Copyright Year: 1998
Author(s): Andrew F. Peterson; Scott L. Ray; Raj Mittra Book Type: Wiley-IEEE Press Content Type : Books & eBooks Topics: Computing & Processing ; Fields, Waves & Electromagnetics |
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This chapter contains sections titled:
TM-Wave Scattering from Conducting Cylinders: EFIE Discretized with Pulse Basis and Delta Testing Functions
TE-Wave Scattering from Conducting Cylinders: MFIE Discretized with Pulse Basis and Delta Testing Functions
Limitations of Pulse Basis/Delta Testing Discretizations
TE-Wave Scattering from Perfectly Conducting Strips or Cylinders: EFIE Discretized with Triangle Basis and Pulse Testing Functions
TM-Wave Scattering from Inhomogeneous Dielectric Cylinders: Volume EFIE Discretized with Pulse Basis and Delta Testing Functions
TE-Wave Scattering from Dielectric Cylinders: Volume EFIE Discretized with Pulse Basis and Delta Testing Functions
TE-Wave Scattering from Inhomogeneous Dielectric Cylinders: Volume MFIE Discretized with Linear Pyramid Basis and Delta Testing Functions
Scattering from Homogeneous Dielectric Cylinders: Surface Integral Equations Discretized with Pulse Basis and Delta Testing Functions
Integral Equations for Two-Dimensional Scatterers Having an Impedance Surface
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References
Problems
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Weak Forms of the Scalar Helmholtz Equations
Incorporation of Perfectly Conducting Boundaries
Exact Near-Zone Radiation Condition on a Circular Boundary
Outward-Looking Formulation Combining the Scalar Helmholtz Equation with the Exact Radiation Boundary Condition
Example: TM-Wave Scattering from a Dielectric Cylinder
Scattering from Cylinders Containing Conductors
Evaluation of Volumetric Integrals for the Matrix Entries
Local Radiation Boundary Conditions on a Circular Surface: The Bayliss-Turkel Conditions
Outward-Looking Formulation Combining the Scalar Helmholtz Equation and the Second-Order Bayliss-Turkel RBC
Exact Near-Zone Radiation Boundary Conditions for Surfaces of General Shape
Connection between the Surface Integral and Eigenfunction RBCs
Inward-Looking Differential Equation Formulation: The Unimoment Method
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References
Problems
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Naive Gaussian Elimination
Pivoting
Condition Numbers and Error Propagation in the Solution of Linear Systems
Cholesky Decomposition for Complex-Symmetric Systems
Reordering Algorithms for Sparse Systems of Equations
Banded Storage for Gaussian Elimination
Variable-Bandwidth or Envelope Storage for Gaussian Elimination
Sparse Matrix Methods Employing Dynamic Storage Allocation
Frontal Algorithm for Gaussian Elimination
Iterative Methods for Matrix Solution
The Conjugate Gradient Algorithm for General Linear Systems
The Conjugate Gradient-Fast Fourier Transform (CG-FFf) Procedure
Fast Matrix-Vector Multiplication: An Introduction to the Fast Multipole Method
Preconditioning Strategies for Iterative Algorithms
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References
Problems
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Inner Product Space
The Method of Moments
Examples of Subsectional Basis Functions
Interpolation Error
Dispersion Analysis
Differentiability Constraints on Basis and Testing Functions
Eigenvalue Projection Theory
Classification of Operators for Several Canonical Equations
Convergence Arguments Based on Galerkin's Method
Convergence Arguments Based on Degenerate Kernel Analogs
Convergence Arguments Based on Projection Operators
The Stationary Character of Functionals Evaluated Using Numerical Solutions
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References
Problems
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Uniqueness of Solutions to the Exterior Surface EFIE and MFIE
The Combined-Field Integral Equation for Scattering from Perfectly Conducting Cylinders
The Combined-Source Integral Equation for Scattering from Perfectly Conducting Cylinders
The Augmented-Field Formulation
Overspecification of the Original EFIE or MFIE at Interior Points
Dual-Surface Integral Equations
Complexification of the Wavenumber
Determination of the Cutoff Frequencies and Propagating Modes of Waveguides of Arbitrary Shape Using Surface Integral Equations
Uniqueness Difficulties Associated with Differential Equation Formulations
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References
Problems
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Fourier Analysis of Periodic Functions
Floquet Harmonics
TM Scattering from a Conducting Strip Grating: EFIE Discretized with Pulse Basis Functions and Delta Testing Functions
Simple Acceleration Procedures for the Green's Function
Alternate Acceleration Procedures
Blind Angles
TE Scattering from a Conducting Strip Grating Backed by a Dielectric Slab: EFIE Formulation
Aperture Formulation for TM Scattering from a Conducting Strip Grating
Scattering Matrix Analysis of Cascaded Periodic Surfaces
TM Scattering from a Half-Space Having a General Periodic Surface: EFIE Discretized with Pulse Basis Functions and Delta Testing Functions
TM Scattering from an Inhomogeneous Grating: Outward-Looking Formulation with an Integral Equation RBC
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References
Problems
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Scattering from Infinite Cylinders Illuminated by Finite Sources
Oblique TM-Wave Scattering from Infinite Conducting Cylinders: CFIE Discretized with Pulse Basis Functions and Delta Testing Functions
Oblique TE-Wave Scattering from Infinite Conducting Cylinders: Augmented MFIE Discretized with Pulse Basis Functionsand Delta Testing Functions
Application: Mutual Admittance between Slot Antennas
