This text/reference is a detailed look at the development and use of integral equation methods for electromagnetic analysis, specifically for antennas and radar scattering. Developers and practitioners will appreciate the broad-based approach to understanding and utilizing integral equation methods and the unique coverage of historical developments that led to the current state-of-the-art. In contrast to existing books, Integral Equation Methods for Electromagnetics lays the groundwork in the initial chapters so students and basic users can solve simple problems and work their way up to the most advanced and current solutions.

This is the first book to discuss the solution of two-dimensional integral equations in many forms of their application and utility. As 2D problems are simpler to discuss, the student and basic reader can gain the necessary expertise before diving into 3D applications. This is also the first basic text to cover fast integral methods for metallic, impedance, and material geometries. It will provide the student or advanced reader with a fairly complete and up-to-date coverage of integral methods for composite scatterers.

KEY FEATURES
• Written by developers and practitioners with over 20 years experience in the field.
• Detailed and informative coverage of integral equation expressions in spatial and integral form.
• Methods and approaches for developing integral equations that can be solved along with assumptions associated with their approximations.
• Derivations of integral equations for printed structures on multilayered substrates.
• Historical sections outlining the development of many popular integral equations.
• Step-by-step solutions of the wire, 2D and 3D integral equation for numerous situations of composite scatterers and radiators.
• Covers a variety of basis functions (triangular, quadrilateral, tetrahedral, curvilinear and hexahedral, including Bezier curves and NURBS) and matrix solutions approaches.

1 Fundamental Concepts and Theorems
1.1 Maxwell’s Equations in Differential Time Domain Form
1.2 Maxwell’s Equations in Integral Form
1.3 Maxwell’s Equations in Phasor Form
1.4 Natural Boundary Conditions
1.5 Poynting’s Theorem
1.6 Uniqueness Theorem
1.7 Superposition Theorem
1.8 Duality Theorem
1.9 Volume equivalence theorem
1.10 Surface equivalence theorem
1.11 Reciprocity and Reaction Theorems
1.12 Approximate Boundary Conditions
Problems

2 Field Solutions and Representations
2.1 Field Solutions in Terms of Vector and Hertz Potentials
2.2 Solution for the Vector and Scalar Potentials
2.3 Near and Far Zone Field Expressions
2.3.1 Near Zone Fields
2.3.2 Field Evaluation in the Source Region
2.3.3 Fresnel and Far Zone Fields
2.4 Direct Solution of the Vector Wave Equation
2.4.1 Vector wave equations
2.4.2 Dyadic representation
2.5 Two-Dimensional Fields
2.5.1 Two-dimensional sources
2.5.2 Exact Integral Expressions
2.5.3 Far Zone Fields
2.5.4 Field evaluation in the source region
2.6 Spectral Field Representations
2.7 Radiation over a Dielectric Half Space
Problems

3 Integral Equations and Other Field Representations
3.1 Three-Dimensional Integral Equations
3.1.1 Kirchho’s Integral Equation
3.1.2 Stratton-Chu Integral Equations
3.1.3 Equations for Homogeneous Dielectrics
3.1.4 Integral Equations for Metallic Bodies
3.1.5 Combined Field Integral Equations
3.1.6 Integral Equations for Piecewise Homogeneous Dielectrics
3.1.7 Integral Equations for Inhomogeneous Dielectrics
3.2 Two-Dimensional Representations
3.2.1 Boundary Integral Equations
3.2.2 Homogeneous Dielectrics
3.2.3 Metallic Cylinders
3.2.4 Piecewise Homogeneous Dielectrics
3.2.5 Domain Integral Equations
Problems

4 Solution of Integral Equations for Wire Radiators and Scatterers
4.1 Formulation
4.2 Basis Functions
4.3 Pulse Basis{Point Matching Solution
4.4 Source Modeling
4.4.1 Delta gap excitation
4.4.2 Magnetic frill generator
4.4.3 Plane Wave Incidence
4.5 Calculation of the Far Zone Field and Antenna Characteristics
4.6 Piecewise Sinusoidal Basis-Point Matching Solution
4.7 Method of Weighted Residuals/Moment Method
4.8 Moment Method for Non-Linear Wires
4.9 Wires of Finite Conductivity
4.10 Construction of Integral Equations via the Reaction/ReciprocityTheorem
4.11 Iterative Solution Methods: The Conjugate Gradient Method
Problems

