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The method of moments in electromagnetics / Walton C. Gibson.

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"The Method of Moments in Electromagnetics, Third Edition details the numerical solution of electromagnetic integral equations via the Method of Moments (MoM). Previous editions focused on the solution of radiation and scattering problems involving conducting, dielectric, and composite objects....

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Bibliographic Details
Online Access: Full Text (via O'Reilly/Safari)
Main Author: Gibson, Walton C. (Author)
Format: eBook
Language:English
Published: Boca Raton : CRC Press, 2022.
Edition:Third edition.
Subjects:
Electromagnetism > Data processing.
Electromagnetic fields > Mathematical models.
Moments method (Statistics)
Electromagnetic theory > Data processing.
Integral equations > Numerical solutions.
Electromagnetic fields > Mathematical models
Electromagnetic theory > Data processing
Electromagnetism > Data processing
Integral equations > Numerical solutions
Table of Contents:
  • Cover
  • Half Title
  • Title Page
  • Copyright Page
  • Contents
  • Preface to the Third Edition
  • Preface to the Second Edition
  • Preface
  • Acknowledgments
  • About the Author
  • 1. Computational Electromagnetics
  • 1.1. CEM Algorithms
  • 1.1.1. Low-Frequency Methods
  • 1.1.1.1. Finite Difference Time Domain Method
  • 1.1.1.2. Finite Element Method
  • 1.1.1.3. Method of Moments
  • 1.1.2. High-Frequency Methods
  • 1.1.2.1. Geometrical Theory of Diffraction
  • 1.1.2.2. Physical Optics
  • 1.1.2.3. Physical Theory of Diffraction
  • 1.1.2.4. Shooting and Bouncing Rays
  • References
  • 2. The Method of Moments
  • 2.1. Electrostatic Problems
  • 2.1.1. Charged Wire
  • 2.1.1.1. Matrix Element Evaluation
  • 2.1.1.2. Solution
  • 2.1.2. Charged Plate
  • 2.1.2.1. Matrix Element Evaluation
  • 2.1.2.2. Solution
  • 2.2. The Method of Moments
  • 2.2.1. Point Matching
  • 2.2.2. Galerkin's Method
  • 2.3. Common One-Dimensional Basis Functions
  • 2.3.1. Pulse Functions
  • 2.3.2. Piecewise Triangular Functions
  • 2.3.3. Piecewise Sinusoidal Functions
  • 2.3.4. Entire-Domain Functions
  • 2.3.5. Number of Basis Functions
  • References
  • 3. Radiation and Scattering
  • 3.1. Maxwell's Equations
  • 3.2. Electromagnetic Boundary Conditions
  • 3.3. Formulations for Radiation
  • 3.3.1. Three-Dimensional Green's Function
  • 3.3.2. Two-Dimensional Green's Function
  • 3.4. Vector Potentials
  • 3.4.1. Magnetic Vector Potential
  • 3.4.1.1. Three-Dimensional Magnetic Vector Potential
  • 3.4.1.2. Two-Dimensional Magnetic Vector Potential
  • 3.4.2. Electric Vector Potential
  • 3.4.2.1. Three-Dimensional Electric Vector Potential
  • 3.4.2.2. Two-Dimensional Electric Vector Potential
  • 3.4.3. Total Fields
  • 3.4.4. Comparison of Radiation Formulas
  • 3.5. Near and Far Field
  • 3.5.1. Three-Dimensional Near Field
  • 3.5.2. Two-Dimensional Near Field.
  • 3.5.3. Three-Dimensional Far Field
  • 3.5.4. Two-Dimensional Far Field
  • 3.6. Formulations for Scattering
  • 3.6.1. Surface Equivalent
  • 3.6.2. Surface Integral Equations
  • 3.6.2.1. Interior Resonance Problem
  • 3.6.2.2. Discretization and Testing
  • 3.6.2.3. Modification of Matrix Elements
  • 3.6.3. Enforcement of Boundary Conditions
  • 3.6.3.1. EFIE-CFIE-PMCHWT Approach
  • 3.6.4. Physical Optics Equivalent
  • References
  • 4. Solution of Matrix Equations
  • 4.1. Direct Methods
  • 4.1.1. Gaussian Elimination
  • 4.1.1.1. Pivoting
  • 4.1.2. LU Factorization
  • 4.1.3. Block LU Factorization
  • 4.1.4. Condition Number
  • 4.2. Iterative Methods
  • 4.2.1. Conjugate Gradient
  • 4.2.2. Biconjugate Gradient
  • 4.2.3. Conjugate Gradient Squared
  • 4.2.4. Biconjugate Gradient Stabilized
  • 4.2.5. GMRES
  • 4.2.6. Stopping Criteria
  • 4.2.7. Preconditioning
  • 4.3. Software for Linear Systems
  • 4.3.1. BLAS
  • 4.3.2. LAPACK
  • 4.3.3. MATLAB
  • References
  • 5. Thin Wires
  • 5.1. Thin Wire Approximation
  • 5.2. Thin Wire Excitations
  • 5.2.1. Delta-Gap Source
  • 5.2.2. Magnetic Frill
  • 5.2.3. Plane Wave
  • 5.3. Hallén's Equation
  • 5.3.1. Symmetric Problems
  • 5.3.1.1. Solution Using Pulse Functions and Point Matching
  • 5.3.2 Asymmetric Problems
  • 5.3.2.1 Solution Using Pulse Functions and Point Matching
  • 5.4. Pocklington's Equation
  • 5.4.1. Solution Using Pulse Functions and Point Matching
  • 5.5. Thin Wires of Arbitrary Shape
  • 5.5.1. Method of Moments Discretization
  • 5.5.2. Solution Using Triangle Basis and Testing Functions
  • 5.5.2.1. Non-Self Terms
  • 5.5.2.2. Self Terms
  • 5.5.3. Solution Using Sinusoidal Basis and Testing Functions
  • 5.5.3.1. Self Terms
  • 5.5.4. Lumped and Distributed Impedances
  • 5.6. Examples
  • 5.6.1. Comparison of Thin Wire Models
  • 5.6.1.1. Input Impedance
  • 5.6.1.2. Induced Current Distribution.
