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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: 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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The prelims comprise: Half Title IEEE/Oup Series Title Copyright IEEE Press Board Page Contents Preface Acknowledgments View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full abstract»
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 View full 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. View full abstract»
This appendix contains sections titled: Implementation 1: Single-Point Approximation Implementation 2: Romberg Quadrature Implementation 3: Generalized Gaussian Quadrature View full abstract»
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