Computational Methods for Electromagnetics

Cover Image 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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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

      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

      Copyright Year: 1998

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      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

    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

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    Copyright Year: 1998

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    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

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    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 Two-Dimensional Structures with One-Dimensional Periodicity

    Computational Methods for Electromagnetics
    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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    Three-Dimensional Problems with Translational or Rotational Symmetry

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    Copyright Year: 1998

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    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 Three-Dimensional Bodies

    Computational Methods for Electromagnetics
    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 Three-Dimensional Problems

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    Copyright Year: 1998

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

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    Copyright Year: 1998

    Wiley-IEEE Press eBook Chapters

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    Index

    Computational Methods for Electromagnetics
    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

    Computational Methods for Electromagnetics
    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»



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