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Method of Moments in Electromagnetics [Hardback]

  • Formāts: Hardback, 288 pages, height x width: 235x156 mm, weight: 544 g, 3 Halftones, black and white; 14 Tables, black and white; 116 Illustrations, black and white
  • Izdošanas datums: 11-Dec-2007
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1420061453
  • ISBN-13: 9781420061451
Citas grāmatas par šo tēmu:
  • Formāts: Hardback, 288 pages, height x width: 235x156 mm, weight: 544 g, 3 Halftones, black and white; 14 Tables, black and white; 116 Illustrations, black and white
  • Izdošanas datums: 11-Dec-2007
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 1420061453
  • ISBN-13: 9781420061451
Citas grāmatas par šo tēmu:
Responding to the need for a clear, up-to-date introduction to the field, The Method of Moments in Electromagnetics explores surface integral equations in electromagnetics and presents their numerical solution using the method of moments (MOM) technique. It provides the numerical implementation aspects at a nuts-and-bolts level while discussing integral equations and electromagnetic theory at a higher level.

The author covers a range of topics in this area, from the initial underpinnings of the MOM to its current applications. He first reviews the frequency-domain electromagnetic theory and then develops Green’s functions and integral equations of radiation and scattering. Subsequent chapters solve these integral equations for thin wires, bodies of revolution, and two- and three-dimensional problems. The final chapters examine the contemporary fast multipole method and describe some commonly used methods of numerical integration, including the trapezoidal rule, Simpson’s rule, area coordinates, and Gaussian quadrature on triangles. The text derives or summarizes the matrix elements used in every MOM problem and explains the approach used in and results of each example.

This book provides both the information needed to solve practical electromagnetic problems using the MOM and the knowledge necessary to understand more advanced topics in the field.

