Computational Methods for Electromagnetics

by Peterson, Andrew F.; Ray, Scott L.; Mittra, Raj

• ISBN13: 9780780311220
• ISBN10: 0780311221
• Edition: 1st
• Format: Hardcover
• Copyright: 1997-12-26
• Publisher: Wiley-IEEE Press

Summary

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.

Author Biography

About the Authors...Andrew F. Peterson is associate professor at the School of Electrical and Computer Engineering at Georgia Institute of Technology. His research interests center on the development of both integral and differential equation based numerical methods for electromagnetic applications.

Table of Contents

PREFACE	xvii	(2)
ACKNOWLEDGMENTS	xix
CHAPTER 1 ELECTROMAGNETIC THEORY	1	(36)
1.1 Maxwell's Equations	1	(3)
1.2 Volumetric Equivalence Principle for Penetrable Scatterers	4	(1)
1.3 General Description of a Scattering Problem	5	(1)
1.4 Source-Field Relationships in Homogeneous Space	6	(4)
1.5 Duality Relationships	10	(1)
1.6 Surface Equivalence Principle	10	(6)
1.7 Surface Integral Equations for Perfectly Conducting Scatterers	16	(2)
1.8 Volume Integral Equations for Penetrable Scatterers	18	(1)
1.9 Surface Integral Equations for Homogeneous Scatterers	19	(3)
1.10 Surface Integral Equation for an Aperture in a Conducting Plane	22	(2)
1.11 Scattering Cross Section Calculation for Two-Dimensional Problems	24	(3)
1.12 Scattering Cross Section Calculation for Three-Dimensional Problems	27	(1)
1.13 Application to Antenna Analysis	28	(2)
1.14 Summary	30	(1)
References	30	(1)
Problems	31	(6)
CHAPTER 2 INTEGRAL EQUATION METHODS FOR SCATTERING FROM INFINITE CYLINDERS	37	(58)
2.1 TM-Wave Scattering from Conducting Cylinders: EFIE Discretized with Pulse Basis and Delta Testing Functions	37	(8)
2.2 TE-Wave Scattering from Conducting Cylinders: MFIE Discretized with Pulse Basis and Delta Testing Functions	45	(5)
2.3 Limitations of Pulse Basis/Delta Testing Discretizations	50	(2)
2.4 TE-Wave Scattering from Perfectly Conducting Strips or Cylinders: EFIE Discretized with Triangle Basis and Pulse Testing Functions	52	(7)
2.5 TM-Wave Scattering from Inhomogeneous Dielectric Cylinders: Volume EFIE Discretized with Pulse Basis and Delta Testing Functions	59	(6)
2.6 TE-Wave Scattering from Dielectric Cylinders: Volume EFIE Discretized with Pulse Basis and Delta Testing Functions	65	(5)
2.7 TE-Wave Scattering from Inhomogeneous Dielectric Cylinders: Volume MFIE Discretized with Linear Pyramid Basis and Delta Testing Functions	70	(6)
2.8 Scattering from Homogeneous Dielectric Cylinders: Surface Integral Equations Discretized with Pulse Basis and Delta Testing Functions	76	(4)
2.9 Integral Equations for Two-Dimensional Scatterers Having an Impedance Surface	80	(5)
2.10 Summary	85	(1)
References	85	(1)
Problems	86	(9)
CHAPTER 3 DIFFERENTIAL EQUATION METHODS FOR SCATTERING FROM INFINITE CYLINDERS	95	(48)
3.1 Weak Forms of the Scalar Helmholtz Equations	95	(3)
3.2 Incorporation of Perfectly Conducting Boundaries	98	(2)
3.3 Exact Near-Zone Radiation Condition on a Circular Boundary	100	(2)
3.4 Outward-Looking Formulation Combining the Scalar Helmholtz Equation with the Exact Radiation Boundary Condition	102	(4)
3.5 Example: TM-Wave Scattering from a Dielectric Cylinder	106	(4)
3.6 Scattering from Cylinders Containing Conductors	110	(2)
3.7 Evaluation of Volumetric Integrals for the Matrix Entries	112	(3)
3.8 Local Radiation Boundary Conditions on a Circular Surface: The Bayliss-Turkel Conditions	115	(5)
