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Computational Methods for Electromagnetics

Cover Image Copyright Year: 1998
Author(s): Peterson, A.; Ray, S.; Mittra, R.
Publisher: Wiley-IEEE Press
Content Type : Books & eBooks
Topics: Computing & Processing (Hardware/Software) ;  Fields, Waves & Electromagnetics
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Abstract

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:
Two- and three-dimensional integral equation/method-of-moments formulations
Open-region finite-element formulations based on the scalar and vector Helmholtz equations
Finite difference time-domain methods
Direct and iterative algorithms for the solutions of linear systems
Error analysis and the convergence behavior of numerical results
Radiation boundary conditions
Acceleration methods for periodic Green's functions
Vector finite elements Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries.

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      Frontmatter

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.fmatter
      Page(s): i - xix
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      The prelims comprise:
      Half Title
      IEEE/Oup Series
      Title
      Copyright
      IEEE Press Board Page
      Contents
      Preface
      Acknowledgments View full abstract»

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      Electromagnetic Theory

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch1
      Page(s): 1 - 36
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: Maxwell's Equations
      Volumetric Equivalence Principle for Penetrable Scatterers
      General Description of a Scattering Problem
      Source-Field Relationships in Homogeneous Space
      Duality Relationships
      Surface Equivalence Principle
      Surface Integral Equations for Perfectly Conducting Scatterers
      Volume Integral Equations for Penetrable Scatterers
      Surface Integral Equations for Homogeneous Scatterers
      Surface Integral Equation for an Aperture in a Conducting Plane
      Scattering Cross Section Calculation for Two-Dimensional Problems
      Scattering Cross Section Calculation for Three-Dimensional Problems
      Application to Antenna Analysis
      Summary

      This chapter contains sections titled: References
      Problems

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      Integral Equation Methods for Scattering from Infinite Cylinders

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch2
      Page(s): 37 - 93
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      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
      Summary

      This chapter contains sections titled: References
      Problems

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      Differential Equation Methods for Scattering from Infinite Cylinders

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch3
      Page(s): 95 - 142
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      Algorithms for the Solution of Linear Systems of Equations

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch4
      Page(s): 143 - 186
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      The Discretization Process: Basis/Testing Functions and Convergence

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch5
      Page(s): 187 - 231
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      Alternative Surface Integral Equation Formulations

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch6
      Page(s): 233 - 259
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      Strip Gratings and Other TwoDimensional Structures with OneDimensional Periodicity

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch7
      Page(s): 261 - 300
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      ThreeDimensional Problems with Translational or Rotational Symmetry

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch8
      Page(s): 301 - 336
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      Subsectional Basis Functions for Multidimensional and Vector Problems

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch9
      Page(s): 337 - 414
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      Integral Equation Methods for ThreeDimensional Bodies

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch10
      Page(s): 415 - 459
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      FrequencyDomain Differential Equation Formulations for Open ThreeDimensional Problems

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch11
      Page(s): 461 - 494
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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
      Summary

      This chapter contains sections titled: References
      Problems

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      FiniteDifference TimeDomain Methods on Orthogonal Meshes

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.ch12
      Page(s): 495 - 523
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This chapter contains sections titled: 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

      This chapter contains sections titled: References
      Problems

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      Appendix A: Quadrature

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.app1
      Page(s): 525 - 530
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This appendix contains sections titled: Romberg Integration
      Gaussian Quadrature
      Gauss-Kronrod Rules
      Incorporation of Logarithmic Singularities
      Gaussian Quadrature for Triangles
      Gaussian Quadrature for Tetrahedrons

      This appendix contains sections titled: References

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      Appendix B: SourceField Relationships for Cylinders Illuminated by an Obliquely Incident Field

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.app2
      Page(s): 531 - 536
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      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:
      Two- and three-dimensional integral equation/method-of-moments formulations
      Open-region finite-element formulations based on the scalar and vector Helmholtz equations
      Finite difference time-domain methods
      Direct and iterative algorithms for the solutions of linear systems
      Error analysis and the convergence behavior of numerical results
      Radiation boundary conditions
      Acceleration methods for periodic Green's functions
      Vector finite elements Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries. View full abstract»

    • Full text access may be available. Click article title to sign in or learn about subscription options.

      Appendix C: Fortran Codes for TM Scattering from Perfect Electric Conducting Cylinders

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.app3
      Page(s): 537 - 552
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      This appendix contains sections titled: Implementation 1: Single-Point Approximation
      Implementation 2: Romberg Quadrature
      Implementation 3: Generalized Gaussian Quadrature

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      Appendix D: Additional Software Available via the Internet

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.app4
      Page(s): 553
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      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:
      Two- and three-dimensional integral equation/method-of-moments formulations
      Open-region finite-element formulations based on the scalar and vector Helmholtz equations
      Finite difference time-domain methods
      Direct and iterative algorithms for the solutions of linear systems
      Error analysis and the convergence behavior of numerical results
      Radiation boundary conditions
      Acceleration methods for periodic Green's functions
      Vector finite elements Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries. View full abstract»

    • Full text access may be available. Click article title to sign in or learn about subscription options.

      Index

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.index
      Page(s): 555 - 561
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      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:
      Two- and three-dimensional integral equation/method-of-moments formulations
      Open-region finite-element formulations based on the scalar and vector Helmholtz equations
      Finite difference time-domain methods
      Direct and iterative algorithms for the solutions of linear systems
      Error analysis and the convergence behavior of numerical results
      Radiation boundary conditions
      Acceleration methods for periodic Green's functions
      Vector finite elements Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries. View full abstract»

    • Full text access may be available. Click article title to sign in or learn about subscription options.

      About the Authors

      Peterson, A. ; Ray, S. ; Mittra, R.
      Computational Methods for Electromagnetics

      DOI: 10.1109/9780470544303.about
      Page(s): 563 - 564
      Copyright Year: 1998

      Wiley-IEEE Press eBook Chapters

      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:
      Two- and three-dimensional integral equation/method-of-moments formulations
      Open-region finite-element formulations based on the scalar and vector Helmholtz equations
      Finite difference time-domain methods
      Direct and iterative algorithms for the solutions of linear systems
      Error analysis and the convergence behavior of numerical results
      Radiation boundary conditions
      Acceleration methods for periodic Green's functions
      Vector finite elements Detail is provided to enable the reader to implement concepts in software and, in addition, a collection of related computer programs are available via the Internet. Computational Methods for Electromagnetics is designed for graduate-level classroom use or self-study, and every chapter includes problems. It will also be of particular interest to engineers working in the aerospace, defense, telecommunications, wireless, electromagnetic compatibility, and electronic packaging industries. View full abstract»