Theory and Computation of Electromagnetic Fields (eBook)
John Wiley & Sons (Verlag)
978-1-119-10808-5 (ISBN)
Reviews the fundamental concepts behind the theory and computation of electromagnetic fields
The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell's equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time-domain method in particular), the finite element method, and the integral equation-based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems.
Theory and Computation of Electromagnetic Fields, Second Edition:
- Provides the foundation necessary for graduate students to learn and understand more advanced topics
- Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates
- Covers computational electromagnetics in both frequency and time domains
- Includes new and updated homework problems and examples
JIAN-MING JIN, Ph.D., is the Y. T. Lo Chair Professor in Electrical and Computer Engineering and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. He authored The Finite Element Method in Electromagnetics, Third Edition (Wiley 2014) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and co-authored Computation of Special Functions (Wiley 1996), Finite Element Analysis of Antennas and Arrays (Wiley 2008), and Fast and Efficient Algorithms in Computational Electromagnetics. A Fellow of the IEEE, he is listed by ISI among the world's most cited authors.
JIAN-MING JIN, Ph.D., is the Y. T. Lo Chair Professor in Electrical and Computer Engineering and Director of the Electromagnetics Laboratory and Center for Computational Electromagnetics at the University of Illinois at Urbana-Champaign. He authored The Finite Element Method in Electromagnetics, Third Edition (Wiley 2014) and Electromagnetic Analysis and Design in Magnetic Resonance Imaging, and co-authored Computation of Special Functions (Wiley 1996), Finite Element Analysis of Antennas and Arrays (Wiley 2008), and Fast and Efficient Algorithms in Computational Electromagnetics. A Fellow of the IEEE, he is listed by ISI among the world's most cited authors.
Cover???????????????????????? 1
Title Page?????????????????????????????????? 5
Copyright???????????????????????????????? 6
Contents?????????????????????????????? 7
Preface???????????????????????????? 17
Acknowledgments???????????????????????????????????????????? 23
Part I Electromagnetic Field Theory???????????????????????????????????????????????????????????????????????????????????? 25
Chapter 1 Basic Electromagnetic Theory?????????????????????????????????????????????????????????????????????????????????????????? 27
1.1 Review of Vector Analysis???????????????????????????????????????????????????????????????????????? 27
1.1.1 Vector Operations and Integral Theorems???????????????????????????????????????????????????????????????????????????????????????????????????????? 28
1.1.2 Symbolic Vector Method?????????????????????????????????????????????????????????????????????? 30
1.1.3 Helmholtz Decomposition Theorem???????????????????????????????????????????????????????????????????????????????????????? 33
1.1.4 Green's Theorems?????????????????????????????????????????????????????????? 33
1.2 Maxwell's Equations in Terms of Total Charges and Currents?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 35
1.2.1 Maxwell's Equations in Integral Form?????????????????????????????????????????????????????????????????????????????????????????????????? 36
1.2.2 Maxwell's Equations in Differential Form?????????????????????????????????????????????????????????????????????????????????????????????????????????? 41
1.2.3 Current Continuity Equation???????????????????????????????????????????????????????????????????????????????? 41
1.2.4 The Lorentz Force Law???????????????????????????????????????????????????????????????????? 42
1.3 Constitutive Relations?????????????????????????????????????????????????????????????????? 42
1.3.1 Electric Polarization???????????????????????????????????????????????????????????????????? 43
1.3.2 Magnetization???????????????????????????????????????????????????? 45
1.3.3 Electric Conduction???????????????????????????????????????????????????????????????? 46
1.3.4 Classification of Media???????????????????????????????????????????????????????????????????????? 47
1.4 Maxwell's Equations in Terms of Free Charges and Currents???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 49
1.5 Boundary Conditions???????????????????????????????????????????????????????????? 51
1.6 Energy, Power, and Poynting's Theorem???????????????????????????????????????????????????????????????????????????????????????????????? 55
1.7 Time-Harmonic Fields?????????????????????????????????????????????????????????????? 57
1.7.1 Time-Harmonic Fields?????????????????????????????????????????????????????????????????? 57
1.7.2 Fourier Transforms?????????????????????????????????????????????????????????????? 59
1.7.3 Complex Power???????????????????????????????????????????????????? 61