3.9 Outward-Looking Formulation Combining the Scalar Helmholtz Equation and the Second-Order Bayliss-Turkel RBC	120	(5)
3.10 Exact Near-Zone Radiation Boundary Conditions for Surfaces of General Shape	125	(3)
3.11 Connection between the Surface Integral and Eigenfunction RBCs	128	(2)
3.12 Inward-Looking Differential Equation Formulation: The Unimoment Method	130	(5)
3.13 Summary	135	(1)
References	136	(1)
Problems	137	(6)
CHAPTER 4 ALGORITHMS FOR THE SOLUTION OF LINEAR SYSTEMS OF EQUATIONS	143	(44)
4.1 Naive Gaussian Elimination	143	(3)
4.2 Pivoting	146	(1)
4.3 Condition Numbers and Error Propagation in the Solution of Linear Systems	146	(3)
4.4 Cholesky Decomposition for Complex-Symmetric Systems	149	(1)
4.5 Reordering Algorithms for Sparse Systems of Equations	150	(6)
4.6 Banded Storage for Gaussian Elimination	156	(1)
4.7 Variable-Bandwidth or Envelope Storage for Gaussian Elimination	156	(2)
4.8 Sparse Matrix Methods Employing Dynamic Storage Allocation	158	(1)
4.9 Frontal Algorithm for Gaussian Elimination	159	(1)
4.10 Iterative Methods for Matrix Solution	160	(1)
4.11 The Conjugate Gradient Algorithm for General Linear Systems	161	(9)
4.12 The Conjugate Gradient-Fast Fourier Transform (CG-FFT) Procedure	170	(5)
4.13 Fast Matrix-Vector Multiplication: An Introduction to the Fast Multipole Method	175	(3)
4.14 Preconditioning Strategies for Iterative Algorithms	178	(1)
4.15 Summary	179	(1)
References	180	(4)
Problems	184	(3)
CHAPTER 5 THE DISCRETIZATION PROCESS: BASIS/TESTING FUNCTIONS AND CONVERGENCE	187	(46)
5.1 Inner Product Spaces	187	(3)
5.2 The Method of Moments	190	(2)
5.3 Examples of Subsectional Basis Functions	192	(5)
5.4 Interpolation Error	197	(1)
5.5 Dispersion Analysis	198	(2)
5.6 Differentiability Constraints on Basis and Testing-Functions	200	(5)
5.7 Eigenvalue Projection Theory	205	(2)
5.8 Classification of Operators for Several Canonical Equations	207	(5)
5.9 Convergence Arguments Based on Galerkin's Method	212	(1)
5.10 Convergence Arguments Based on Degenerate Kernel Analogs	213	(4)
5.11 Convergence Arguments Based on Projection Operators	217	(2)
5.12 The Stationary Character of Functionals Evaluated Using Numerical Solutions	219	(5)
5.13 Summary	224	(1)
References	224	(2)
Problems	226	(7)
CHAPTER 6 ALTERNATIVE SURFACE INTEGRAL EQUATION FORMULATIONS	233	(28)
6.1 Uniqueness of Solutions to the Exterior Surface EFIE and MFIE	233	(7)
6.2 The Combined-Field Integral Equation for Scattering from Perfectly Conducting Cylinders	240	(6)
6.3 The Combined-Source Integral Equation for Scattering from Perfectly Conducting Cylinders	246	(2)
6.4 The Augmented-Field Formulation	248	(1)
6.5 Overspecification of the Original EFIE or MFIE at Interior Points	248	(2)
6.6 Dual-Surface Integral Equations	250	(2)
6.7 Complexification of the Wavenumber	252	(1)
6.8 Determination of the Cutoff Frequencies and Propagating Modes of Waveguides of Arbitrary Shape Using Surface Integral Equations	252	(2)
6.9 Uniqueness Difficulties Associated with Differential Equation Formulations	254	(1)
6.10 Summary	255	(1)
References	256	(1)
Problems	257	(4)
CHAPTER 7 STRIP GRATINGS AND OTHER TWO-DIMENSIONAL STRUCTURES WITH ONE-DIMENSIONAL PERIODICITY	261	(40)
7.1 Fourier Analysis of Periodic Functions	261	(3)
7.2 Floquet Harmonics	264	(2)
7.3 TM Scattering from a Conducting Strip Grating: EFIE Discretized with Pulse Basis Functions and Delta Testing Functions	266	(3)
7.4 Simple Acceleration Procedures for the Green's Function	269	(3)
