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Method of Moments in Electromagnetics 3rd edition [Hardback]

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(Tripoint Industries Inc., Harvest, Alabama, USA)
  • Formāts: Hardback, 510 pages, height x width: 229x152 mm, weight: 807 g, 228 Line drawings, black and white; 228 Illustrations, black and white
  • Izdošanas datums: 07-Sep-2021
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 0367365065
  • ISBN-13: 9780367365066
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Method of Moments in Electromagnetics 3rd editionPalielināt
  • Formāts: Hardback, 510 pages, height x width: 229x152 mm, weight: 807 g, 228 Line drawings, black and white; 228 Illustrations, black and white
  • Izdošanas datums: 07-Sep-2021
  • Izdevniecība: Chapman & Hall/CRC
  • ISBN-10: 0367365065
  • ISBN-13: 9780367365066
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9780367365066.html
Keywords:
"The Method of Moments in Electromagnetics, Third Edition details the numerical solution of electromagnetic integral equations via the Method of Moments (MoM). Previous editions focused on the solution of radiation and scattering problems involving conducting, dielectric, and composite objects. This new edition adds a significant amount of material on new, state-of-the art compressive techniques. Included are new chapters on the Adaptive Cross Approximation (ACA) and Multi-Level Adaptive Cross Approximation (MLACA), advanced algorithms that permit a direct solution of the MoM linear system via LU decomposition in compressed form. Significant attention is paid to parallel software implementation of these methods on traditional central processing units (CPUs) as well as new, high performance graphics processing units (GPUs). Existing material on the Fast Multipole Method (FMM) and Multi-Level Fast Multipole Algorithm (MLFMA) is also updated, blending in elements of the ACA algorithm to further reduce theirmemory demands. The Method of Moments in Electromagnetics is intended for students, researchers and industry experts working in area of computational electromagnetics (CEM) and the MoM. Providing a bridge between theory and software implementation, the book incorporates significant background material, while presenting practical, nuts-and-bolts implementation details. It first derives a generalized set of surface integral equations used to treat electromagnetic radiation and scattering problems, for objects comprising conducting and dielectric regions. Subsequent chapters apply and these integral equations for progressively more difficult problems such as thin wires, bodies of revolution, and two- and three-dimensional bodies. Radiation and scattering problems of many different types are considered, with numerical results compared against analytical theory as well as measurements"--

The Method of Moments in Electromagnetics, Third Edition details the numerical solution of electromagnetic integral equations via the Method of Moments (MoM). Previous editions focused on the solution of radiation and scattering problems involving conducting, dielectric, and composite objects. This new edition adds a significant amount of material on new, state-of-the art compressive techniques. Included are new chapters on the Adaptive Cross Approximation (ACA) and Multi-Level Adaptive Cross Approximation (MLACA), advanced algorithms that permit a direct solution of the MoM linear system via LU decomposition in compressed form. Significant attention is paid to parallel software implementation of these methods on traditional central processing units (CPUs) as well as new, high performance graphics processing units (GPUs). Existing material on the Fast Multipole Method (FMM) and Multi-Level Fast Multipole Algorithm (MLFMA) is also updated, blending in elements of the ACA algorithm to further reduce their memory demands.

The Method of Moments in Electromagnetics

is intended for students, researchers and industry experts working in area of computational electromagnetics (CEM) and the MoM. Providing a bridge between theory and software implementation, the book incorporates significant background material, while presenting practical, nuts-and-bolts implementation details. It first derives a generalized set of surface integral equations used to treat electromagnetic radiation and scattering problems, for objects comprising conducting and dielectric regions. Subsequent chapters apply and these integral equations for progressively more difficult problems such as thin wires, bodies of revolution, and two- and three-dimensional bodies. Radiation and scattering problems of many different types are considered, with numerical results compared against analytical theory as well as measurements.



This book is intended for students, researchers and industry experts working in area of computational electromagnetics and the MoM. Providing a bridge between theory and software implementation, the book incorporates significant background material, while presenting practical, nuts-and-bolts implementation details.

