Theory and computation of electromagnetic fields 11.8.1 Traditional Formulation 11.8.2 Symmetric Formulation 11.8.3 Numerical Examples 11.9 Summary CHAPTER 12 CONCLUDING REMARKS ON COMPUTATIONAL ELECTROMAGNETICS 12.1 Overview of Computational Electromagnetics 12.1.1 Frequency versus Time Domain Analysis 12.1.2 High Frequency Asymptotic Techniques 12.1.3 First Principle Numerical Methods 12.1.4 Time Domain Simulation Methods 12.1.5 Hybrid Techniques 12.2 Applications of Computational Electromagnetics 12.3 Challenges in Computational Electromagnetics References APPENDIX Vector Identities Integral Theorems Coordinate Transformation INDEX A unique textbook for both entry and advanced level graduate courseworkTheory and Computation of Electromagnetic Fields doubles as a textbook for both an entry level graduate course on electromagnetics and an advanced level graduate course on computational electromagnetics. It presents the fundamental concepts in a systematic manner so that students can advance from the first course to the second with little difficulty.The book consists of two parts. Part I covers the standard basic electromagnetic theory in a different manner than most texts; the contents cover both fundamental theories (such as vector analysis Maxwells equations and boundary conditions 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. Part II covers major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the finite difference method (and the finite difference time domain method in particular) the finite element method and the integral equation based moment method.Additional benefits of Theory and Computation of Electromagnetic Fields include:. Maxwells equations as the starting point for the treatment of every subject. Added coverage of fast algorithms for solving integral equations and hybrid techniques for combining different numerical methods to seek more efficient solutions to complicated electromagnetic problems. Material designed for classroom teaching and self learning in two semesters and tested over fifteen years at the University of Illinois. Homework problems in every chapter to test and reinforce understanding of course material. Accompanying Instructors GuideTheory and Computation of Electromagnetic Fields serves as a textbook for entry and advanced level graduate electrical engineering students. It is also an ideal reference for professional engineers who wish to brush up on their analysis and computation skills 10.1 Introduction to the Method of Moments 10.2 Two Dimensional Analysis 10.2.1 Formulation of Integral Equations 10.2.2 Scattering by a Conducting Cylinder 10.2.3 Scattering by a Conducting Strip 10.2.4 Scattering by a Homogeneous Dielectric Cylinder 10.3 Three Dimensional Analysis 10.3.1 Formulation of Integral Equations 10.3.2 Scattering and Radiation by a Conducting Wire 10.3.3 Scattering by a Conducting Body 10.3.4 Scattering by a Homogeneous Dielectric Body 10.3.5 Scattering by an Inhomogeneous Dielectric Body 10.4 Analysis of Periodic Structures 10.4.1 Scattering by a Planar Periodic Conducting Patch Array 10.4.2 Scattering by a Discrete Body of Revolution Object 10.5 Analysis of Microstrip Antennas and Circuits 10.5.1 Formulation of Integral Equations 10.5.2 The Moment Method Solution 10.5.3 Evaluation of Greens Functions 10.5.4 Far Field Calculation and Application Examples 10.6 The Moment Method in the Time Domain 10.6.1 Time Domain Integral Equations 10.6.2 Marching On in Time Solution 10.7 Summary CHAPTER 11 FAST ALGORITHMS AND HYBRID TECHNIQUES 11.1 Introduction to Fast Algorithms 11.2 Conjugate Gradient FFT Method 11.2.1 Scattering by a Conducting Strip or Wire 11.2.2 Scattering by a Conducting Plate 11.2.3 Scattering by a Dielectric Object 11.3 Adaptive Integral Method 11.3.1 Planar Structures 11.3.2 Three Dimensional Objects 11.4 Fast Multipole Method 11.4.1 Two Dimensional Analysis 11.4.2 Three Dimensional Analysis 11.4.3 Multilevel Fast