Wavelets in Electromagnetics and Device Modeling: 132 (Wiley Series in Microwave and Optical Engineering)

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* The first book on the subject. * Written by an acknowledged expert in the field. * The techniques discussed have important applications to wireless engineering. Wavelets in Electromagnetics and Device Modeling Wavelets in Electromagnetics and Device Modeling Copyright Contents Preface ACKNOWLEDGMENTS 1 Notations and Mathematical Preliminaries 1.1 NOTATIONS AND ABBREVIATIONS 1.2 MATHEMATICAL PRELIMINARIES 1.2.1 Functions and Integration 1.2.2 The Fourier Transform 1.2.3 Regularity 1.2.4 Linear Spaces 1.2.5 Functional Spaces 1.2.6 Sobolev Spaces 1.2.7 Bases in Hilbert Space H 1.2.8 Linear Operators BIBLIOGRAPHY 2 Intuitive Introduction to Wavelets 2.1 TECHNICAL HISTORY AND BACKGROUND 2.1.1 Historical Development 2.1.2 When Do Wavelets Work? 2.1.3 A Wave Is a Wave but What Is a Wavelet? 2.2 WHAT CAN WAVELETS DOIN ELECTROMAGNETICS AND DEVICE MODELING? 2.2.1 Potential Bene . ts of Using Wavelets 2.2.2 Limitations and Future Direction of Wavelets 2.3 THE HAAR WAVELETS AND MULTIRESOLUTION ANALYSIS 2.4 HOW DO WAVELETS WORK? BIBLIOGRAPHY 3 Basic Orthogonal Wavelet Theory 3.1 MULTIRESOLUTION ANALYSIS 3.2 CONSTRUCTION OF SCALETS .( ¦Ó) 3.2.1 Franklin Scalet 3.2.2 Battle ¨C Lemarie Scalets 3.2.3 Preliminary Properties of Scalets 3.3 WAVELET ¦×( ¦Ó) 3.4 FRANKLIN WAVELET 3.5 PROPERTIES OF SCALETS .( . ¦Ø) 3.6 DAUBECHIES WAVELETS 3.7 COIFMAN WAVELETS ( COIFLETS) 3.8 CONSTRUCTING WAVELETS BY RECURSION AND ITERATION 3.8.1 Construction of Scalets 3.8.2 Construction of Wavelets 3.9 MEYER WAVELETS 3.9.1 Basic Properties of Meyer Wavelets 3.9.2 Meyer Wavelet Family 3.9.3 Other Examples of Meyer Wavelets 3.10 MALLAT¡¯S DECOMPOSITION AND RECONSTRUCTION 3.10.1 Reconstruction 3.10.2 Decomposition 3.11 PROBLEMS 3.11.1 Exercise 1 3.11.2 Exercise 2 3.11.3 Exercise 3 3.11.4 Exercise 4 BIBLIOGRAPHY 4 Wavelets in Boundary Integral Equations 4.1 WAVELETS IN ELECTROMAGNETICS 4.2 LINEAR OPERATORS 4.3 METHOD OF MOMENTS ( MoM) 4.4 FUNCTIONAL EXPANSION OF A GIVEN FUNCTION 4.5 OPERATOR EXPANSION: NONSTANDARD FORM 4.5.1 Operator Expansion in Haar Wavelets 4.5.2 Operator Expansion in General Wavelet Systems 4.5.3 Numerical Example 4.6 PERIODIC WAVELETS 4.6.1 Construction of Periodic Wavelets 4.6.2 Properties of Periodic Wavelets 4.6.3 Expansion of a Function in Periodic Wavelets 4.7 APPLICATION OF PERIODIC WAVELETS: 2D SCATTERING 4.8 FAST WAVELET TRANSFORM ( FWT) 4.8.1 Discretization of Operation Equations 4.8.2 Fast Algorithm 4.8.3 Matrix Sparsi . cation Using FWT 4.9 APPLICATIONS OF THE FWT 4.9.1 Formulation 4.9.2 Circuit Parameters 4.9.3 