5 Two-Dimensional Scattering
5.1 Flat Resistive Strip
5.1.1 E-polarization
5.1.2 H-polarization
5.2 Metallic Cylinders
5.2.1 E-polarization
5.2.2 H-polarization
5.3 H-Polarized (TE) Scattering by Curved Resistive Strips
5.4 Piecewise Homogeneous Dielectric Cylinders
5.5 Elimination of Interior Resonances
5.6 Simulation of Inhomogeneous Dielectric Cylinders
5.6.1 Volume Integral Equation
5.6.2 Volume-Surface Integral Equation

6 Three-Dimensional Scattering
6.1 Scattering by Metallic Bodies
6.1.1 Electric, Magnetic, and Combined Field Integral Equations
6.1.2 Triangular Element Mesh Representations
6.1.3 Rao-Wilton-Glisson Basis Functions
6.1.4 Method of Moments Matrix Assembly
6.2 Curved triangular and quadrilateral elements
6.2.1 Parametric Representations
6.2.2 Polynomial Interpolations
6.2.3 Free-form Representations
6.2.4 Curvilinear Coordinates
6.2.5 Parametric Representations of Surface and Volume Elements
6.2.6 Example Representations of Surface and Volume Basis Functions
6.3 Evaluation of MoM Matrix Entries
6.3.1 Element Matrices and Assembly Process
6.3.2 Evaluation of Integrals with Singular Kernels
6.3.3 Singularity Annihilation Techniques
6.3.4 Regularization for Triangular Subdomains
6.3.5 Annihilation Transforms for Square Subdomains
6.3.6 Numerical Integration
6.3.7 Source Modeling and Antenna Applications
6.3.8 Matrix Solution Methods
6.4 Volumetric Modeling
6.4.1 Volume Integral Equation Formulation
6.4.2 VIE formulation for dielectrics
6.4.3 Zeroth-Order Volumetric Basis Functions
6.4.4 First-Order Volumetric Basis Functions
6.4.5 Second-Order Volumetric Basis Functions
6.4.6 Scattering by Dielectric Bodies
6.4.7 VIE Solution for Magnetically Permeable Structures
6.5 Numerical Examples

7 Fast Multipole Method and Its Multilevel Implementation
7.1 Fast Multipole Method
7.2 Multilevel Fast Multipole Method
7.3 Multilevel Fast Multipole Method Formulation
7.4 Radiation and Scattering Examples
7.5 MLFMM for Volume Integral Equations

8 Integral Equation Formulation for Microstrip Antennas and Scatterers
8.1 Spectral Green’s functions for Substrate Geometry
8.2 Geometry
8.3 Maxwell’s Equations in Spatial Form
8.4 Maxwell’s Equations in Spectral Form
8.5 Solutions in Spectral Form
8.6 Dyadic Green’s Function
8.7 Patch Geometry and Current Formulation
8.8 Far Zone Fields From Microstrip Patch

John (Yiannis) L. Volakis received his Ph.D. from The Ohio State University in 1982. He is the R. & L. Chope Chair Professor at The Ohio State University, Electrical and Computer Engineering Department since 2003. He is also the Director of the ElectroScience Laboratory, one of the largest University laboratories on wireless communications (hardware, analysis, and design). He is the author of five widely used books including the well referenced text Finite Element Methods for Electromagnetics, and the 4th Edition classic Antenna Engineering Handbook. He has also authored over 280 journal papers and over 480 conference papers. He has served as the IEEE Antennas and Propagation Society President (2004) and is listed by ISI among the top 250 most referenced authors in Engineering/Computer Science. He is internationally known for his contributions to numerical electromagnetic, metamaterial antennas and RF materials for high performance hardware.

Kubilay Sertel received his Ph.D. in Electrical Engineering and Computer Science from the University of Michigan at Ann Arbor in 2003. He is currently an Adjunct Assistant Professor with the Electrical and Computer Engineering Department and a Research Scientist with the ElectroScience Laboratory, The Ohio State University. He has over 15 years experience in applied electromagnetics. His publications include the book Frequency Domain Hybrid Finite Element Methods in Electromagnetics (Morgan & Claypool, 2006), over 35 journal articles, and over 100 conference papers. Dr. Sertel is a Senior Member of IEEE and a member of URSI Commission B.