Recenzijas

"The Method of Moments in Electromagnetics offers a complete guide to the implementation and numerical solution of surface integral equations in electromagnetics. The formulations and procedures are presented in an orderly easy-to-follow approach, along with references to software resources available online. General metallic and piecewise-homogeneous material antenna and scattering problems are covered. Efficient solution algorithms are presented, such as the fast multi-pole method (FMM) and the adaptive cross-approximation (ACA). The 3rd Edition adds the multi-level ACA and hybridization of ACA with FMM. A large number of solved example problems are included, along with tips for efficient programming and parallelization. The book provides a comprehensive reference for the implementation of state-of-the-art algorithms in the Method of Moments." Emeritus Research Professor Robert J. Burkholder, Dept. of Electrical and Computer Engineering, ElectroScience Laboratory, The Ohio State University

"Gibson has, no doubt, generated a classic with the third edition of his book, comprising extensive and approachable compendium of his in-depth knowledge in the Moment Method and development of numerical software codes. This book is well-written, easy to follow, and will likely serve as a practical text of great utility to students and practicing engineers alike. Simply put, this new third edition sets the standard in the subject matter for many years to come." Bassem Mahafza, President and Founder of Phased n Research and author of Introduction to Radar Analysis and Handbook of Radar Signal Analysis

"Mr. Gibson has put forward the definitive text for solving Electromagnetic problems with the Method of Moments (MoM). It is an outstanding blend of both theoretical and practical applications and expertly covers all subject matter necessary for the understanding and implementation of MoM based computational electromagnetic software codes. This text is ideal for a graduate level course as well as seasoned engineers and is sure to become a classic." Andrew Lee Harrison, Hill Technical Solutions

Preface to the Third Edition xix
Preface to the Second Edition xxi
Preface xxiii
Acknowledgments xxvii
About the Author xxix
1 Computational Electromagnetics
1(6)
1.1 CEM Algorithms
1(3)
1.1.1 Low-Frequency Methods
2(1)
1.1.1.1 Finite Difference Time Domain Method
2(1)
1.1.1.2 Finite Element Method
2(1)
1.1.1.3 Method of Moments
3(1)
1.1.2 High-Frequency Methods
3(1)
1.1.2.1 Geometrical Theory of Diffraction
3(1)
1.1.2.2 Physical Optics
3(1)
1.1.2.3 Physical Theory of Diffraction
4(1)
1.1.2.4 Shooting and Bouncing Rays
4(1)
References
4(3)
2 The Method of Moments
7(18)
2.1 Electrostatic Problems
7(10)
2.1.1 Charged Wire
8(2)
2.1.1.1 Matrix Element Evaluation
10(1)
2.1.1.2 Solution
10(3)
2.1.2 Charged Plate
13(1)
2.1.2.1 Matrix Element Evaluation
14(1)
