Lecture #12 INTEGRAL EQUATION METHODS FOR ELECTROMAGNETIC AND ELASTIC WAVES.part1.rar

周大牛新作..~~
Integral Equation Methods for Electromagnetic and Elastic Waves (Synthesis Lectures on Computational Electromagnetics)

Weng Cho Chew‌ University of Hong Kong and University of Illinois at Urbana-Champaign

Mei Song Tong‌ University of Illinois at Urbana-Champaign

Bin Hu‌ Intel Research




    * Publisher:   Morgan and Claypool Publishers
    * Number Of Pages:   260
    * Publication Date:   2007-07-15
    * ISBN-10 / ASIN:   1598291483
    * ISBN-13 / EAN:   9781598291483
    * Binding:   Paperback




Product Description:

Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms

Preface v
Acknowledgements vii
1 Introduction to Computational Electromagnetics 1
1.1 Mathematical Modeling—A Historical Perspective . . . . . . . . . . . . . . . 1
1.2 Some Things Do Not Happen in CEM Frequently—Nonlinearity . . . . . . . 3
1.3 The Morphing of Electromagnetic Physics . . . . . . . . . . . . . . . . . . . . 3
1.3.1 Comparison of Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3.2 Low-Frequency Regime . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3.3 Mid Frequency Regime . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.4 High-Frequency Regime . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.5 QuantumRegime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Matched Asymptotics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Why CEM? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Time Domain versus Frequency Domain . . . . . . . . . . . . . . . . . . . . . 8
1.7 Differential Equation versus Integral Equation . . . . . . . . . . . . . . . . . . 9
1.8 Nondissipative Nature of Electromagnetic Field . . . . . . . . . . . . . . . . . 11
1.9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Linear Vector Space, Reciprocity, and Energy Conservation 21
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.2 Linear Vector Spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3 Inner Products for Electromagnetics . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.1 Comparison with Mathematics . . . . . . . . . . . . . . . . . . . . . . 25
2.3.2 Comparison with Quantum Mechanics . . . . . . . . . . . . . . . . . . 25
2.4 Transpose and Adjoint of an Operator . . . . . . . . . . . . . . . . . . . . . . 26
2.5 Matrix Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.6 Compact versus Noncompact Operators . . . . . . . . . . . . . . . . . . . . . 28
2.7 Extension of Bra and Ket Notations . . . . . . . . . . . . . . . . . . . . . . . 29
2.8 Orthogonal Basis versus Nonorthogonal Basis . . . . . . . . . . . . . . . . . . 30
2.9 Integration by Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.10 Reciprocity Theorem—A New Look . . . . . . . . . . . . . . . . . . . . . . . 33
2.10.1 Lorentz Reciprocity Theorem . . . . . . . . . . . . . . . . . . . . . . . 35
2.11 Energy Conservation Theorem—A New Look . . . . . . . . . . . . . . . . . . 36
2.12 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3 Introduction to Integral Equations 43
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2 The Dyadic Green’s Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.3 Equivalence Principle and Extinction Theorem . . . . . . . . . . . . . . . . . 44
3.4 Electric Field Integral Equation—A Simple Physical Description . . . . . . . 48
3.4.1 EFIE—A Formal Derivation . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Understanding the Method of Moments—A Simple Example . . . . . . . . . . 51
3.6 Choice of Expansion Function . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
3.7 Closed Surface versus Open Surface . . . . . . . . . . . . . . . . . . . . . . . 55
3.7.1 EFIE for Open Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.7.2 MFIE andMore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
3.8 Internal Resonance and Combined Field Integral Equation . . . . . . . . . . . 56
3.9 Other Boundary Conditions—Impedance Boundary Condition, Thin Dielectric
Sheet, and R-Card . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.10 Matrix Solvers–A Pedestrian Introduction . . . . . . . . . . . . . . . . . . . . 59
3.10.1 Iterative Solvers and Krylov Subspace Methods . . . . . . . . . . . . . 59
3.10.2 Effect of the Right-Hand Side—A Heuristic Understanding . . . . . . 62
3.11 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
4 Integral Equations for Penetrable Objects 71
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2 Scattering by a Penetrable Object Using SIE . . . . . . . . . . . . . . . . . . 72
4.3 Gedanken Experiments for Internal Resonance Problems . . . . . . . . . . . . 75
4.3.1 Impenetrable Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.3.2 Penetrable Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.3.3 A Remedy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
4.3.4 Connection to Cavity Resonance . . . . . . . . . . . . . . . . . . . . . 82
4.3.5 Other remedies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.4 Volume Integral Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