7.5 Alternate Acceleration Procedures	272	(5)
7.6 Blind Angles	277	(1)
7.7 TE Scattering from a Conducting Strip Grating Backed by a Dielectric Slab: EFIE Formulation	277	(4)
7.8 Aperture Formulation for TM Scattering from a Conducting Strip Grating	281	(1)
7.9 Scattering Matrix Analysis of Cascaded Periodic Surfaces	282	(2)
7.10 TM Scattering from a Half-Space Having a General Periodic Surface: EFIE Discretized with Pulse Basis Functions and Delta Testing Functions	284	(5)
7.11 TM Scattering from an Inhomogeneous Grating: Outward-Looking Formulation with an Integral Equation RBC	289	(7)
7.12 Summary	296	(1)
References	296	(1)
Problems	297	(4)
CHAPTER 8 THREE-DIMENSIONAL PROBLEMS WITH TRANSLATIONAL OR ROTATIONAL SYMMETRY	301	(36)
8.1 Scattering from Infinite Cylinders Illuminated by Finite Sources	302	(3)
8.2 Oblique TM-Wave Scattering from Infinite Conducting Cylinders: CFIE Discretized with Pulse Basis Functions and Delta Testing Functions	305	(2)
8.3 Oblique TE-Wave Scattering from Infinite Conducting Cylinders: Augmented MFIE Discretized with Pulse Basis Functions and Delta Testing Functions	307	(3)
8.4 Application: Mutual Admittance between Slot Antennas	310	(3)
8.5 Oblique Scattering from Inhomogeneous Cylinders: Volume Integral Equation Formulation	313	(4)
8.6 Oblique Scattering from Inhomogeneous Cylinders: Scalar Differential Equation Formulation	317	(6)
8.7 Scattering from a Finite-Length, Hollow Conducting Right-Circular Cylinder: The Body-of-Revolution EFIE Formulation	323	(8)
8.8 Differential Equation Formulation for Axisymmetric Scatterers	331	(2)
8.9 Summary	333	(1)
References	333	(1)
Problems	334	(3)
CHAPTER 9 SUBSECTIONAL BASIS FUNCTIONS FOR MULTIDIMENSIONAL AND VECTOR PROBLEMS	337	(78)
9.1 Higher Order Lagrangian Basis Functions on Triangles	338	(4)
9.2 Example: Use of Higher Order Basis Functions with the Two-Dimensional Scalar Helmholtz Equation	342	(7)
9.3 Lagrangian Basis Functions for Rectangular and Quadrilateral Cells	349	(5)
9.4 Scalar Basis Functions for Two-Dimensional Cells with Curved Sides	354	(3)
9.5 Discretization of Two-Dimensional Surface Integral Equations Using an Isoparametric Quadratic Representation	357	(2)
9.6 Scalar Lagrangian Functions in Three Dimensions	359	(2)
9.7 Scalar Lagrangian Discretization of the Vector Helmholtz Equation for Cavities: Spurious Eigenvalues and Other Difficulties	361	(6)
9.8 Polynomial-Complete Vector Basis Functions that Impose Tangential Continuity but not Normal Continuity between Triangular Cells	367	(4)
9.9 Mixed-Order Vector Basis Functions that Impose Tangential but not Normal Continuity for Triangular and Rectangular Cells	371	(11)
9.10 TE Scattering Using the Vector Helmholtz Equation with CT/LN and LT/QN Vector Basis Functions Defined on Triangular Cells	382	(6)
9.11 Analysis of Dielectric-Loaded Waveguides Using Curl-Conforming Vector Basis Functions	388	(4)
9.12 Mixed-Order Curl-Conforming Vector Basis Functions for Tetrahedral and Hexahedral Cells	392	(3)
9.13 Divergence-Conforming Vector Basis Functions for Discretizations of the EFIE	395	(4)
9.14 Mapping Vector Basis Functions to Curvilinear Cells in Two and Three Dimensions	399	(7)
9.15 Summary	406	(1)
References	406	(2)
Problems	408	(7)
CHAPTER 10 INTEGRAL EQUATION METHODS FOR THREE-DIMENSIONAL BODIES	415	(46)
10.1 Scattering from Flat Perfectly Conducting Plates: EFIE Discretized with CN/LT Rooftop Basis Functions Defined on Rectangular Cells	416	(9)