2.1.2.2 Solution
14(3)
2.2 The Method of Moments
17(2)
2.2.1 Point Matching
18(1)
2.2.2 Galerkin's Method
19(1)
2.3 Common One-Dimensional Basis Functions
19(4)
2.3.1 Pulse Functions
19(1)
2.3.2 Piecewise Triangular Functions
20(1)
2.3.3 Piecewise Sinusoidal Functions
21(1)
2.3.4 Entire-Domain Functions
22(1)
2.3.5 Number of Basis Functions
22(1)
References
23(2)
3 Radiation and Scattering
25(36)
3.1 Maxwell's Equations
25(1)
3.2 Electromagnetic Boundary Conditions
26(1)
3.3 Formulations for Radiation
26(5)
3.3.1 Three-Dimensional Green's Function
28(1)
3.3.2 Two-Dimensional Green's Function
29(2)
3.4 Vector Potentials
31(6)
3.4.1 Magnetic Vector Potential
31(1)
3.4.1.1 Three-Dimensional Magnetic Vector Potential
32(1)
3.4.1.2 Two-Dimensional Magnetic Vector Potential
32(1)
3.4.2 Electric Vector Potential
32(1)
3.4.2.1 Three-Dimensional Electric Vector Potential
33(1)
3.4.2.2 Two-Dimensional Electric Vector Potential
33(1)
3.4.3 Total Fields
33(1)
3.4.4 Comparison of Radiation Formulas
34(3)
3.5 Near and Far Field
37(7)
3.5.1 Three-Dimensional Near Field
37(2)
3.5.2 Two-Dimensional Near Field
39(2)
3.5.3 Three-Dimensional Far Field
41(2)
3.5.4 Two-Dimensional Far Field
43(1)
3.6 Formulations for Scattering
44(14)
3.6.1 Surface Equivalent
44(6)
3.6.2 Surface Integral Equations
50(1)
3.6.2.1 Interior Resonance Problem
51(1)
3.6.2.2 Discretization and Testing
52(2)
3.6.2.3 Modification of Matrix Elements
54(2)
3.6.3 Enforcement of Boundary Conditions
56(1)
3.6.3.1 EFIE-CFIE-PMCHWT Approach
56(1)
3.6.4 Physical Optics Equivalent
57(1)
References
58(3)
4 Solution of Matrix Equations
61(20)
4.1 Direct Methods
61(7)
4.1.1 Gaussian Elimination
61(2)
4.1.1.1 Pivoting
63(1)
4.1.2 LU Factorization
63(2)
4.1.3 Block LU Factorization
65(2)
4.1.4 Condition Number
67(1)
4.2 Iterative Methods
68(9)
4.2.1 Conjugate Gradient
68(1)
4.2.2 Biconjugate Gradient
69(1)
4.2.3 Conjugate Gradient Squared
69(1)
4.2.4 Biconjugate Gradient Stabilized
69(1)
4.2.5 GMRES
70(6)
4.2.6 Stopping Criteria
76(1)
4.2.7 Preconditioning
76(1)
4.3 Software for Linear Systems
77(2)
4.3.1 BLAS
77(1)
4.3.2 LAPACK
78(1)
4.3.3 MATLAB
78(1)
References
79(2)
5 Thin Wires
81(42)
5.1 Thin Wire Approximation
81(2)
5.2 Thin Wire Excitations
83(3)
5.2.1 Delta-Gap Source
84(1)
5.2.2 Magnetic Frill
84(1)
5.2.3 Plane Wave
85(1)
5.3 Hallen's Equation
86(5)
5.3.1 Symmetric Problems
88(1)
5.3.1.1 Solution Using Pulse Functions and Point Matching
89(1)
5.3.2 Asymmetric Problems
90(1)
5.3.2.1 Solution Using Pulse Functions and Point Matching
91(1)
5.4 Pocklington's Equation
91(2)
5.4.1 Solution Using Pulse Functions and Point Matching
92(1)
5.5 Thin Wires of Arbitrary Shape
93(6)
5.5.1 Method of Moments Discretization
93(1)
5.5.2 Solution Using Triangle Basis and Testing Functions
94(1)
5.5.2.1 Non-Self Terms
95(1)
5.5.2.2 Self Terms
95(1)
5.5.3 Solution Using Sinusoidal Basis and Testing Functions
96(1)
