Title:
Integral equation methods for electromagnetics
Personal Author:
Publication Information:
Raleigh, NC : SciTech Pub., c2011.
Physical Description:
p. cm.
ISBN:
9781891121937
Added Author:
On Order
Summary
Summary
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.
llic, 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.llic, 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.llic, 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.Table of Contents
| 1 Introduction |
| 1.1 Maxwell's Equation 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/Reciprocity |
| Theorem |
| 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 |