1.7.4 Complex Permittivity and Permeability???????????????????????????????????????????????????????????????????????????????????????????????????? 66
References?????????????????????????????????? 70
Problems?????????????????????????????? 70
Chapter 2 Electromagnetic Radiation in Free Space???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 77
2.1 Scalar and Vector Potentials?????????????????????????????????????????????????????????????????????????????? 77
2.1.1 Static Fields???????????????????????????????????????????????????? 78
2.1.2 Time-Harmonic Fields and the Lorenz Gauge Condition???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 82
2.2 Solution of Vector Potentials in Free Space???????????????????????????????????????????????????????????????????????????????????????????????????????????? 85
2.2.1 Delta Function and Green's Function???????????????????????????????????????????????????????????????????????????????????????????????? 85
2.2.2 Green's Function in Free Space?????????????????????????????????????????????????????????????????????????????????????? 86
2.2.3 Field-Source Relations in Free Space?????????????????????????????????????????????????????????????????????????????????????????????????? 87
2.2.4 Why Use Auxiliary Potential Functions???????????????????????????????????????????????????????????????????????????????????????????????????? 88
2.2.5 Free-Space Dyadic Green's Functions???????????????????????????????????????????????????????????????????????????????????????????????? 90
2.3 Electromagnetic Radiation in Free Space???????????????????????????????????????????????????????????????????????????????????????????????????? 93
2.3.1 Infinitesimal Electric Dipole???????????????????????????????????????????????????????????????????????????????????? 93
2.3.2 Finite Electric Dipole?????????????????????????????????????????????????????????????????????? 96
2.3.3 Far-Field Approximation and the Sommerfeld Radiation Condition?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 97
2.3.4 Circular Current Loop and Magnetic Dipole???????????????????????????????????????????????????????????????????????????????????????????????????????????? 100
2.4 Radiation by Surface Currents and Phased Arrays???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 102
2.4.1 Radiation by a Surface Current?????????????????????????????????????????????????????????????????????????????????????? 102
2.4.2 Radiation by a Phased Array???????????????????????????????????????????????????????????????????????????????? 105
References?????????????????????????????????? 108
Problems?????????????????????????????? 109
Chapter 3 Electromagnetic Theorems and Principles???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 113
3.1 Uniqueness Theorem?????????????????????????????????????????????????????????? 114
3.2 Image Theory?????????????????????????????????????????????? 118
3.2.1 Basic Image Theory?????????????????????????????????????????????????????????????? 118
3.2.2 Half-Space Field-Source Relations???????????????????????????????????????????????????????????????????????????????????????????? 123
3.3 Reciprocity Theorems?????????????????????????????????????????????????????????????? 125
3.3.1 General Reciprocity Theorem???????????????????????????????????????????????????????????????????????????????? 125
3.3.2 Lorentz Reciprocity Theorem???????????????????????????????????????????????????????????????????????????????? 126
3.3.3 Rayleigh-Carson Reciprocity Theorem???????????????????????????????????????????????????????????????????????????????????????????????? 127
3.4 Equivalence Principles?????????????????????????????????????????????????????????????????? 131
3.4.1 Surface Equivalence Principle???????????????????????????????????????????????????????????????????????????????????? 131
3.4.2 Application to Scattering by a Conducting Object?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 133
3.4.3 Application to Scattering by a Dielectric Object?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 138
3.4.4 Volume Equivalence Principle?????????????????????????????????????????????????????????????????????????????????? 140
3.5 Duality Principle???????????????????????????????????????????????????????? 144
3.6 Aperture Radiation and Scattering???????????????????????????????????????????????????????????????????????????????????????? 145
3.6.1 Equivalent Problems???????????????????????????????????????????????????????????????? 145
3.6.2 Babinet's Principle???????????????????????????????????????????????????????????????? 148
3.6.3 Complementary Antennas?????????????????????????????????????????????????????????????????????? 151
References?????????????????????????????????? 152
Problems?????????????????????????????? 153
Chapter 4 Transmission Lines and Plane Waves?????????????????????????????????????????????????????????????????????????????????????????????????????? 159