5.5.3.1 Self Terms
96(2)
5.5.4 Lumped and Distributed Impedances
98(1)
5.6 Examples
99(21)
5.6.1 Comparison of Thin Wire Models
99(1)
5.6.1.1 Input Impedance
99(2)
5.6.1.2 Induced Current Distribution
101(1)
5.6.2 Half-Wavelength Dipole
102(3)
5.6.3 Circular Loop Antenna
105(4)
5.6.4 Folded Dipole Antenna
109(2)
5.6.5 Two-Wire Transmission Line
111(4)
5.6.6 Yagi Antenna for 146 MHz
115(5)
References
120(3)
6 Two-Dimensional Problems
123(50)
6.1 Conducting Objects
123(30)
6.1.1 EFIE: TM Polarization
123(1)
6.1.1.1 Solution Using Pulse Functions
124(2)
6.1.1.2 Solution Using Triangle Functions
126(3)
6.1.2 Generalized EFIE: TM Polarization
129(1)
6.1.2.1 MoM Discretization
129(1)
6.1.2.2 Solution Using Triangle Functions
129(1)
6.1.3 EFIE: TE Polarization
130(2)
6.1.3.1 Pulse Function Solution
132(3)
6.1.4 Generalized EFIE: TE Polarization
135(1)
6.1.4.1 MoM Discretization
135(1)
6.1.4.2 Solution Using Triangle Functions
136(1)
6.1.5 nMFIE: TM Polarization
137(2)
6.1.5.1 Solution Using Triangle Functions
139(1)
6.1.6 nMFIE: TE Polarization
139(1)
6.1.6.1 Solution Using Triangle Functions
140(1)
6.1.7 Examples
141(1)
6.1.7.1 Conducting Cylinder: TM Polarization
141(6)
6.1.7.2 Conducting Cylinder: TE Polarization
147(6)
6.2 Dielectric and Composite Objects
153(18)
6.2.1 Basis Function Orientation
153(1)
6.2.2 EFIE: TM Polarization
154(1)
6.2.2.1 MoM Discretization
155(1)
6.2.3 MFIE: TM Polarization
155(1)
6.2.3.1 MoM Discretization
155(1)
6.2.4 Nmfie: TM Polarization
156(1)
6.2.4.1 MoM Discretization
156(1)
6.2.5 EFIE: TE Polarization
157(1)
6.2.5.1 MoM Discretization
157(1)
6.2.6 MFIE: TE Polarization
157(1)
6.2.6.1 MoM Discretization
157(1)
6.2.7 Nmfie: TE Polarization
157(1)
6.2.7.1 MoM Discretization
157(1)
6.2.8 Numerical Stability
158(1)
6.2.9 Examples
158(1)
6.2.9.1 Dielectric Cylinder
158(1)
6.2.9.2 Dielectric Cylinder: TM Polarization
159(4)
6.2.9.3 Dielectric Cylinder: TE Polarization
163(3)
6.2.9.4 Coated Cylinder
166(1)
6.2.9.5 Coated Cylinder: TM Polarization
166(2)
6.2.9.6 Coated Cylinder: TE Polarization
168(1)
6.2.9.7 Effect of Number of Segments per Wave-length on Accuracy
169(2)
References
171(2)
7 Bodies of Revolution
173(64)
7.1 BoR Surface Description
173(1)
7.2 Expansion of Surface Currents
174(1)
7.3 EFIE
175(10)
7.3.1 L Operator
176(1)
7.3.1.1 L Matrix Elements
176(3)
7.3.2 L Operator
179(1)
7.3.2.1 K Matrix Elements
179(2)
7.3.3 Excitation
181(1)
7.3.3.1 Plane Wave Excitation
181(4)
7.4 MFIE
185(1)
7.4.1 Excitation
185(1)
7.4.1.1 Plane Wave Excitation
185(1)
7.5 Solution
186(5)
7.5.1 Plane Wave Solution
186(1)
7.5.1.1 Currents
187(1)
7.5.2 Scattered Field
188(1)
7.5.2.1 Scattered Far Fields
188(3)
7.6 nMFIE
191(3)
7.6.1 N × L Operator
191(1)
7.6.1.1 NL Matrix Elements
192(1)
7.6.2 N × Κ Operator
192(1)
7.6.2.1 Nk Matrix Elements
192(1)
7.6.3 Excitation
193(1)
7.6.3.1 Plane Wave Excitation
193(1)
7.6.3.2 Plane Wave Solution