Oblique Scattering from Inhomogeneous Cylinders: Volume Integral Equation Formulation
Oblique Scattering from Inhomogeneous Cylinders: Scalar Differential Equation Formulation
Scattering from a Finite-Length, Hollow Conducting Right-Circular Cylinder: The Body-of-Revolution EFIE Formulation
Differential Equation Formulation for Axisymmetric Scatterers
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References
Problems
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Higher Order Lagrangian Basis Functions on Triangles
Example: Use of Higher Order Basis Functions with the Two-Dimensional Scalar Helmholtz Equation
Lagrangian Basis Functions for Rectangular and Quadrilateral Cells
Scalar Basis Functions for Two-Dimensional Cells with Curved Sides
Discretization of Two-Dimensional Surface Integral Equations Using an Isoparametric Quadratic Representation
Scalar Lagrangian Functions in Three Dimensions
Scalar Lagrangian Discretization of the Vector Helmholtz Equation for Cavities: Spurious Eigenvalues and Other Difficulties
Polynomial-Complete Vector Basis Functions that Impose Tangential Continuity but not Normal Continuity between Triangular Cells
Mixed-Order Vector Basis Functions that Impose Tangential but not Normal Continuity for Triangular and Rectangular Cells
TE Scattering Using the Vector Helmholtz Equation with CT/LN and LT/QN Vector Basis Functions Defined on Triangular Cells
Analysis of Dielectric-Loaded Waveguides Using Curl-Conforming Vector Basis Functions
Mixed-Order Curl-Conforming Vector Basis Functions for Tetrahedral and Hexahedral Cells
Divergence-Conforming Vector Basis Functions for Discretizations of the EFIE
Mapping Vector Basis Functions to Curvilinear Cells in Two and Three Dimensions
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References
Problems
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Scattering from Flat Perfectly Conducting Plates: EFIE Discretized with CN/LT Rooftop Basis Functions Defined on Rectangular Cells
Scattering from Perfectly Conducting Bodies: EFIE Discretized with CN/LT Triangular-Cell Rooftop Basis Functions
Scattering from Perfectly Conducting Bodies: MFIE Discretized with Triangular-Cell CN/LT Basis Functions
Scattering from Perfectly Conducting Bodies: CFIE Discretized with Triangular-Cell CN/LT Basis Functions
Performance of the CFIE with LN/QT Basis Functions and Curved Patches
Treatment of Electrically Small Scatterers Using Surface Integral Equations
Scattering from Homogeneous Dielectric Bodies: CFIE Discretized with Triangular-Cell CN/LT Basis Functions
Radiation and Scattering from Thin Wires
Scattering from Planar Periodic Geometries
Analysis of Microstrip Structures
A Brief Survey of Volume Integral Formulations for Heterogeneous Dielectric Bodies
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References
Problems
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Weak Vector Helmholtz Equation and Boundary Conditions
Discretization using CT/LN and LT/QN Functions for Three-Dimensional Cavities
Eigenfunction RBC for Spherical Boundary Shapes
Surface Integral Equation RBC for General Boundary Shapes
Outward-Looking versus Inward-Looking Formulations
Integral Equation RBC for Axisymmetric Boundary Shapes
Local RBCs for Spherical Boundaries
Local RBCs for General Three-Dimensional Boundary Shapes
RBCs Based on Fictitious Absorbers
Vector Formulation for Axisymmetric Heterogeneous Scatterers
Alternative Formulations for Three-Dimensional Scattering
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Maxwell's Equations in the Time Domain
Centered Finite-Difference Approximations
FDTD Spatial Discretization
FDTD Time Discretization
Divergence Conservation in the FDTD
Extensionto Three Dimensions
Other Coordinate Systems
Numerical Analysis of the FDTD Algorithm: Stability, Dispersion, and Anisotropy
Treating Lossy/Conductive Media
Frequency-Dependent Media
Simple Boundary and Interface Conditions
Absorbing Boundary Condition
Internal and External Sources
Far-Field Projections
Extensions to the Orthogonal Mesh FDTD Method
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References
Problems
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This appendix contains sections titled:
Romberg Integration
Gaussian Quadrature
Gauss-Kronrod Rules
Incorporation of Logarithmic Singularities
Gaussian Quadrature for Triangles
Gaussian Quadrature for Tetrahedrons
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References
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This appendix contains sections titled:
Implementation 1: Single-Point Approximation
Implementation 2: Romberg Quadrature
Implementation 3: Generalized Gaussian Quadrature
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Wiley-IEEE Press eBook Chapters
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Computational Methods for Electromagnetics is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment. Employing a unified coherent approach that is unmatched in the field, the authors detail both integral and differential equations using the method of moments and finite-element procedures. In addition, readers will gain a thorough understanding of numerical solution procedures.
Topics covered include:
Wiley-IEEE Press eBook Chapters
| Quick Abstract | Full Text: PDF
Computational Methods for Electromagnetics is an indispensable resource for making efficient and accurate formulations for electromagnetics applications and their numerical treatment. Employing a unified coherent approach that is unmatched in the field, the authors detail both integral and differential equations using the method of moments and finite-element procedures. In addition, readers will gain a thorough understanding of numerical solution procedures.
Topics covered include: