNCTIONS......Page 224
5.6.2 Formulation......Page 234
5.7.1 Dispersion Relation and Stability Analysis......Page 238
5.7.2 Stability Analysis for the SBTD......Page 241
5.8.1 Numerical Dispersion......Page 242
5.8.2 Convergence Analysis......Page 244
5.9 NUMERICAL EXAMPLES......Page 247
5.10 APPENDIX: OPERATOR FORM OF THE MRTD......Page 252
5.11.1 Exercise 9......Page 255
5.11.3 Project 2......Page 256
BIBLIOGRAPHY......Page 257
6.1 VECTOR- MATRIX DILATION EQUATION......Page 259
6.2 TIME DOMAIN APPROACH......Page 261
6.3 CONSTRUCTION OF MULTISCALETS......Page 264
6.4 ORTHOGONAL MULTIWAVELETS ¦×( t)......Page 274
6.5 INTERVALLIC MULTIWAVELETS ¦×( t)......Page 277
6.6 MULTIWAVELET EXPANSION......Page 280
6.7 INTERVALLIC DUAL MULTIWAVELETS ¦×( t)......Page 283
6.8 WORKING EXAMPLES......Page 288
6.9 MULTISCALET- BASED 1D FINITE ELEMENT METHOD ( FEM)......Page 295
6.10 MULTISCALET- BASED EDGE ELEMENT METHOD......Page 299
6.11 SPURIOUS MODES......Page 304
6.12 APPENDIX......Page 306
6.13.1 Exercise 11......Page 315
BIBLIOGRAPHY......Page 316
7.1 SCATTERING FROM A 2D GROOVE......Page 318
7.1.1 Method of Moments ( MoM) Formulation......Page 319
7.1.2 Coi . et- Based MoM......Page 323
7.1.4 Numerical Results......Page 324
7.2.1 Intervallic Scalets on [ 0, 1]......Page 328
7.2.2 Expansion in Coifman Intervallic Wavelets......Page 331
7.2.3 Numerical Integration and Error Estimate......Page 332
7.2.4 Fast Construction of Impedance Matrix......Page 336
7.2.5 Conducting Cylinders, TM Case......Page 338
7.2.6 Conducting Cylinders with Thin Magnetic Coating......Page 341
7.2.7 Perfect Electrically Conducting ( PEC) Spheroids......Page 343
7.3 SCATTERING AND RADIATION OF CURVED THIN WIRES......Page 348
7.3.1 Integral Equation for Curved Thin- Wire Scatterers and Antennae......Page 349
7.3.2 Numerical Examples......Page 350
7.4 SMOOTH LOCAL COSINE ( SLC) METHOD......Page 359
7.4.1 Construction of Smooth Local Cosine Basis......Page 360
7.4.2 Formulation of 2D Scattering Problems......Page 363
7.4.3 SLC- Based Galerkin Procedure and Numerical Results......Page 366
7.4.4 Application of the SLC to Thin- Wire Scatterers and Antennas......Page 374
7.5 MICROSTRIP ANTENNA ARRAYS......Page 376
7.5.1 Impedance Matched Source......Page 377
7.5.2 Far- Zone Fields and Antenna Patterns......Page 379
BIBLIOGRAPHY......Page 382
8.1 SCATTERING OF EM WAVES FROM RANDOMLY ROUGH SURFACES......Page 385
8.2 GENERATION OF RANDOM SURFACES......Page 387
8.2.1 Autocorrelation Method......Page 389
8.2.2 Spectral Domain Method......Page 392
8.3.1 Moment Method Formulation of 2D Scattering......Page 395
8.3.2 Wavelet- Based Galerkin Method for 2D Scattering......Page 399
8.3.3 Numerical Results of 2D Scattering......Page 400
8.4 3D ROUGH SURFACE SCATTERING......Page 406
8.4.1 Tapered Wave of Incidence......Page 407
8.4.2 Formulation of 3D Rough Surface Scattering Using Wavelets......Page 410
8.4.3 Numerical Results of 3D Scattering......Page 413
BIBLIOGRAPHY......Page 418
9 Wavelets in Packaging, Interconnects, and EMC......Page 420
9.1.1 What Is Quasi- static?......Page 421
9.1.2 Formulation......Page 422
9.1.3 Orthogonal Wavelets in L 2([ 0, 1])......Page 425
9.1.4 Boundary Element Method and Wavelet Expansion......Page 427
9.1.5 Numerical Examples......Page 431
9.2 SPATIAL DOMAIN LAYERED GREEN¡¯S FUNCTIONS......Page 434
9.2.1 Formulation......Page 436
9.2.2 Prony¡¯s Method......Page 442
9.2.3 Implementation of the Coifman Wavelets......Page 443
9.2.4 Numerical Examples......Page 445
9.3 SKIN- EFFECT RESISTANCE AND TOTAL INDUCTANCE......Page 448
9.3.1 Formulation......Page 450
9.3.2 Moment Method Solution of Coupled Integral Equations......Page 452
9.3.3 Circuit Parameter Extraction......Page 454
9.3.4 Wavelet Implementation......Page 456
9.3.5 Measurement and Simulation Results......Page 457
9.4.1 Basic Formulation......Page 459
9.4.2 Wavelet Expansion and Matrix Equation......Page 463
9.4.3 Evaluation of Sommerfeld- Type Integrals......Page 466
9.4.4 Numerical Results and Sparsity of Impedance Matrix......Page 470
9.5 FULL- WAVE EDGE ELEMENT METHOD FOR 3D LOSSY STRUCTURES......Page 474
9.5.1 Formulation of Asymmetric Functionals with Truncation Conditions......Page 475
9.5.2 Edge Element Procedure......Page 479
9.5.3 Excess Capacitance and Inductance......Page 483
9.5.4 Numerical Examples......Page 485
BIBLIOGRAPHY......Page 488
10.1 PHYSICAL MODELS AND COMPUTATIONAL EFFORTS......Page 493
10.2 AN INTERPOLATING SUBDIVISION SCHEME......Page 495
10.3 THE SPARSE POINT REPRESENTATION ( SPR)......Page 497
10.4 INTERPOLATION WAVELETS IN THE FDM......Page 498
10.4.1 1D Example of the SPR Application......Page 499
10.4.2 2D Example of the SPR Application......Page 500
10.5 THE DRIFT- DIFFUSION MODEL......Page 503
10.5.1 Scaling......Page 505
10.5.2 Discretization......Page 506
10.5.3 Transient Solution......Page 508
10.5.4 Grid Adaptation and Interpolating Wavelets......Page 509
10.5.5 Numerical Results......Page 511
10.6 MULTIWAVELET BASED DRIFT- DIFFUSION MODEL......Page 517
10.6.1 Precision and Stability versus Reynolds......Page 518
10.6.2 MWFEM- Based 1D Simulation......Page 521
10.7 THE BOLTZMANN TRANSPORT EQUATION ( BTE) MODEL......Page 523
10.7.2 Spherical Harmonic Expansion of the BTE......Page 524
10.7.3 Arbitrary Order Expansion and Galerkin¡¯s Procedure......Page 528
10.7.4 The Coupled Boltzmann ¨C Poisson System......Page 534
10.7.5 Numerical Results......Page 536
BIBLIOGRAPHY......Page 543
Index......Page 546