  • 5.6.2. Half-Wavelength Dipole
  • 5.6.3. Circular Loop Antenna
  • 5.6.4. Folded Dipole Antenna
  • 5.6.5. Two-Wire Transmission Line
  • 5.6.6. Yagi Antenna for 146 MHz
  • References
  • 6. Two-Dimensional Problems
  • 6.1. Conducting Objects
  • 6.1.1. EFIE: TM Polarization
  • 6.1.1.1. Solution Using Pulse Functions
  • 6.1.1.2. Solution Using Triangle Functions
  • 6.1.2. Generalized EFIE: TM Polarization
  • 6.1.2.1. MoM Discretization
  • 6.1.2.2. Solution Using Triangle Functions
  • 6.1.3. EFIE: TE Polarization
  • 6.1.3.1. Pulse Function Solution
  • 6.1.4. Generalized EFIE: TE Polarization
  • 6.1.4.1. MoM Discretization
  • 6.1.4.2. Solution Using Triangle Functions
  • 6.1.5. nMFIE: TM Polarization
  • 6.1.5.1. Solution Using Triangle Functions
  • 6.1.6. nMFIE: TE Polarization
  • 6.1.6.1. Solution Using Triangle Functions
  • 6.1.7. Examples
  • 6.1.7.1. Conducting Cylinder: TM Polarization
  • 6.1.7.2. Conducting Cylinder: TE Polarization
  • 6.2. Dielectric and Composite Objects
  • 6.2.1. Basis Function Orientation
  • 6.2.2. EFIE: TM Polarization
  • 6.2.2.1. MoM Discretization
  • 6.2.3. MFIE: TM Polarization
  • 6.2.3.1. MoM Discretization
  • 6.2.4. nMFIE: TM Polarization
  • 6.2.4.1. MoM Discretization
  • 6.2.5. EFIE: TE Polarization
  • 6.2.5.1. MoM Discretization
  • 6.2.6. MFIE: TE Polarization
  • 6.2.6.1. MoM Discretization
  • 6.2.7. nMFIE: TE Polarization
  • 6.2.7.1. MoM Discretization
  • 6.2.8. Numerical Stability
  • 6.2.9. Examples
  • 6.2.9.1. Dielectric Cylinder
  • 6.2.9.2. Dielectric Cylinder: TM Polarization
  • 6.2.9.3. Dielectric Cylinder: TE Polarization
  • 6.2.9.4. Coated Cylinder
  • 6.2.9.5. Coated Cylinder: TM Polarization
  • 6.2.9.6. Coated Cylinder: TE Polarization
  • 6.2.9.7. Effect of Number of Segments per Wavelength on Accuracy
  • References
  • 7. Bodies of Revolution
  • 7.1. BoR Surface Description
  • 7.2. Expansion of Surface Currents.
