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Numerical Methods for Engineering: An introduction using MATLAB® and computational electromagnetics examples [Kõva köide]

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(Brigham Young University, Department of Electrical and Computer Engineering, USA)
  • Formaat: Hardback, 359 pages, kõrgus x laius: 254x203 mm
  • Sari: Electromagnetic Waves
  • Ilmumisaeg: 15-Dec-2010
  • Kirjastus: SciTech Publishing Inc
  • ISBN-10: 1891121995
  • ISBN-13: 9781891121999
Teised raamatud teemal:
Numerical Methods for Engineering: An introduction using MATLAB® and computational electromagnetics examplesSuurem pilt
  • Formaat: Hardback, 359 pages, kõrgus x laius: 254x203 mm
  • Sari: Electromagnetic Waves
  • Ilmumisaeg: 15-Dec-2010
  • Kirjastus: SciTech Publishing Inc
  • ISBN-10: 1891121995
  • ISBN-13: 9781891121999
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781891121999.html
Märksõnad:
This textbook teaches students to create computer codes used to engineer antennas, microwave circuits, and other critical technologies for wireless communications and other applications of electromagnetic fields and waves. Worked code examples are provided for MATLAB technical computing software. It is the only textbook on numerical methods that begins at the undergraduate engineering student level but brings students to the state-of-the-art by the end of the book. It focuses on the most important and popular numerical methods, going into depth with examples and problem sets of escalating complexity. This book requires only one core course of electromagnetics, allowing it to be useful both at the senior and beginning graduate levels. Developing and using numerical methods in a powerful tool for students to learn the principles of intermediate and advanced electromagnetics. This book fills the missing space of current textbooks that either lack depth on key topics (particularly integral equations and the method of moments) and where the treatment is not accessible to students without an advanced theory course. Important topics include: Method of Moments; Finite Difference Time Domain Method; Finite Element Method; Finite Element Method-Boundary Element Method; Numerical Optimization; and Inverse Scattering.
Preface xiii
Chapter 1 Introduction
1(36)
1.1 Scientific Computation, Numerical Analysis, and Engineering
2(1)
1.2 Computational Electromagnetics
3(4)
1.2.1 Applications of CEM Tools
5(1)
1.2.2 Types of CEM Methods
6(1)
1.2.3 Mesh and Grid Generation
7(1)
1.3 Accuracy and Efficiency
7(2)
1.4 Programming Languages
9(1)
1.5 Writing and Debugging Numerical Codes
9(2)
1.6 Overview of Electromagnetic Field Theory
11(22)
1.6.1 Electromagnetic Field and Source Quantities
11(1)
1.6.2 Maxwell's Equations
12(1)
1.6.3 Constitutive Relations
12(1)
1.6.4 Impressed and Induced Currents
13(1)
1.6.5 The Equivalence Principle and Magnetic Currents
13(1)
1.6.6 Coordinate Systems
14(3)
1.6.7 Gradient, Curl, and Divergence
17(1)
1.6.8 Laplacian
18(1)
1.6.9 Wave Propagation
18(2)
1.6.10 Boundary Conditions
20(1)
1.6.11 Time-and Frequency-Domain Representations
20(1)
1.6.12 Plane Waves
21(3)
1.6.13 Propagating, Standing, and Evanescent Waves
24(1)
1.6.14 Bessel Functions
25(3)
1.6.15 Power and Energy
28(1)
1.6.16 Initial Value Problems and Boundary Value Problems
29(1)
1.6.17 Modes
30(1)
1.6.18 2-D Problems and the Transverse Electric and Transverse Magnetic Polarizations
30(2)
1.6.19 Radiation and Scattering Problems
32(1)
1.6.20 Inverse Problems
33(1)
1.6.21 Other Topics
33(1)
1.7 References
33(1)
1.8 Problems
34(3)
Chapter 2 Basic Numerical Tasks
37(18)
2.1 Introduction to MATLAB Programming
37(8)
2.1.1 Vectors and Arrays
38(1)
2.1.2 Working with Plots
39(3)
2.1.3 Scripts
42(2)
2.1.4 Functions
44(1)
2.1.5 Other MATLAB Commands
45(1)
2.2 Numerical Differentiation
45(2)
2.2.1 Code Example: Central Difference Rule
47(1)
2.3 Numerical Integration
47(2)
2.3.1 Code Example: Midpoint Integration Rule
48(1)
2.4 Interpolation
49(1)
2.5 Curve Fitting
50(3)
2.5.1 Code Example: Polynomial Fitting
51(2)
2.6 Newton's Method
53(1)
2.7 References
53(1)
2.8 Problems
53(2)
Chapter 3 Finite Difference Methods
55(68)
3.1 Basic Components of Finite Difference Solvers