4.1 Transmission Line Theory?????????????????????????????????????????????????????????????????????? 159
4.1.1 Governing Differential Equations and General Solutions?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 159
4.1.2 Reflection and Transmission???????????????????????????????????????????????????????????????????????????????? 162
4.1.3 Green's Function and Eigenfunction Expansion?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 164
4.2 Wave Equations and General Solutions?????????????????????????????????????????????????????????????????????????????????????????????? 168
4.2.1 Wave Equations and Solution by Separation of Variables?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 168
4.2.2 Characteristics of a Plane Wave???????????????????????????????????????????????????????????????????????????????????????? 170
4.2.3 Wave Velocities and Attenuation???????????????????????????????????????????????????????????????????????????????????????? 171
4.2.4 Linear, Circular, and Elliptical Polarizations?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 175
4.2.5 Wave Propagation in Metamaterials???????????????????????????????????????????????????????????????????????????????????????????? 178
4.3 Plane Waves Generated by a Current Sheet?????????????????????????????????????????????????????????????????????????????????????????????????????? 180
4.4 Reflection and Transmission???????????????????????????????????????????????????????????????????????????? 183
4.4.1 Reflection and Transmission at Normal Incidence???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 183
4.4.2 Reflection and Transmission at Oblique Incidence?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 185
4.4.3 Total Transmission and Total Reflection???????????????????????????????????????????????????????????????????????????????????????????????????????? 188
4.4.4 Transmission into a Left-Handed Medium?????????????????????????????????????????????????????????????????????????????????????????????????????? 192
4.4.5 Plane Waves Versus Transmission Lines???????????????????????????????????????????????????????????????????????????????????????????????????? 194
4.5 Plane Waves in Anisotropic and Bi-Isotropic Media???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 198
4.5.1 Plane Waves in Uniaxial Media???????????????????????????????????????????????????????????????????????????????????? 198
4.5.2 Plane Waves in Gyrotropic Media???????????????????????????????????????????????????????????????????????????????????????? 203
4.5.3 Plane Waves in Chiral Media???????????????????????????????????????????????????????????????????????????????? 207
References?????????????????????????????????? 214
Problems?????????????????????????????? 215
Chapter 5 Fields and Waves in Rectangular Coordinates???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 223
5.1 Uniform Waveguides?????????????????????????????????????????????????????????? 223
5.1.1 General Analysis?????????????????????????????????????????????????????????? 224
5.1.2 General Characteristics???????????????????????????????????????????????????????????????????????? 228
5.1.3 Uniform Rectangular Waveguide???????????????????????????????????????????????????????????????????????????????????? 232
5.1.4 Losses in Waveguides and Attenuation Constant???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 239
5.2 Uniform Cavities?????????????????????????????????????????????????????? 244
5.2.1 General Theory?????????????????????????????????????????????????????? 245
5.2.2 Rectangular Cavity?????????????????????????????????????????????????????????????? 247
5.2.3 Material and Geometry Perturbations???????????????????????????????????????????????????????????????????????????????????????????????? 250
5.3 Partially Filled Waveguides and Dielectric Slab Waveguides?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 253
5.3.1 General Theory?????????????????????????????????????????????????????? 253
5.3.2 Partially Filled Rectangular Waveguide?????????????????????????????????????????????????????????????????????????????????????????????????????? 255
5.3.3 Dielectric Slab Waveguide on a Ground Plane???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 260
5.4 Field Excitation in Waveguides?????????????????????????????????????????????????????????????????????????????????? 265
5.4.1 Excitation by Planar Surface Currents???????????????????????????????????????????????????????????????????????????????????????????????????? 266
5.4.2 Excitation by General Volumetric Currents???????????????????????????????????????????????????????????????????????????????????????????????????????????? 267
5.5 Fields in Planar Layered Media?????????????????????????????????????????????????????????????????????????????????? 269
5.5.1 Spectral Green's Function and Sommerfeld Identity???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 269
5.5.2 Vertical Electric Dipole above a Layered Medium???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 271