Multipole Algorithm 11.5 Adaptive Cross Approximation Algorithm 11.5.1 Low Rank Matrix 11.5.2 Adaptive Cross Approximation 11.5.3 Application to the Moment Method Solution 11.6 Introduction to Hybrid Techniques 11.7 Hybrid Finite Difference Finite Element Method 11.7.1 Relation between FETD and FDTD 11.7.2 Hybridization of FETD and FDTD 11.7.3 Application Example 11.8 Hybrid Finite Element Boundary Integral Method 7.5.2 Radiation of a Spherical Surface Current 7.5.3 Radiation in the Presence of a Sphere 7.5.4 Radiation in the Presence of a Conducting Cone PART II ELECTROMAGNETIC FIELD COMPUTATION CHAPTER 8 THE FINITE DIFFERENCE METHOD 8.1 Finite Differencing Formulas 8.2 One Dimensional Analysis 8.2.1 Solution of the Diffusion Equation 8.2.2 Solution of the Wave Equation 8.2.3 Stability Analysis 8.2.4 Numerical Dispersion Analysis 8.3 Two Dimensional Analysis 8.3.1 Analysis in the Time Domain 8.3.2 Analysis in the Frequency Domain 8.4 Yees FDTD Scheme 8.4.1 Two Dimensional Analysis 8.4.2 Three Dimensional Analysis 8.5 Absorbing Boundary Conditions 8.5.1 One Dimensional ABC 8.5.2 Two Dimensional ABCs 8.5.3 Perfectly Matched Layers 8.6 Modeling of Dispersive Media 8.6.1 Recursive Convolution Approach 8.6.2 Auxiliary Differential Equation Approach 8.7 Wave Excitation and Far Field Calculation 8.7.1 Modeling of Wave Excitation 8.7.2 Near to Far Field Transformation 8.8 Summary CHAPTER 9 THE FINITE ELEMENT METHOD 9.1 Introduction to the Finite Element Method 9.1.1 The General Principle 9.1.2 One Dimensional Example 9.2 Finite Element Analysis of Scalar Fields 9.2.1 The Boundary Value Problem 9.2.2 Finite Element Formulation 9.2.3 Application Examples 9.3 Finite Element Analysis of Vector Fields 9.3.1 The Boundary Value Problem 9.3.2 Finite Element Formulation 9.3.3 Application Examples 9.4 Finite Element Analysis in the Time Domain 9.4.1 The Boundary Value Problem 9.4.2 Finite Element Formulation 9.4.3 Application Examples 9.5 Absorbing Boundary Conditions 9.5.1 Two Dimensional ABCs 9.5.2 Three Dimensional ABCs 9.5.3 Perfectly Matched Layers 9.6 Some Numerical Aspects 9.6.1 Mesh Generation 9.6.2 Matrix Solvers 9.6.3 Higher Order Elements 9.6.4 Curvilinear Elements 9.6.5 Adaptive Finite Element Analysis CHAPTER 10 THE METHOD OF MOMENTS PREFACE ACKNOWLEDGMENTS PART I ELECTROMAGNETIC FIELD THEORY CHAPTER 1 BASIC ELECTROMAGNETIC THEORY 1.1 Review of Vector Analysis 1.1.1 Vector Operations and Integral Theorems 1.1.2 Symbolic Vector Method 1.1.3 Helmholtz Decomposition Theorem 1.1.4 Greens Theorems 1.2 Maxwells Equations in Terms of Total Charges and Currents 1.2.1 Maxwells Equations in Integral Form 1.2.2 Maxwells Equations in Differential Form 1.2.3 Current Continuity Equation 1.2.4 The Lorentz Force Law 1.3 Constitutive Relations 1.3.1 Electric Polarization 1.3.2 Magnetization 1.3.3 Electric Conduction 1.3.4 Classifi cation of Media 1.4 Maxwells Equations in Terms of Free Charges and Currents 1.5 Boundary Conditions 1.6 Energy Power and Poyntings Theorem 1.7 Time Harmonic Fields 1.7.1 Time Harmonic Fields 1.7.2 Fourier Transforms 1.7.3 Complex Power 1.7.4 Complex Permittivity and Permeability CHAPTER 2 ELECTROMAGNETIC RADIATION IN FREE SPACE 2.1 Scalar and Vector Potentials 2.1.1 Static Fields 2.1.2 Time Harmonic Fields and the Lorenz Gauge Condition 2.2 Solution of Vector Potentials in Free Space 2.2.1 Delta Function and Greens Function 2.2.2 Greens Function in Free Space 2.2.3 Field Source Relations in Free Space 2.2.4 Why Use Auxiliary Potential Functions 2.2.5 Free Space Dyadic Greens Functions 2.3 Electromagnetic Radiation in Free Space 2.3.1 Infi nitesimal Electric Dipole 2.3.2 Finite Electric Dipole 2.3.3 Far Field Approximation and the Sommerfeld Radiation Condition 2.3.4 Circular Current Loop and Magnetic Dipole 2.4 Radiation by Surface Currents and Phased Arrays 2.4.1 Radiation by a Surface Current 2.4.2 Radiation by a Phased Array CHAPTER 3 ELECTROMAGNETIC THEOREMS AND PRINCIPLES 3.1 