  • 7.3. EFIE
  • 7.3.1. L Operator
  • 7.3.1.1. L Matrix Elements
  • 7.3.2. K Operator
  • 7.3.2.1. K Matrix Elements
  • 7.3.3. Excitation
  • 7.3.3.1. Plane Wave Excitation
  • 7.4. MFIE
  • 7.4.1. Excitation
  • 7.4.1.1. Plane Wave Excitation
  • 7.5. Solution
  • 7.5.1. Plane Wave Solution
  • 7.5.1.1. Currents
  • 7.5.2. Scattered Field
  • 7.5.2.1. Scattered Far Fields
  • 7.6. nMFIE
  • 7.6.1. n × L Operator
  • 7.6.1.1. nL Matrix Elements
  • 7.6.2. n × K Operator
  • 7.6.2.1. nK Matrix Elements
  • 7.6.3. Excitation
  • 7.6.3.1. Plane Wave Excitation
  • 7.6.3.2. Plane Wave Solution
  • 7.7. Numerical Discretization
  • 7.8. Notes on Software Implementation
  • 7.8.1. Geometry Processing and Basis Function Assignment
  • 7.8.2. Parallelization
  • 7.8.3. Convergence
  • 7.9. Examples
  • 7.9.1. Spheres
  • 7.9.1.1. Conducting Sphere
  • 7.9.1.2. Stratified Sphere
  • 7.9.1.3. Dielectric Sphere
  • 7.9.1.4. Coated Sphere
  • 7.9.2. EMCC Benchmark Targets
  • 7.9.2.1. EMCC Ogive
  • 7.9.2.2. EMCC Double Ogive
  • 7.9.2.3. EMCC Cone-Sphere
  • 7.9.2.4. EMCC Cone-Sphere with Gap
  • 7.9.3. Biconic Reentry Vehicle
  • 7.10. Treatment of Junctions
  • 7.10.1. Orientation of Basis Functions
  • 7.10.1.1. Longitudinal Basis Vectors
  • 7.10.1.2. Azimuthal Basis Vectors
  • 7.10.2. Examples with Junctions
  • 7.10.2.1. Dielectric Sphere with Septum
  • 7.10.2.2. Coated Sphere with Septum
  • 7.10.2.3. Stratified Sphere with Septum
  • 7.10.2.4. Monoconic Reentry Vehicle with Dielectric Nose
  • References
  • 8. Three-Dimensional Problems
  • 8.1. Modeling of Three-Dimensional Surfaces
  • 8.1.1. Facet File
  • 8.1.2. Edge-Finding Algorithm
  • 8.1.2.1. Shared Nodes
  • 8.2. Expansion of Surface Currents
  • 8.2.1. Divergence of the RWG Function
  • 8.2.2. Assignment and Orientation of Basis Functions
  • 8.3. EFIE
  • 8.3.1. L Operator
  • 8.3.1.1. Non-Near Terms
  • 8.3.1.2. Near and Self Terms.
  • 8.3.2. K Operator
  • 8.3.2.1. Non-Near Terms
  • 8.3.2.2. Near Terms
  • 8.3.3. Excitation
  • 8.3.3.1. Plane Wave Excitation
  • 8.3.3.2. Planar Antenna Excitation
  • 8.4. MFIE
  • 8.4.1. Excitation
  • 8.4.1.1. Plane Wave Excitation
  • 8.5. nMFIE
  • 8.5.1. n × K Operator
  • 8.5.1.1. Non-Near Terms
  • 8.5.1.2. Near Terms
  • 8.5.2. n × L Operator
  • 8.5.2.1. Non-Near Terms
  • 8.5.2.2. Near and Self Terms
  • 8.5.3. Excitation
  • 8.5.3.1. Plane Wave Excitation
  • 8.6. Enforcement of Boundary Conditions
  • 8.6.1. Classification of Edges and Junctions
  • 8.6.1.1. Dielectric Edges and Junctions
  • 8.6.1.2. Conducting Edges and Junctions
  • 8.6.1.3. Composite Conducting-Dielectric Junctions
  • 8.6.2. Reducing the Overdetermined System
  • 8.6.2.1. PMCHWT at Dielectric Edges and Junctions
  • 8.6.2.2. EFIE and CFIE at Conducting Edges and Junctions
  • 8.6.2.3. EFIE and CFIE at Composite Conducting-Dielectric Junctions
  • 8.7. Software Implementation Notes
  • 8.7.1. Pre-Processing and Bookkeeping
  • 8.7.1.1. Region and Interface Assignments
  • 8.7.1.2. Geometry Processing
  • 8.7.1.3. Assignment and Orientation of Basis Functions
  • 8.7.2. Matrix and Right-Hand Side Fill
  • 8.7.3. Parallelization
  • 8.7.3.1. Shared Memory Systems
  • 8.7.3.2. Distributed Memory Systems
  • 8.7.4. Triangle Mesh Considerations
  • 8.7.4.1. Aspect Ratio
  • 8.7.4.2. T-Junctions
  • 8.8. Numerical Examples
  • 8.8.1. Serenity
  • 8.8.2. Compute Platform
  • 8.8.3. Spheres
  • 8.8.3.1. Conducting Sphere
  • 8.8.3.2. Dielectric Sphere
  • 8.8.3.3. Coated Sphere
  • 8.8.4. EMCC Plate Benchmark Targets
  • 8.8.4.1. Wedge Cylinder
  • 8.8.4.2. Wedge-Plate Cylinder
  • 8.8.4.3. Plate Cylinder
  • 8.8.4.4. Business Card
  • 8.8.5. Strip Dipole Antenna
  • 8.8.6. Bowtie Antenna
  • 8.8.7. Archimedean Spiral Antenna
  • 8.8.8. Monoconic Reentry Vehicle with Dielectric Nose
  • 8.8.9. Summary of Examples
  • References.

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