5.5.3 Horizontal Electric Dipole above a Layered Medium???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 273
5.5.4 Dipoles on a Grounded Dielectric Slab???????????????????????????????????????????????????????????????????????????????????????????????????? 275
References?????????????????????????????????? 281
Problems?????????????????????????????? 281
Chapter 6 Fields and Waves in Cylindrical Coordinates???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 285
6.1 Solution of Wave Equation???????????????????????????????????????????????????????????????????????? 285
6.1.1 Solution by Separation of Variables???????????????????????????????????????????????????????????????????????????????????????????????? 286
6.1.2 Cylindrical Wave Functions?????????????????????????????????????????????????????????????????????????????? 287
6.2 Circular and Coaxial Waveguides and Cavities?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 290
6.2.1 Circular Waveguide?????????????????????????????????????????????????????????????? 291
6.2.2 Coaxial Waveguide???????????????????????????????????????????????????????????? 297
6.2.3 Cylindrical Cavity?????????????????????????????????????????????????????????????? 300
6.3 Circular Dielectric Waveguide???????????????????????????????????????????????????????????????????????????????? 303
6.3.1 Analysis of Hybrid Modes?????????????????????????????????????????????????????????????????????????? 303
6.3.2 Characteristics of Hybrid Modes???????????????????????????????????????????????????????????????????????????????????????? 307
6.4 Wave Transformation and Scattering Analysis???????????????????????????????????????????????????????????????????????????????????????????????????????????? 311
6.4.1 Wave Transformation???????????????????????????????????????????????????????????????? 312
6.4.2 Scattering by a Circular Conducting Cylinder?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 313
6.4.3 Scattering by a Circular Dielectric Cylinder?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 317
6.4.4 Scattering by a Circular Multilayer Dielectric Cylinder???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 320
6.5 Radiation by Infinitely Long Currents???????????????????????????????????????????????????????????????????????????????????????????????? 324
6.5.1 Line Current Radiation in Free Space?????????????????????????????????????????????????????????????????????????????????????????????????? 324
6.5.2 Radiation by a Cylindrical Surface Current?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 328
6.5.3 Radiation in the Presence of a Circular Conducting Cylinder???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 330
6.5.4 Radiation in the Presence of a Conducting Wedge???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 333
6.5.5 Radiation by a Finite Current???????????????????????????????????????????????????????????????????????????????????? 336
References?????????????????????????????????? 343
Problems?????????????????????????????? 344
Chapter 7 Fields and Waves in Spherical Coordinates???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 349
7.1 Solution of Wave Equation???????????????????????????????????????????????????????????????????????? 349
7.1.1 Solution by Separation of Variables???????????????????????????????????????????????????????????????????????????????????????????????? 349
7.1.2 Spherical Wave Functions?????????????????????????????????????????????????????????????????????????? 352
7.1.3 TEr and TMr Modes???????????????????????????????????????????????????????????? 353
7.2 Spherical Cavity?????????????????????????????????????????????????????? 355
7.3 Biconical Antenna???????????????????????????????????????????????????????? 359
7.3.1 Infinitely Long Model???????????????????????????????????????????????????????????????????? 359
7.3.2 Finite Biconical Antenna?????????????????????????????????????????????????????????????????????????? 363
7.4 Wave Transformation and Scattering Analysis???????????????????????????????????????????????????????????????????????????????????????????????????????????? 365
7.4.1 Wave Transformation???????????????????????????????????????????????????????????????? 366
7.4.2 Expansion of a Plane Wave???????????????????????????????????????????????????????????????????????????? 368
7.4.3 Scattering by a Conducting Sphere???????????????????????????????????????????????????????????????????????????????????????????? 371
7.4.4 Scattering by a Dielectric Sphere???????????????????????????????????????????????????????????????????????????????????????????? 376
7.4.5 Scattering by a Multilayer Dielectric Sphere?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 381
7.5 Addition Theorem and Radiation Analysis???????????????????????????????????????????????????????????????????????????????????????????????????? 384
7.5.1 Addition Theorem for Spherical Wave Functions???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 384