Uniqueness Theorem 3.2 Image Theory 3.2.1 Basic Image Theory 3.2.2 Half Space Field Source Relations 3.3 Reciprocity Theorems 3.3.1 General Reciprocity Theorem 5.4 Field Excitation in Waveguides 5.4.1 Excitation by Planar Surface Currents 5.4.2 Excitation by General Volumetric Currents 5.5 Fields in Planar Layered Media 5.5.1 Spectral Greens Function and Sommerfeld Identity 5.5.2 Vertical Electric Dipole above a Layered Medium 5.5.3 Horizontal Electric Dipole above a Layered Medium 5.5.4 Dipoles on a Grounded Dielectric Slab CHAPTER 6 FIELDS AND WAVES IN CYLINDRICAL COORDINATES 6.1 Solution of Wave Equation 6.1.1 Solution by Separation of Variables 6.1.2 Cylindrical Wave Functions 6.2 Circular and Coaxial Waveguides and Cavities 6.2.1 Circular Waveguide 6.2.2 Coaxial Waveguide 6.2.3 Cylindrical Cavity 6.3 Circular Dielectric Waveguide 6.3.1 Analysis of Hybrid Modes 6.3.2 Characteristics of Hybrid Modes 6.4 Wave Transformation and Scattering Analysis 6.4.1 Wave Transformation 6.4.2 Scattering by a Circular Conducting Cylinder 6.4.3 Scattering by a Circular Dielectric Cylinder 6.4.4 Scattering by a Circular Multilayer Dielectric Cylinder 6.5 Radiation by Infi nitely Long Currents 6.5.1 Line Current Radiation in Free Space 6.5.2 Radiation by a Cylindrical Surface Current 6.5.3 Radiation in the Presence of a Circular Conducting Cylinder 6.5.4 Radiation in the Presence of a Conducting Wedge 6.5.5 Radiation by a Finite Current CHAPTER 7 FIELDS AND WAVES IN SPHERICAL COORDINATES 7.1 Solution of Wave Equation 7.1.1 Solution by Separation of Variables 7.1.2 Spherical Wave Functions 7.1.3 TEr and TMr Modes 7.2 Spherical Cavity 7.3 Biconical Antenna 7.3.1 Infi nitely Long Model 7.3.2 Finite Biconical Antenna 7.4 Wave Transformation and Scattering Analysis 7.4.1 Wave Transformation 7.4.2 Expansion of a Plane Wave 7.4.3 Scattering by a Conducting Sphere 7.4.4 Scattering by a Dielectric Sphere 7.4.5 Scattering by a Multilayer Dielectric Sphere 7.5 Addition Theorem and Radiation Analysis 7.5.1 Addition Theorem for Spherical Wave Functions 3.3.2 Lorentz Reciprocity Theorem 3.3.3 Rayleigh Carson Reciprocity Theorem 3.4 Equivalence Principles 3.4.1 Surface Equivalence Principle 3.4.2 Application to Scattering by a Conducting Object 3.4.3 Application to Scattering by a Dielectric Object 3.4.4 Volume Equivalence Principle 3.5 Duality Principle 3.6 Aperture Radiation and Scattering 3.6.1 Equivalent Problems 3.6.2 Babinets Principle 3.6.3 Complementary Antennas CHAPTER 4 TRANSMISSION LINES AND PLANE WAVES 4.1 Transmission Line Theory 4.1.1 Governing Differential Equations and General Solutions 4.1.2 Refl ection and Transmission 4.1.3 Greens Function and Eigenfunction Expansion 4.2 Wave Equations and General Solutions 4.2.1 Wave Equations and Solution by Separation of Variables 4.2.2 Characteristics of a Plane Wave 4.2.3 Wave Velocities and Attenuation 4.2.4 Linear Circular and Elliptical Polarizations 4.2.5 Wave Propagation in Metamaterials 4.3 Plane Waves Generated by A Current Sheet 4.4 Refl ection and Transmission 4.4.1 Refl ection and Transmission at Normal Incidence 4.4.2 Refl ection and Transmission at Oblique Incidence 4.4.3 Total Transmission and Total Reflection 4.4.4 Transmission into a Left Handed Medium 4.4.5 Plane Waves versus Transmission Lines 4.5 Plane Waves in Anisotropic and Bi Isotropic Media 4.5.1 Plane Waves in Uniaxial Media 4.5.2 Plane Waves in Gyrotropic Media 4.5.3 Plane Waves in Chiral Media CHAPTER 5 FIELDS AND WAVES IN RECTANGULAR COORDINATES 5.1 Uniform Waveguides 5.1.1 General Analysis 5.1.2 General Characteristics 5.1.3 Uniform Rectangular Waveguide 5.1.4 Losses in Waveguides and Attenuation Constant 5.2 Uniform Cavities 5.2.1 General Theory 5.2.2 Rectangular Cavity 5.2.3 Material and Geometry Perturbations 5.3 Partially Filled Waveguides and Dielectric Slab Waveguides 5.3.1 General Theory 5.3.2 Partially Filled Rectangular Waveguide 5.3.3 Dielectric Slab Waveguide on a Ground Plane