4.4.1 Alternative Forms of VIE . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4.2 Matrix Representation of VIE . . . . . . . . . . . . . . . . . . . . . . . 87
4.5 Curl Conforming versus Divergence Conforming Expansion Functions . . . . 89
4.6 Thin Dielectric Sheet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4.6.1 A New TDS Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.7 Impedance Boundary Condition . . . . . . . . . . . . . . . . . . . . . . . . . . 95
4.7.1 Generalized Impedance Boundary Condition . . . . . . . . . . . . . . 95
4.7.2 Approximate Impedance Boundary Condition . . . . . . . . . . . . . . 96
4.7.3 Reflection by a Flat Lossy Ground Plane . . . . . . . . . . . . . . . . 96
4.7.4 Reflection by a Lossy Cylinder . . . . . . . . . . . . . . . . . . . . . . 98
4.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5 Low-Frequency Problems in Integral Equations 107
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
5.2 Low-Frequency Breakdown of Electric Field Integral Equation . . . . . . . . . 107
5.3 Remedy—Loop-Tree Decomposition and Frequency Normalization . . . . . . 109
5.3.1 Loop-Tree Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . 112
5.3.2 The Electrostatic Problem . . . . . . . . . . . . . . . . . . . . . . . . . 113
5.3.3 Basis Rearrangement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
5.3.4 Computation of K−1
· Q in O(N) Operations . . . . . . . . . . . . . . 118
5.3.5 Motivation for Inverting K Matrix in O(N) Operations . . . . . . . . 119
5.3.6 Reason for Ill-Convergence Without Basis Rearrangement . . . . . . . 122
5.4 Testing of the Incident Field with the Loop Function . . . . . . . . . . . . . . 124
5.5 The Multi-Dielectric-Region Problem . . . . . . . . . . . . . . . . . . . . . . . 124
5.5.1 Numerical Error with Basis Rearrangement . . . . . . . . . . . . . . . 127
5.6 Multiscale Problems in Electromagnetics . . . . . . . . . . . . . . . . . . . . . 128
5.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
6 Dyadic Green’s Function for Layered Media and Integral Equations 135
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.2 Dyadic Green’s Function for Layered Media . . . . . . . . . . . . . . . . . . . 136
6.3 Matrix Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
6.4 The r×Ge Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
6.5 The L and K Operators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
6.6 The Ez-Hz Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
6.6.1 Example 1: Half Space . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6.6.2 Example 2: Three-Layer Medium . . . . . . . . . . . . . . . . . . . . . 150
6.7 Validation and Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
6.8 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
7 Fast Inhomogeneous Plane Wave Algorithm for Layered Media 159
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
7.2 Integral Equations for Layered Medium . . . . . . . . . . . . . . . . . . . . . 160
7.3 FIPWA for Free Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
7.4 FIPWA for LayeredMedium . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
7.4.1 Groups not aligned in ˆz axis . . . . . . . . . . . . . . . . . . . . . . . 166
7.4.2 Groups aligned in ˆz axis . . . . . . . . . . . . . . . . . . . . . . . . . . 174
7.4.3 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
7.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
7.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8 Electromagnetic Wave versus Elastic Wave 193
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
8.2 Derivation of the Elastic Wave Equation . . . . . . . . . . . . . . . . . . . . . 193
8.3 Solution of the Elastic Wave Equation—A Succinct Derivation . . . . . . . . 197
8.3.1 Time-Domain Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . 199
8.4 Alternative Solution of the Elastic Wave Equation via Fourier-Laplace Transform200
8.5 Boundary Conditions for Elastic Wave Equation . . . . . . . . . . . . . . . . 202
8.6 Decomposition of Elastic Wave into SH, SV and P Waves for Layered Media 203
8.7 Elastic Wave Equation for Planar Layered Media . . . . . . . . . . . . . . . . 205
8.7.1 Three-LayerMediumCase . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.8 Finite Difference Scheme for the Elastic Wave Equation . . . . . . . . . . . . 210
8.9 Integral Equation for Elastic Wave Scattering . . . . . . . . . . . . . . . . . 211
8.10 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
Glossary of Acronyms 223
About the Authors 227

[ 本帖最后由 gosila_chy 于 2008-10-28 03:42 编辑 ]

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感謝樓主分享
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積極下載學習中

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除了感谢还是由衷的感谢:30bb

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牛人的书
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Parallel Finite-Difference Time-Domain Method

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