7.5.2 Radiation of a Spherical Surface Current?????????????????????????????????????????????????????????????????????????????????????????????????????????? 386
7.5.3 Radiation in the Presence of a Sphere???????????????????????????????????????????????????????????????????????????????????????????????????? 392
7.5.4 Radiation in the Presence of a Conducting Cone?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 394
References?????????????????????????????????? 401
Problems?????????????????????????????? 401
Part II Electromagnetic Field Computation???????????????????????????????????????????????????????????????????????????????????????????????? 407
Chapter 8 The Finite Difference Method?????????????????????????????????????????????????????????????????????????????????????????? 409
8.1 Finite Differencing Formulas?????????????????????????????????????????????????????????????????????????????? 409
8.2 One-Dimensional Analysis?????????????????????????????????????????????????????????????????????? 411
8.2.1 Solution of the Diffusion Equation?????????????????????????????????????????????????????????????????????????????????????????????? 411
8.2.2 Solution of the Wave Equation???????????????????????????????????????????????????????????????????????????????????? 413
8.2.3 Stability Analysis?????????????????????????????????????????????????????????????? 414
8.2.4 Numerical Dispersion Analysis???????????????????????????????????????????????????????????????????????????????????? 416
8.3 Two-Dimensional Analysis?????????????????????????????????????????????????????????????????????? 417
8.3.1 Analysis in the Time Domain???????????????????????????????????????????????????????????????????????????????? 417
8.3.2 Analysis in the Frequency Domain?????????????????????????????????????????????????????????????????????????????????????????? 419
8.4 Yee's FDTD Scheme???????????????????????????????????????????????????????? 421
8.4.1 Two-Dimensional Analysis?????????????????????????????????????????????????????????????????????????? 421
8.4.2 Three-Dimensional Analysis?????????????????????????????????????????????????????????????????????????????? 423
8.5 Absorbing Boundary Conditions???????????????????????????????????????????????????????????????????????????????? 426
8.5.1 One-Dimensional ABC???????????????????????????????????????????????????????????????? 427
8.5.2 Two-Dimensional ABCs?????????????????????????????????????????????????????????????????? 428
8.5.3 Perfectly Matched Layers?????????????????????????????????????????????????????????????????????????? 430
8.6 Modeling of Dispersive Media?????????????????????????????????????????????????????????????????????????????? 441
8.6.1 Recursive Convolution Approach?????????????????????????????????????????????????????????????????????????????????????? 441
8.6.2 Auxiliary Differential Equation Approach?????????????????????????????????????????????????????????????????????????????????????????????????????????? 444
8.7 Wave Excitation and Far-Field Calculation???????????????????????????????????????????????????????????????????????????????????????????????????????? 446
8.7.1 Modeling of Wave Excitation???????????????????????????????????????????????????????????????????????????????? 446
8.7.2 Near-to-Far-Field Transformation?????????????????????????????????????????????????????????????????????????????????????????? 450
8.8 Summary???????????????????????????????????? 451
References?????????????????????????????????? 452
Problems?????????????????????????????? 453
Chapter 9 The Finite Element Method???????????????????????????????????????????????????????????????????????????????????? 457
9.1 Introduction to the Finite Element Method???????????????????????????????????????????????????????????????????????????????????????????????????????? 458
9.1.1 The General Principle???????????????????????????????????????????????????????????????????? 458
9.1.2 One-Dimensional Example???????????????????????????????????????????????????????????????????????? 459
9.2 Finite Element Analysis of Scalar Fields?????????????????????????????????????????????????????????????????????????????????????????????????????? 463
9.2.1 The Boundary-Value Problem?????????????????????????????????????????????????????????????????????????????? 463
9.2.2 Finite Element Formulation?????????????????????????????????????????????????????????????????????????????? 464
9.2.3 Application Examples?????????????????????????????????????????????????????????????????? 470
9.3 Finite Element Analysis of Vector Fields?????????????????????????????????????????????????????????????????????????????????????????????????????? 474
9.3.1 The Boundary-Value Problem?????????????????????????????????????????????????????????????????????????????? 474
9.3.2 Finite Element Formulation?????????????????????????????????????????????????????????????????????????????? 476
9.3.3 Application Examples?????????????????????????????????????????????????????????????????? 480