194(1)
7.7 Numerical Discretization
194(3)
7.8 Notes on Software Implementation
197(1)
7.8.1 Geometry Processing and Basis Function Assignment
197(1)
7.8.2 Parallelization
197(1)
7.8.3 Convergence
197(1)
7.9 Examples
198(29)
7.9.1 Spheres
198(1)
7.9.1.1 Conducting Sphere
199(6)
7.9.1.2 Stratified Sphere
205(2)
7.9.1.3 Dielectric Sphere
207(4)
7.9.1.4 Coated Sphere
211(5)
7.9.2 EMCC Benchmark Targets
216(1)
7.9.2.1 EMCC Ogive
216(1)
7.9.2.2 EMCC Double Ogive
216(1)
7.9.2.3 EMCC Cone-Sphere
217(1)
7.9.2.4 EMCC Cone-Sphere with Gap
217(6)
7.9.3 Biconic Reentry Vehicle
223(4)
7.10 Treatment of Junctions
227(8)
7.10.1 Orientation of Basis Functions
227(1)
7.10.1.1 Longitudinal Basis Vectors
227(1)
7.10.1.2 Azimuthal Basis Vectors
228(1)
7.10.2 Examples with Junctions
229(1)
7.10.2.1 Dielectric Sphere with Septum
229(1)
7.10.2.2 Coated Sphere with Septum
229(1)
7.10.2.3 Stratified Sphere with Septum
230(2)
7.10.2.4 Monoconic Reentry Vehicle with Dielectric Nose
232(3)
References
235(2)
8 Three-Dimensional Problems
237(68)
8.1 Modeling of Three-Dimensional Surfaces
238(4)
8.1.1 Facet File
238(2)
8.1.2 Edge-Finding Algorithm
240(1)
8.1.2.1 Shared Nodes
241(1)
8.2 Expansion of Surface Currents
242(2)
8.2.1 Divergence of the RWG Function
243(1)
8.2.2 Assignment and Orientation of Basis Functions
243(1)
8.3 EFIE
244(14)
8.3.1 L Operator
244(1)
8.3.1.1 Non-Near Terms
245(1)
8.3.1.2 Near and Self Terms
245(8)
8.3.2 K, Operator
253(1)
8.3.2.1 Non-Near Terms
253(1)
8.3.2.2 Near Terms
254(3)
8.3.3 Excitation
257(1)
8.3.3.1 Plane Wave Excitation
257(1)
8.3.3.2 Planar Antenna Excitation
257(1)
8.4 MFIE
258(1)
8.4.1 Excitation
259(1)
8.4.1.1 Plane Wave Excitation
259(1)
8.5 nMFIE
259(3)
8.5.1 N × Κ Operator
259(1)
8.5.1.1 Non-Near Terms
260(1)
8.5.1.2 Near Terms
260(1)
8.5.2 N × L Operator
260(1)
8.5.2.1 Non-Near Terms
261(1)
8.5.2.2 Near and Self Terms
261(1)
8.5.3 Excitation
262(1)
8.5.3.1 Plane Wave Excitation
262(1)
8.6 Enforcement of Boundary Conditions
262(5)
8.6.1 Classification of Edges and Junctions
262(1)
8.6.1.1 Dielectric Edges and Junctions
263(1)
8.6.1.2 Conducting Edges and Junctions
263(1)
8.6.1.3 Composite Conducting-Dielectric Junctions
264(1)
8.6.2 Reducing the Overdetermined System
265(1)
8.6.2.1 PMCHWT at Dielectric Edges and Junctions
265(1)
8.6.2.2 EFIE and CFIE at Conducting Edges and Junctions
266(1)
8.6.2.3 EFIE and CFIE at Composite Conducting-Dielectric Junctions
266(1)
8.7 Software Implementation Notes
267(6)
8.7.1 Pre-Processing and Bookkeeping
268(1)
8.7.1.1 Region and Interface Assignments
268(1)
8.7.1.2 Geometry Processing
268(1)
8.7.1.3 Assignment and Orientation of Basis Functions
268(1)
8.7.2 Matrix and Right-Hand Side Fill
269(1)
8.7.3 Parallelization
270(1)
8.7.3.1 Shared Memory Systems
270(1)
8.7.3.2 Distributed Memory Systems
270(1)
8.7.4 Triangle Mesh Considerations
271(1)
8.7.4.1 Aspect Ratio
271(1)
8.7.4.2 T-Junctions