Integral Equations and Wavelet Expansion 4.9.4 Numerical Results 4.10 INTERVALLIC COIFMAN WAVELETS 4.10.1 Intervallic Scalets 4.10.2 Intervallic Wavelets on [ 0, 1] 4.11 LIFTING SCHEME AND LAZY WAVELETS 4.11.1 Lazy Wavelets 4.11.2 Lifting Scheme Algorithm 4.11.3 Cascade Algorithm 4.12 GREEN¡¯S SCALETS AND SAMPLING SERIES 4.12.1 Ordinary Differential Equations ( ODEs) 4.12.2 Partial Differential Equations ( PDEs) 4.13 APPENDIX: DERIVATION OF INTERVALLIC WAVELETS ON [ 0, 1] 4.14 PROBLEMS 4.14.1 Exercise 5 4.14.2 Exercise 6 4.14.3 Exercise 7 4.14.4 Exercise 8 4.14.5 Project 1 BIBLIOGRAPHY 5 Sampling Biorthogonal Time Domain Method (SBTD) 5.1 BASIS FDTD FORMULATION 5.2 STABILITY ANALYSIS FOR THE FDTD 5.3 FDTD AS MAXWELL¡¯S EQUATIONS WITH HAAR EXPANSION 5.4 FDTD WITH BATTLE ¨C LEMARIE WAVELETS 5.5 POSITIVE SAMPLING AND BIORTHOGONAL TESTING FUNCTIONS 5.6 SAMPLING BIORTHOGONAL TIME DOMAIN METHOD 5.6.1 SBTD versus MRTD 5.6.2 Formulation 5.7 STABILITY CONDITIONS FOR WAVELET- BASED METHODS 5.7.1 Dispersion Relation and Stability Analysis 5.7.2 Stability Analysis for the SBTD 5.8 CONVERGENCE ANALYSIS AND NUMERICAL DISPERSION 5.8.1 Numerical Dispersion 5.8.2 Convergence Analysis 5.9 NUMERICAL EXAMPLES 5.10 APPENDIX: OPERATOR FORM OF THE MRTD 5.11 PROBLEMS 5.11.1 Exercise 9 5.11.2 Exercise 10 5.11.3 Project 2 BIBLIOGRAPHY 6 Canonical Multiwavelets 6.1 VECTOR- MATRIX DILATION EQUATION 6.2 TIME DOMAIN APPROACH 6.3 CONSTRUCTION OF MULTISCALETS 6.4 ORTHOGONAL MULTIWAVELETS ¦×( t) 6.5 INTERVALLIC MULTIWAVELETS ¦×( t) 6.6 MULTIWAVELET EXPANSION 6.7 INTERVALLIC DUAL MULTIWAVELETS ¦×( t) 6.8 WORKING EXAMPLES 6.9 MULTISCALET- BASED 1D FINITE ELEMENT METHOD ( FEM) 6.10 MULTISCALET- BASED EDGE ELEMENT METHOD 6.11 SPURIOUS MODES 6.12 APPENDIX 6.13 PROBLEMS 6.13.1 Exercise 11 BIBLIOGRAPHY 7 Wavelets in Scattering and Radiation 7.1 SCATTERING FROM A 2D GROOVE 7.1.1 Method of Moments ( MoM) Formulation 7.1.2 Coi . et- Based MoM 7.1.3 Bi- CGSTAB Algorithm 7.1.4 Numerical Results 7.2 2D AND 3D SCATTERING USING INTERVALLIC COIFLETS 7.2.1 Intervallic Scalets on [ 0, 1] 7.2.2 Expansion in Coifman Intervallic Wavelets 7.2.3 Numerical Integration and Error Estimate 7.2.4 Fast Construction of Impedance Matrix 7.2.5 Conducting Cylinders, TM Case 7.2.6 Conducting Cylinders with Thin Magnetic Coating 7.2.7 Perfect Electrically Conducting ( PEC) Spheroids 7.3 SCATTERING AND RADIATION OF CURVED THIN WIRES 7.3.1 Integral Equation for Curved Thin- Wire Scatterers and Antennae 7.3.2 Numerical Examples 7.4 SMOOTH LOCAL COSINE ( SLC) METHOD 7.4.1 Construction of Smooth Local Cosine Basis 7.4.2 Formulation of 2D Scattering Problems 7.4.3 SLC- Based Galerkin Procedure and Numerical Results 7.4.4 Application