9.4 Finite Element Analysis in the Time Domain?????????????????????????????????????????????????????????????????????????????????????????????????????????? 489
9.4.1 The Boundary-Value Problem?????????????????????????????????????????????????????????????????????????????? 489
9.4.2 Finite Element Formulation?????????????????????????????????????????????????????????????????????????????? 490
9.4.3 Application Examples?????????????????????????????????????????????????????????????????? 494
9.5 Discontinuous Galerkin Time-Domain Method???????????????????????????????????????????????????????????????????????????????????????????????????????? 496
9.5.1 Basic Idea?????????????????????????????????????????????? 497
9.5.2 Central-Flux DGTD Method?????????????????????????????????????????????????????????????????????????? 499
9.5.3 Upwind-Flux DGTD Method???????????????????????????????????????????????????????????????????????? 502
9.5.4 Application Example???????????????????????????????????????????????????????????????? 505
9.6 Absorbing Boundary Conditions???????????????????????????????????????????????????????????????????????????????? 507
9.6.1 Two-Dimensional ABCs?????????????????????????????????????????????????????????????????? 507
9.6.2 Three-Dimensional ABCs?????????????????????????????????????????????????????????????????????? 510
9.6.3 Perfectly Matched Layers?????????????????????????????????????????????????????????????????????????? 512
9.7 Some Numerical Aspects?????????????????????????????????????????????????????????????????? 518
9.7.1 Mesh Generation???????????????????????????????????????????????????????? 518
9.7.2 Matrix Solvers?????????????????????????????????????????????????????? 518
9.7.3 Higher-Order Elements???????????????????????????????????????????????????????????????????? 519
9.7.4 Curvilinear Elements?????????????????????????????????????????????????????????????????? 520
9.7.5 Adaptive Finite Element Analysis?????????????????????????????????????????????????????????????????????????????????????????? 520
9.8 Summary???????????????????????????????????? 521
References?????????????????????????????????? 521
Problems?????????????????????????????? 523
Chapter 10 The Method of Moments?????????????????????????????????????????????????????????????????????????????? 529
10.1 Introduction to the Method of Moments?????????????????????????????????????????????????????????????????????????????????????????????????? 530
10.2 Two-Dimensional Analysis???????????????????????????????????????????????????????????????????????? 534
10.2.1 Formulation of Integral Equations?????????????????????????????????????????????????????????????????????????????????????????????? 534
10.2.2 Scattering by a Conducting Cylinder?????????????????????????????????????????????????????????????????????????????????????????????????? 538
10.2.3 Scattering by a Conducting Strip???????????????????????????????????????????????????????????????????????????????????????????? 542
10.2.4 Scattering by a Homogeneous Dielectric Cylinder?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 546
10.3 Three-Dimensional Analysis???????????????????????????????????????????????????????????????????????????? 547
10.3.1 Formulation of Integral Equations?????????????????????????????????????????????????????????????????????????????????????????????? 547
10.3.2 Scattering and Radiation by a Conducting Wire?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 552
10.3.3 Scattering by a Conducting Body?????????????????????????????????????????????????????????????????????????????????????????? 556
10.3.4 Scattering by a Homogeneous Dielectric Body?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 562
10.3.5 Scattering by an Inhomogeneous Dielectric Body???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 566
10.4 Analysis of Periodic Structures?????????????????????????????????????????????????????????????????????????????????????? 568
10.4.1 Scattering by a Planar Periodic Conducting Patch Array???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 568
10.4.2 Scattering by a Discrete Body-of-Revolution Object???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 573
10.5 Analysis of Microstrip Antennas and Circuits???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 575
10.5.1 Formulation of Integral Equations?????????????????????????????????????????????????????????????????????????????????????????????? 576
10.5.2 The Moment-Method Solution???????????????????????????????????????????????????????????????????????????????? 580
10.5.3 Evaluation of Green's Functions?????????????????????????????????????????????????????????????????????????????????????????? 580
10.5.4 Far-Field Calculation and Application Examples???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 585
10.6 The Moment Method in the Time Domain???????????????????????????????????????????????????????????????????????????????????????????????? 585