10.2 Scattering from Perfectly Conducting Bodies: EFIE Discretized with CN/LT Triangular-Cell Rooftop Basis Functions	425	(3)
10.3 Scattering from Perfectly Conducting Bodies: MFIE Discretized with Triangular-Cell CN/LT Basis Functions	428	(2)
10.4 Scattering from Perfectly Conducting Bodies: CFIE Discretized with Triangular-Cell CN/LT Basis Functions	430	(1)
10.5 Performance of the CFIE with LN/QT Basis Functions and Curved Patches	430	(3)
10.6 Treatment of Electrically Small Scatterers Using Surface Integral Equations	433	(2)
10.7 Scattering from Homogeneous Dielectric Bodies: CFIE Discretized with Triangular-Cell CN/LT Basis Functions	435	(5)
10.8 Radiation and Scattering from Thin Wires	440	(3)
10.9 Scattering from Planar Periodic Geometries	443	(2)
10.10 Analysis of Microstrip Structures	445	(5)
10.11 A Brief Survey of Volume Integral Formulations for Heterogeneous Dielectric Bodies	450	(2)
10.12 Summary	452	(1)
References	452	(3)
Problems	455	(6)
CHAPTER 11 FREQUENCY-DOMAIN DIFFERENTIAL EQUATION FORMULATIONS FOR OPEN THREE-DIMENSIONAL PROBLEMS	461	(34)
11.1 Weak Vector Helmholtz Equation and Boundary Conditions	461	(2)
11.2 Discretization using CT/LN and LT/QN Functions for Three-Dimensional Cavities	463	(6)
11.3 Eigenfunction RBC for Spherical Boundary Shapes	469	(1)
11.4 Surface Integral Equation RBC for General Boundary Shapes	470	(3)
11.5 Outward-Looking versus Inward-Looking Formulations	473	(2)
11.6 Integral Equation RBC for Axisymmetric Boundary Shapes	475	(1)
11.7 Local RBCs for Spherical Boundaries	476	(5)
11.8 Local RBCs for General Three-Dimensional Boundary Shapes	481	(2)
11.9 RBCs Based on Fictitious Absorbers	483	(1)
11.10 Vector Formulation for Axisymmetric Heterogeneous Scatterers	484	(3)
11.11 Alternative Formulations for Three-Dimensional Scattering	487	(1)
11.12 Summary	488	(1)
References	489	(3)
Problems	492	(3)
CHAPTER 12 FINITE-DIFFERENCE TIME-DOMAIN METHODS ON ORTHOGONAL MESHES	495	(30)
12.1 Maxwell's Equations in the Time Domain	496	(1)
12.2 Centered Finite-Difference Approximations	496	(1)
12.3 FDTD Spatial Discretization	497	(2)
12.4 FDTD Time Discretization	499	(1)
12.5 Divergence Conservation in the FDTD	500	(1)
12.6 Extension to Three Dimensions	501	(1)
12.7 Other Coordinate Systems	501	(1)
12.8 Numerical Analysis of the FDTD Algorithm: Stability, Dispersion, and Anisotropy	502	(4)
12.9 Treating Lossy/Conductive Media	506	(1)
12.10 Frequency-Dependent Media	507	(2)
12.11 Simple Boundary and Interface Conditions	509	(1)
12.12 Absorbing Boundary Conditions	510	(7)
12.13 Internal and External Sources	517	(1)
12.14 Far-Field Projections	518	(2)
12.15 Extensions to the Orthogonal Mesh FDTD Method	520	(1)
References	520	(2)
Problems	522	(3)
APPENDIX A QUADRATURE	525	(6)
A.1 Romberg Integration	525	(2)
A.2 Gaussian Quadrature	527	(1)
A.3 Gauss-Kronrod Rules	528	(1)
A.4 Incorporation of Logarithmic Singularities	528	(1)
A.5 Gaussian Quadrature for Triangles	529	(1)
A.6 Gaussian Quadrature for Tetrahedrons	530	(1)
References	530	(1)
APPENDIX B SOURCE-FIELD RELATIONSHIPS FOR CYLINDERS ILLUMINATED BY AN OBLIQUELY INCIDENT FIELD	531	(6)
APPENDIX C FORTRAN CODES FOR TM SCATTERING FROM PERFECT ELECTRIC CONDUCTING CYLINDERS	537	(16)
C.1 Implementation 1: Single-Point Approximation	537	(7)
C.2 Implementation 2: Romberg Quadrature	544	(4)
C.3 Implementation 3: Generalized Gaussian Quadrature	548	(5)
APPENDIX D ADDITIONAL SOFTWARE AVAILABLE VIA THE INTERNET	553	(2)
INDEX	555	(8)
ABOUT THE AUTHORS	563