of the SLC to Thin- Wire Scatterers and Antennas 7.5 MICROSTRIP ANTENNA ARRAYS 7.5.1 Impedance Matched Source 7.5.2 Far- Zone Fields and Antenna Patterns BIBLIOGRAPHY 8 Wavelets in Rough Surface Scattering 8.1 SCATTERING OF EM WAVES FROM RANDOMLY ROUGH SURFACES 8.2 GENERATION OF RANDOM SURFACES 8.2.1 Autocorrelation Method 8.2.2 Spectral Domain Method 8.3 2D ROUGH SURFACE SCATTERING 8.3.1 Moment Method Formulation of 2D Scattering 8.3.2 Wavelet- Based Galerkin Method for 2D Scattering 8.3.3 Numerical Results of 2D Scattering 8.4 3D ROUGH SURFACE SCATTERING 8.4.1 Tapered Wave of Incidence 8.4.2 Formulation of 3D Rough Surface Scattering Using Wavelets 8.4.3 Numerical Results of 3D Scattering BIBLIOGRAPHY 9 Wavelets in Packaging, Interconnects, and EMC 9.1 QUASI- STATIC SPATIAL FORMULATION 9.1.1 What Is Quasi- static? 9.1.2 Formulation 9.1.3 Orthogonal Wavelets in L 2([ 0, 1]) 9.1.4 Boundary Element Method and Wavelet Expansion 9.1.5 Numerical Examples 9.2 SPATIAL DOMAIN LAYERED GREEN¡¯S FUNCTIONS 9.2.1 Formulation 9.2.2 Prony¡¯s Method 9.2.3 Implementation of the Coifman Wavelets 9.2.4 Numerical Examples 9.3 SKIN- EFFECT RESISTANCE AND TOTAL INDUCTANCE 9.3.1 Formulation 9.3.2 Moment Method Solution of Coupled Integral Equations 9.3.3 Circuit Parameter Extraction 9.3.4 Wavelet Implementation 9.3.5 Measurement and Simulation Results 9.4 Spectral Domain Green’s Function-Based Full-Wave Analysis 9.4.1 Basic Formulation 9.4.2 Wavelet Expansion and Matrix Equation 9.4.3 Evaluation of Sommerfeld- Type Integrals 9.4.4 Numerical Results and Sparsity of Impedance Matrix 9.4.5 Further Improvements 9.5 FULL- WAVE EDGE ELEMENT METHOD FOR 3D LOSSY STRUCTURES 9.5.1 Formulation of Asymmetric Functionals with Truncation Conditions 9.5.2 Edge Element Procedure 9.5.3 Excess Capacitance and Inductance 9.5.4 Numerical Examples BIBLIOGRAPHY 10 Wavelets in Nonlinear Semiconductor Devices 10.1 PHYSICAL MODELS AND COMPUTATIONAL EFFORTS 10.2 AN INTERPOLATING SUBDIVISION SCHEME 10.3 THE SPARSE POINT REPRESENTATION ( SPR) 10.4 INTERPOLATION WAVELETS IN THE FDM 10.4.1 1D Example of the SPR Application 10.4.2 2D Example of the SPR Application 10.5 THE DRIFT- DIFFUSION MODEL 10.5.1 Scaling 10.5.2 Discretization 10.5.3 Transient Solution 10.5.4 Grid Adaptation and Interpolating Wavelets 10.5.5 Numerical Results 10.6 MULTIWAVELET BASED DRIFT- DIFFUSION MODEL 10.6.1 Precision and Stability versus Reynolds 10.6.2 MWFEM- Based 1D Simulation 10.7 THE BOLTZMANN TRANSPORT EQUATION ( BTE) MODEL 10.7.1 Why BTE? 10.7.2 Spherical Harmonic Expansion of the BTE 10.7.3 Arbitrary Order Expansion and Galerkin¡¯s Procedure 10.7.4 The Coupled Boltzmann ¨C Poisson System 10.7.5 Numerical Results BIBLIOGRAPHY Index