10.6.1 Time-Domain Integral Equations???????????????????????????????????????????????????????????????????????????????????????? 587
10.6.2 Marching-On-in-Time Solution???????????????????????????????????????????????????????????????????????????????????? 588
10.7 Summary?????????????????????????????????????? 592
References?????????????????????????????????? 592
Problems?????????????????????????????? 595
Chapter 11 Fast Algorithms and Hybrid Techniques?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 599
11.1 Introduction to Fast Algorithms?????????????????????????????????????????????????????????????????????????????????????? 600
11.2 Conjugate Gradient-FFT Method?????????????????????????????????????????????????????????????????????????????????? 602
11.2.1 Scattering by a Conducting Strip or Wire???????????????????????????????????????????????????????????????????????????????????????????????????????????? 602
11.2.2 Scattering by a Conducting Plate???????????????????????????????????????????????????????????????????????????????????????????? 603
11.2.3 Scattering by a Dielectric Object?????????????????????????????????????????????????????????????????????????????????????????????? 609
11.3 Adaptive Integral Method???????????????????????????????????????????????????????????????????????? 615
11.3.1 Planar Structures?????????????????????????????????????????????????????????????? 616
11.3.2 Three-Dimensional Objects?????????????????????????????????????????????????????????????????????????????? 620
11.4 Fast Multipole Method?????????????????????????????????????????????????????????????????? 626
11.4.1 Two-Dimensional Analysis???????????????????????????????????????????????????????????????????????????? 626
11.4.2 Three-Dimensional Analysis???????????????????????????????????????????????????????????????????????????????? 630
11.4.3 Multilevel Fast Multipole Algorithm?????????????????????????????????????????????????????????????????????????????????????????????????? 634
11.5 Adaptive Cross-Approximation Algorithm???????????????????????????????????????????????????????????????????????????????????????????????????? 638
11.5.1 Low-Rank Matrix?????????????????????????????????????????????????????????? 639
11.5.2 Adaptive Cross-Approximation???????????????????????????????????????????????????????????????????????????????????? 641
11.5.3 Application to the Moment-Method Solution?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 643
11.6 Introduction to Hybrid Techniques?????????????????????????????????????????????????????????????????????????????????????????? 647
11.7 Hybrid Finite Difference-Finite Element Method???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 648
11.7.1 Relation Between FETD and FDTD???????????????????????????????????????????????????????????????????????????????????????? 649
11.7.2 Hybridization of FETD and FDTD???????????????????????????????????????????????????????????????????????????????????????? 651
11.7.3 Application Example?????????????????????????????????????????????????????????????????? 653
11.8 Hybrid Finite Element-Boundary Integral Method???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 654
11.8.1 Traditional Formulation?????????????????????????????????????????????????????????????????????????? 655
11.8.2 Symmetric Formulation?????????????????????????????????????????????????????????????????????? 659
11.8.3 Numerical Examples???????????????????????????????????????????????????????????????? 662
11.9 Summary?????????????????????????????????????? 666
References?????????????????????????????????? 667
Problems?????????????????????????????? 673
Chapter 12 Concluding Remarks on Computational Electromagnetics???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 675
12.1 Overview of Computational Electromagnetics???????????????????????????????????????????????????????????????????????????????????????????????????????????? 675
12.1.1 Frequency- Versus Time-Domain Analysis???????????????????????????????????????????????????????????????????????????????????????????????????????? 675
12.1.2 High-Frequency Asymptotic Techniques???????????????????????????????????????????????????????????????????????????????????????????????????? 677
12.1.3 First-Principle Numerical Methods?????????????????????????????????????????????????????????????????????????????????????????????? 678
12.1.4 Time-Domain Simulation Methods???????????????????????????????????????????????????????????????????????????????????????? 680
12.1.5 Hybrid Techniques?????????????????????????????????????????????????????????????? 682
12.2 Applications of Computational Electromagnetics???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 683
12.3 Challenges in Computational Electromagnetics???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 694
References?????????????????????????????????? 695
Appendix A Vector Identities, Integral Theorems, and Coordinate Transformation?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 705