271(2)
8.8 Numerical Examples
273(28)
8.8.1 Serenity
273(1)
8.8.2 Compute Platform
273(1)
8.8.3 Spheres
274(1)
8.8.3.1 Conducting Sphere
274(4)
8.8.3.2 Dielectric Sphere
278(5)
8.8.3.3 Coated Sphere
283(5)
8.8.4 EMCC Plate Benchmark Targets
288(1)
8.8.4.1 Wedge Cylinder
289(1)
8.8.4.2 Wedge-Plate Cylinder
289(1)
8.8.4.3 Plate Cylinder
290(1)
8.8.4.4 Business Card
290(2)
8.8.5 Strip Dipole Antenna
292(1)
8.8.6 Bowtie Antenna
293(2)
8.8.7 Archimedean Spiral Antenna
295(3)
8.8.8 Monoconic Reentry Vehicle with Dielectric Nose
298(2)
8.8.9 Summary of Examples
300(1)
References
301(4)
9 Adaptive Cross Approximation
305(56)
9.1 Rank Deficiency
306(2)
9.1.1 Limitations of Using SVD For Compression
307(1)
9.2 Adaptive Cross Approximation
308(3)
9.2.1 Modifications
308(1)
9.2.1.1 Initialization
309(1)
9.2.1.2 Early Termination
309(1)
9.2.1.3 Pathological Failure Case
310(1)
9.2.2 QR/SVD Recompression
310(1)
9.3 Clustering Techniques
311(3)
9.3.1 Target Group Size For ACA
313(1)
9.4 LU Factorization of ACA-Compressed Matrix
314(2)
9.4.1 ACA-Compressed Block LU Factorization
314(2)
9.4.1.1 Compressibility of the LU Matrix
316(1)
9.5 Solution of the ACA-Compressed Matrix System
316(2)
9.6 Software Implementation Notes
318(11)
9.6.1 Software Class Support
318(1)
9.6.1.1 Element Engine Class
318(1)
9.6.1.2 Matrix Classes
319(1)
9.6.2 Shared Memory Processing
320(1)
9.6.2.1 ACA CPU Thread Class
321(1)
9.6.2.2 ACA GPU Thread Class
322(3)
9.6.3 Distributed Memory Processing
325(1)
9.6.3.1 Parallelization Strategy
325(1)
9.6.3.2 Block LU Factorization Using MPI
326(1)
9.6.3.3 Block-RHS Solution Using MPI
326(3)
9.7 Numerical Examples
329(29)
9.7.1 Compute Platform
329(1)
9.7.2 Adaptive ACA Tolerance
329(1)
9.7.3 Spheres
330(1)
9.7.3.1 Conducting Sphere
330(1)
9.7.3.2 Dielectric Sphere
330(1)
9.7.3.3 Coated Sphere
330(4)
9.7.4 EMCC Benchmark Targets
334(1)
9.7.4.1 EMCC Ogive
334(1)
9.7.4.2 EMCC Double Ogive
334(1)
9.7.4.3 EMCC Cone-Sphere
334(1)
9.7.4.4 EMCC Cone-Sphere with Gap
335(1)
9.7.4.5 NASA Almond
336(4)
9.7.4.6 EMCC Cube
340(1)
9.7.4.7 EMCC Prism
340(2)
9.7.5 Dielectric Cube and Ogive
342(1)
9.7.5.1 Small Polyethylene Cube
342(1)
9.7.5.2 Polyethylene Ogive
342(3)
9.7.6 UT Austin Benchmark Targets
345(1)
9.7.6.1 PEC Almond
345(1)
9.7.6.2 Solid Resin Almond
345(1)
9.7.6.3 Closed-Tail Almond
345(4)
9.7.6.4 Open-Tail Almond
349(1)
9.7.6.5 EXPEDITE-RCS Aircraft
349(4)
9.7.7 Monoconic Reentry Vehicle
353(1)
9.7.7.1 Conducting RV
353(1)
9.7.7.2 RV with Dielectric Nose
353(3)
9.7.8 Summary of Examples
356(2)
References
358(3)
10 Multi-Level Adaptive Cross Approximation
361(28)
10.1 MLACA Compression of Matrix Blocks
362(4)
10.1.1 MLACA Fundamentals
362(1)
10.1.1.1 SVD-Based Compression on Higher Levels
363(1)
10.1.2 Hierarchical Clustering of Sub-Groups
364(1)
10.1.3 Compression of Diagonal Blocks
365(1)
10.2 Direct Solution of MLACA-Compressed Matrix System