Preface ix
Acknowledgments xiii
About the Author xv
Computational Electromagnetics
1(4)
Computational Electromagnetics Algorithms
1(4)
Low-Frequency Methods
2(1)
High-Frequency Methods
2(2)
References
4(1)
A Brief Review of Electromagnetics
5(28)
Maxwell's Equations
5(1)
Electromagnetic Boundary Conditions
6(1)
Formulations for Radiation
6(4)
Three-Dimensional Green's Function
8(1)
Two-Dimensional Green's Function
9(1)
Vector Potentials
10(4)
Magnetic Vector Potential
11(1)
Electric Vector Potential
12(1)
Comparison of Radiation Formulas
13(1)
Near and Far Fields
14(4)
Near Field
15(1)
Far Field
16(2)
Equivalent Problems
18(7)
Surface Equivalent
18(2)
Physical Equivalent
20(5)
Surface Integral Equations
25(8)
Electric Field Integral Equation
25(1)
Magnetic Field Integral Equation
26(2)
Combined Field Integral Equation
28(2)
References
30(3)
The Method of Moments
33(30)
Electrostatic Problems
33(10)
Charged Wire
34(5)
Charged Plate
39(4)
The Method of Moments
43(2)
Point Matching
44(1)
Galerkin's Method
44(1)
Common Two-Dimensional Basis Functions
45(3)
Pulse Functions
45(1)
Piecewise Triangular Functions
45(1)
Piecewise Sinusoidal Functions
46(1)
Entire-Domain Functions
47(1)
Number of Basis Functions
47(1)
Solution of Matrix Equations
48(15)
Gaussian Elimination
48(2)
LU Decompositon
50(2)
Condition Number
52(1)
Iterative Methods
53(4)
Examples
57(1)
Commonly Used Matrix Algebra Software
58(3)
References
61(2)
Thin Wires
63(32)
Thin Wire Approximation
63(2)
Thin Wire Excitations
65(3)
Delta-Gap Source
65(1)
Magnetic Frill
66(1)
Plane Wave
67(1)
Solving Hallen's Equation
68(4)
Symmetric Problems
69(2)
Asymmetric Problems
71(1)
Solving Pocklington's Equation
72(1)
Solution by Pulse Functions and Point Matching
73(1)
Thin Wires of Arbitrary Shape
73(6)
Redistribution of EFIE Differential Operators
74(1)
Solution Using Triangle Basis and Testing Functions
75(2)
Solution Using Sinusoidal Basis and Testing Functions
77(1)
Lumped and Distributed Impedances
78(1)
Examples
79(16)
Comparison of Thin Wire Models
79(4)
Circular Loop Antenna
83(3)
Folded Dipole Antenna
86(1)
Two-Wire Transmission Line
87(2)
Matching a Yagi Antenna
89(5)
References
94(1)
Two-Dimensional Problems
95(30)
Two-Dimensional EFIE
95(14)
EFIE for a Strip: TM Polarization
95(5)
Generalized EFIE: TM Polarization
100(2)
EFIE for a Strip: TE Polariation
102(5)
Generalized EFIE: TE Polarization
107(2)
Two-Dimensional MFIE
109(4)
MFIE: TM Polarization
109(2)
MFIE: TE Polarization
111(2)
Examples
113(12)
Scattering by an Infinite Cylinder: TM Polarization
113(2)
Scattering by an Infinite Cylinder: TE Polarization
115(9)
References
124(1)
Bodies of Revolution
125(36)
BOR Surface Description
125(1)
Surface Current Expansion on a BOR
126(1)
EFIE for a Conducting BOR
127(9)
EFIE Matrix Elements
127(3)
Excitation
130(4)
Scattered Field
134(2)
MFIE for a Conducting BOR
136(5)
MFIE Matrix Elements
137(3)
Excitation
140(1)
Scattered Field
141(1)
Notes on Software Implementation
141(1)
Parallelization
141(1)
Convergence
142(1)
Examples
142(19)
Galaxy
142(1)
Conducting Sphere
142(3)
EMCC Benchmark Targets
145(7)
Biconic Reentry Vehicle
152(7)
Summary of Examples
159(1)
References
159(2)
Three-Dimensional Problems
161(48)
Representation of Three-Dimensional Surfaces
161(3)
Surface Currents on a Triangle
164(3)
Edge Finding Algorithm
165(2)
EFIE for Three-Dimensional Conducting Surfaces
167(12)
EFIE Matrix Elements
167(1)
Singular Matrix Element Evaluation
168(8)
EFIE Excitation Vector Elements
176(2)
Radiated Field
178(1)
MFIE for Three-Dimensional Conducting Surfaces
179(6)
MFIE Matrix Elements
179(5)
MFIE Excitation Vector Elements
184(1)
Radiated Field
184(1)
Accuracy of RWG Functions in MFIE
184(1)
Notes on Software Implementation
185(2)
Memory Management
185(1)
Parallelization
185(2)
Considerations for Modeling with Triangles
187(1)
Triangle Aspect Ratios
187(1)
Watertight Meshes and T-Junctions
188(1)
Examples
188(21)
Serenity
189(1)
RCS of a Sphere
189(1)
EMCC Plate Benchmark Targets
189(9)
Strip Dipole Antenna
198(1)
Bowtie Antenna
199(2)
Archimedean Spiral Antenna
201(3)
Summary of Examples
204(1)
References
205(4)
The Fast Multipole Method
209(46)
The Matrix-Vector Product
210(1)
Addition Theorem
210(3)
Wave Translation
212(1)
FMM Matrix Elements
213(2)
EFIE Matrix Elements
213(1)
MFIE Matrix Elements
214(1)
CFIE Matrix Elements
215(1)
Matrix Transpose
215(1)
One-Level Fast Multipole Algorithm
215(7)
Grouping of Basis Functions
215(1)
Near and Far Groups
216(1)
Number of Multipoles
216(2)
Sampling Rates and Integration
218(1)
Transfer Functions
219(1)
Radiation and Receive Functions
220(1)
Near-Matrix Elements
220(1)
Matrix-Vector Product
221(1)
Computational Complexity
222(1)
Multi-Level Fast Multipole Algorithm (MLFMA)
222(9)
Grouping via Octree
222(1)
Matrix-Vector Product
223(4)
Interpolation Algorithms
227(2)
Transfer Functions
229(1)
Radiation and Receive Functions
230(1)
Interpolation Steps in MLFMA
230(1)
Computational Complexity
231(1)
Notes on Software Implementation
231(4)
Initial Guess in Iterative Solution
231(1)
Memory Management
232(2)
Parallelization
234(1)
Vectorization
234(1)
Preconditioning
235(5)
Diagonal Preconditioner
235(1)
Block Diagonal Preconditioner
236(1)
Inverse LU Preconditioner
236(1)
Sparse Approximate Inverse
237(3)
Examples
240(15)
Bistatic RCS of a Sphere
240(1)
EMCC Benchmark Targets
240(5)
Summary of Examples
245(7)
References
252(3)
Integration
255(16)
One-Dimensional Integration
255(5)
Centroidal Approximation
255(1)
Trapezoidal Rule
256(2)
Simpson's Rule
258(1)
One-Dimensional Gaussian Quadrature
259(1)
Integration over Triangles
260(11)
Simplex Coordinates
260(2)
Radiation Integrals with a Constant Source
262(3)
Radiation Integrals with a Linear Source
265(2)
Gaussian Quadrature on Triangles
267(2)
References
269(2)
Index 271


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