A.1 Vector Identities???????????????????????????????????????????????????????? 705
A.2 Integral Theorems???????????????????????????????????????????????????????? 706
A.3 Coordinate Transformation???????????????????????????????????????????????????????????????????????? 706
Appendix B Bessel Functions???????????????????????????????????????????????????????????????????? 707
B.1 Definition?????????????????????????????????????????? 707
B.2 Series Expressions?????????????????????????????????????????????????????????? 707
B.3 Integral Representation???????????????????????????????????????????????????????????????????? 709
B.4 Asymptotic Expressions?????????????????????????????????????????????????????????????????? 709
B.5 Recurrence and Derivative Relations???????????????????????????????????????????????????????????????????????????????????????????? 709
B.6 Symmetry Relations?????????????????????????????????????????????????????????? 710
B.7 Wronskian Relation?????????????????????????????????????????????????????????? 710
B.8 Useful Integrals?????????????????????????????????????????????????????? 710
Appendix C Modified Bessel Functions?????????????????????????????????????????????????????????????????????????????????????? 711
C.1 Definition?????????????????????????????????????????? 711
C.2 Series Expressions?????????????????????????????????????????????????????????? 711
C.3 Integral Representations?????????????????????????????????????????????????????????????????????? 712
C.4 Asymptotic Expressions?????????????????????????????????????????????????????????????????? 712
C.5 Recurrence and Derivative Relations???????????????????????????????????????????????????????????????????????????????????????????? 713
C.6 Symmetry Relations?????????????????????????????????????????????????????????? 714
C.7 Wronskian Relation?????????????????????????????????????????????????????????? 714
C.8 Useful Integrals?????????????????????????????????????????????????????? 714
Appendix D Spherical Bessel Functions???????????????????????????????????????????????????????????????????????????????????????? 715
D.1 Definition?????????????????????????????????????????? 715
D.2 Series Expressions?????????????????????????????????????????????????????????? 716
D.3 Asymptotic Expressions?????????????????????????????????????????????????????????????????? 717
D.4 Recurrence and Derivative Relations???????????????????????????????????????????????????????????????????????????????????????????? 717
D.5 Symmetry Relations?????????????????????????????????????????????????????????? 718
D.6 Wronskian Relation?????????????????????????????????????????????????????????? 719
D.7 Riccati-Bessel Functions?????????????????????????????????????????????????????????????????????? 719
D.8 Modified Spherical Bessel Functions???????????????????????????????????????????????????????????????????????????????????????????? 719
Appendix E Associated Legendre Polynomials?????????????????????????????????????????????????????????????????????????????????????????????????? 721
E.1 Definition?????????????????????????????????????????? 721
E.2 Series Expression???????????????????????????????????????????????????????? 722
E.3 Special Values?????????????????????????????????????????????????? 724
E.4 Symmetry Relations?????????????????????????????????????????????????????????? 725
E.5 Recurrence and Derivative Relations???????????????????????????????????????????????????????????????????????????????????????????? 725
E.6 Orthogonal Relations?????????????????????????????????????????????????????????????? 726
E.7 Fourier-Legendre Series???????????????????????????????????????????????????????????????????? 726
Index???????????????????????? 727
EULA?????????????????????? 740
| Erscheint lt. Verlag | 10.8.2015 |
|---|---|
| Reihe/Serie | IEEE Press |
| Wiley - IEEE | Wiley - IEEE |
| Sprache | englisch |
| Themenwelt | Naturwissenschaften ► Physik / Astronomie ► Elektrodynamik |
| Technik ► Elektrotechnik / Energietechnik | |
| Schlagworte | Bessel functions • Electrical & Electronics Engineering • electromagnetic field theory • Electromagnetic theory • Elektromagnetismus • Elektrotechnik u. Elektronik • Finite Electric Dipole • Green’s Theorems • Helmholtz decomposition theorem • Infinitesimal Electric Dipole • Lorenz Gauge Condition • Maxwell’s equations • Numerical Methods & Algorithms • Numerische Methoden u. Algorithmen • Plane waves • Poynting’s Theorem • Reciprocity theorems • Scattering Analysis • The Finite Difference Method • the finite element method • The Lorentz Force Law • The Method of Moments • Time-Harmonic Fields • Transmission Line Theory • Uniform Cavities • Uniform Waveguides • Vector analysis • Wave Transformation • Yee’s FDTD Scheme |
| ISBN-10 | 1-119-10808-X / 111910808X |
| ISBN-13 | 978-1-119-10808-5 / 9781119108085 |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
| Haben Sie eine Frage zum Produkt? |
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