366(8)
10.2.1 MLACA Block Reconstruction
366(1)
10.2.2 Matrix Product and V-Type MLACA
367(1)
10.2.2.1 Top-Level Matrix Product
368(1)
10.2.2.2 Bottom-Level Matrix Product
369(3)
10.2.3 MLACA Block-RHS Solution
372(2)
10.3 Software Implementation Notes
374(4)
10.3.1 Software Class Support
374(1)
10.3.1.1 Abstract Matrix Class
374(1)
10.3.1.2 Element Engine Class
374(1)
10.3.1.3 MLACA Translator Class
375(1)
10.3.1.4 MLACAMatrix and MLACANode Classes
375(1)
10.3.1.5 HMatrix Class
375(1)
10.3.2 Shared Memory Processing
376(1)
10.3.2.1 Reconstruction of Blocks and Intermediate Products
376(1)
10.3.2.2 MLACA CPU Thread Class
376(1)
10.3.2.3 MLACA GPU Thread Class
376(1)
10.3.3 Distributed Memory Processing
377(1)
10.4 Numerical Examples
378(9)
10.4.1 Compute Platform
378(1)
10.4.2 Conducting Spheres
378(2)
10.4.2.1 Variation of Target Group Size
380(2)
10.4.3 Polyethylene Cone-Sphere
382(2)
10.4.4 Monoconic Reentry Vehicle
384(2)
10.4.4.1 EMCC Prism
386(1)
References
387(2)
11 The Fast Multipole Method
389(64)
11.1 The N-Body Problem
389(1)
11.2 Matrix-Vector Product
390(9)
11.2.1 Addition Theorem
392(1)
11.2.2 Wave Translation
393(2)
11.2.2.1 Complex Wavenumbers
395(1)
11.2.3 Far Matrix Elements
395(1)
11.2.3.1 EFIE
395(2)
11.2.3.2 MFIE
397(1)
11.2.3.3 nMFIE
397(2)
11.2.4 Unit Sphere Decomposition
399(1)
11.3 One-Level Fast Multipole Algorithm
399(14)
11.3.1 Clustering of Basis Functions
400(1)
11.3.1.1 Classification of Near and Far Groups
400(1)
11.3.2 Near Matrix
401(1)
11.3.2.1 Compression of Near Matrix
401(4)
11.3.3 Number of Multipoles
405(1)
11.3.3.1 Limiting L for Transfer Functions
405(1)
11.3.3.2 L for Complex Wavenumbers
405(1)
11.3.4 Integration on the Sphere
406(1)
11.3.4.1 Spherical Harmonic Representation
406(1)
11.3.4.2 Total Bandwidth
407(1)
11.3.4.3 Computation and Storage of Transfer Functions
408(1)
11.3.4.4 Computation of Radiation and Receive Functions
408(1)
11.3.4.5 Compression of Radiation and Receive Functions
408(3)
11.3.5 Matrix-Vector Product
411(1)
11.3.5.1 Near Product
411(1)
11.3.5.2 Far Product
411(2)
11.4 Multi-Level Fast Multipole Algorithm (MLFMA)
413(10)
11.4.1 MLFMA/SVD
413(1)
11.4.2 Spatial Subdivision and Clustering via Octree
413(1)
11.4.3 Near Matrix and Near Product
414(1)
11.4.4 Unit Sphere Sampling Rates
415(1)
11.4.5 Far Product
415(2)
11.4.5.1 Upward Pass (Aggregation)
417(1)
11.4.5.2 Downward Pass (Disaggregation)
418(2)
11.4.6 Interpolation Algorithms
420(1)
11.4.6.1 Statement of the Problem
420(1)
11.4.6.2 Global Interpolation by Spherical Harmonics
420(1)
11.4.6.3 Local Interpolation by Lagrange Polynomials
421(2)
11.5 Preconditioners
423(4)
11.5.1 Information Content
423(1)
11.5.2 Diagonal Preconditioner
423(1)
11.5.3 Incomplete Block LU (ILU) Preconditioners
424(1)
11.5.3.1 Block Diagonal
424(1)
11.5.3.2 Block ILU with Zero Fill-In (ILU(0))
424(1)
11.5.3.3 Block ILU with Threshold (ILUT)
424(1)
11.5.4 Sparse Approximate Inverse (SAI)
425(1)
11.5.4.1 Dense QR Factorization
426(1)
11.6 Software Implementation Notes
427(5)
11.6.1 Software Class Support
428(1)
11.6.1.1 Element Engine Class
428(1)
11.6.1.2 Sparse Block Matrix Class
428(1)
11.6.1.3 FMM Region Class
429(1)
11.6.1.4 FMM Octree Class
429(1)
11.6.2 Shared Memory Processing
429(1)
11.6.2.1 FMM CPU Thread Class
429(3)
11.7 Numerical Examples
432(17)
11.7.1 Compute Platform
432(1)
11.7.2 Run Parameters
432(1)
11.7.3 Spheres
432(1)
11.7.3.1 Conducting Sphere
432(1)
11.7.3.2 Dielectric Sphere
433(1)
11.7.3.3 Coated Sphere
433(1)
11.7.4 Thin Square Plate
433(1)
11.7.5 Monoconic Reentry Vehicle
433(1)
11.7.6 Business Jet
434(8)
11.7.7 Summary of Examples
442(1)
11.7.8 Preconditioner Performance
443(1)
11.7.8.1 Compressed versus Uncompressed Preconditioners
443(2)
11.7.8.2 Performance versus Incident Angle
445(1)
11.7.8.3 Performance versus Cube Size
445(2)
11.7.9 Initial Guess in Iterative Solution
447(2)
References
449(4)
12 Integration
453(16)
12.1 One-Dimensional Integration
453(7)
12.1.1 Centroidal Approximation
453(1)
12.1.2 Rectangular Rule
454(1)
12.1.3 Trapezoidal Rule
455(1)
12.1.3.1 Romberg Integration
456(1)
12.1.4 Simpson's Rule
457(1)
12.1.4.1 Adaptive Simpson's Rule
458(1)
12.1.5 One-Dimensional Gaussian Quadrature
459(1)
12.2 Integration over Triangles
460(8)
12.2.1 Simplex Coordinates
460(2)
12.2.2 Radiation Integrals with a Constant Source
462(2)
12.2.2.1 Special Cases
464(1)
12.2.3 Radiation Integrals with a Linear Source
464(1)
12.2.3.1 General Case
465(1)
12.2.3.2 Special Cases
465(1)
12.2.4 Gaussian Quadrature on Triangles
466(1)
12.2.4.1 Comparison with Analytic Solution
467(1)
References
468(1)
A Scattering Using Physical Optics
469(8)
A.1 Field Scattered at a Conducting Interface
469(1)
A.2 Plane Wave Decomposition at a Planar Interface
470(2)
A.3 Field Scattered at a Dielectric Interface
472(1)
A.4 Layered Dielectrics over Conductor
473(2)
References
475(2)
Index 477
Walton C. Gibson was born in Birmingham, Alabama, USA on December 9, 1975. He received the B.S. degree in electrical engineering from Auburn University in 1996, and the M.S. degree in electrical engineering from the University of Illinois Urbana-Champaign in 1998. He is a recognized authority in the area of computational electromagnetics (CEM), and has authored The Method of Moments in Electromagnetics, a textbook geared to graduate-level courses in CEM, as well as the research community and practicing professionals. He is the owner and President of Tripoint Industries, Inc., through which he has authored lucernhammer, an industry-standard suite of radar cross section solver codes implementing low and high-frequency numerical techniques. His professional interests include electromagnetic theory, computational electromagnetics, moment methods, numerical algorithms and parallel computing.