56(4)
3.1.1 Grid
56(1)
3.1.2 Stencil
57(1)
3.1.3 Boundary Conditions
58(1)
3.1.4 Sources
59(1)
3.1.5 Solution Method
60(1)
3.2 Wave Equation: 1-D FDTD Method
60(15)
3.2.1 1-D Grid
61(1)
3.2.2 Update Equation for the 1-D Wave Equation
61(1)
3.2.3 Initial Condition
62(1)
3.2.4 Boundary Conditions
62(1)
3.2.5 Sources
63(1)
3.2.6 Source Turn-On Functions
64(1)
3.2.7 Code Example: 1-D FDTD Algorithm
65(3)
3.2.8 Numerical Results
68(1)
3.2.9 Stability
69(3)
3.2.10 Accuracy
72(3)
3.3 Laplace's Equation: 2-D Finite Difference Method
75(9)
3.3.1 Example: 2-D FD Method on a 4 by 4 Grid
77(1)
3.3.2 Waveguide Modes
78(4)
3.3.3 2-D FD for Transmission Lines with Dielectric Materials
82(2)
3.4 2-D FDTD Method
84(25)
3.4.1 2-D EM Problems
84(1)
3.4.2 Yee Cell and 2-D FDTD Method for TM Polarized Fields
85(3)
3.4.3 Conductive Materials
88(1)
3.4.4 Anisotropic Materials
89(1)
3.4.5 Stability Criterion
89(1)
3.4.6 Preprocessing
90(1)
3.4.7 Scattering Problems
90(6)
3.4.8 Postprocessing
96(3)
3.4.9 Near Field to Far Field Transformation
99(6)
3.4.10 Other Types of Postprocessing
105(2)
3.4.11 Code Verification
107(2)
3.5 3-D FDTD Method
109(3)
3.5.1 PEC Cavity
111(1)
3.6 Perfectly Matched Layer
112(6)
3.6.1 UPML for the TMz Polarization
115(3)
3.7 References
118(1)
3.8 Problems
119(4)
Chapter 4 Numerical Integration
123(28)
4.1 Types of Integration Rules
124(1)
4.2 Classical Polynomial Rules
125(8)
4.2.1 Error Analysis of the Midpoint Rule
126(3)
4.2.2 Higher-Order Polynomial Rules
129(2)
4.2.3 Newton-Cotes Rules
131(2)
4.2.4 Romberg Integration
133(1)
4.3 Gaussian Quadrature
133(6)
4.3.1 Orthogonal Polynomials and Gaussian Quadrature
135(3)
4.3.2 Gauss-Legendre Quadrature (w(x) = 1)
138(1)
4.4 Nonclassical Gaussian Quadrature Rules
139(4)
4.4.1 Lanczos Algorithm
140(2)
4.4.2 Weights and Nodes
142(1)
4.5 Implementation
143(1)
4.6 Other Methods for Singular Integrands
143(3)
4.6.1 Singularity Subtraction
143(2)
4.6.2 Transformation Rules
145(1)
4.7 Multidimensional Integrals
146(2)
4.8 MATLAB's Built-in Numerical Integration Functions
148(1)
4.9 References
149(1)
4.10 Problems
149(2)
Chapter 5 Integral Equations and the Method of Moments
151(60)
5.1 Integral Operators
151(3)
5.1.1 Solving Integral Equations Numerically
153(1)
5.2 Integral Equations in Electromagnetics
154(8)
5.2.1 Electric Field Integral Equation, 2-D Transverse Magnetic Polarization (TM-EFIE)
155(2)
5.2.2 Electric Field Integral Equation, 2-D Transverse Electric Polarization (TE-EFIE)
157(1)
5.2.3 Magnetic Field Integral Equation (MFIE)
158(1)
5.2.4 Combined Field Integral Equation (CFIE)
158(1)
5.2.5 Thin-Wire Integral Equations
159(3)
5.3 Method of Weighted Residuals
162(5)
5.3.1 Basis Functions
164(2)
5.3.2 MoM Implementation
166(1)
5.4 Method of Moments for the TM-EFIE
167(14)
5.4.1 Mesh
167(1)
5.4.2 Path Integrals
168(1)
5.4.3 Testing Integration
168(1)
5.4.4 Source Integration
169(1)
5.4.5 Incident Field
170(1)
5.4.6 Physical Interpretation of the Method of Moments
170(1)
5.4.7 Mesh Element Density
171(1)
5.4.8 MoM Code Overview
172(1)
5.4.9 Mesh Generation
173(2)
5.4.10 Postprocessing
175(1)
5.4.11 Scattering Amplitude
175(3)
5.4.12 MoM Implementation
178(3)
5.5 Accuracy and Efficiency of the Method of Moments
181(13)
5.5.1 Computational Cost
181(2)
5.5.2 Error Analysis
183(3)
5.5.3 Sources of Error
186(8)
5.6 Dielectric Structures
194(4)
5.6.1 Volume Method of Moments
195(3)
5.7 2.5-Dimensional Methods
198(1)
5.8 3-D Electric Field Integral Equation
198(9)
5.8.1 Rooftop Functions
199(1)
5.8.2 Rao-Wilton-Glisson Basis
200(2)
5.8.3 Method of Moments
202(5)
5.9 References
207(1)
5.10 Problems
207(4)
Chapter 6 Solving Linear Systems
211(36)
6.1 Linear Operators
212(9)
6.1.1 Linear Spaces
212(1)
6.1.2 Norms on Linear Spaces
213(1)
6.1.3 Linear Operators
214(1)
6.1.4 Operator Norms
215(1)
6.1.5 Range, Null Space, and Rank
215(1)
6.1.6 Operator Inverse and Adjoint
216(1)
6.1.7 Classes of Operators
216(2)
6.1.8 Eigenvalues and Eigenvectors
218(1)
6.1.9 Field of Values
218(1)
6.1.10 Matrix Decompositions
218(3)
6.1.11 Other Matrix Formulas
221(1)
6.2 Direct and Iterative Solution Methods
221(2)
6.3 LU Decomposition
223(1)
6.4 Iterative Methods
224(5)
6.4.1 Stationary Iterations
225(2)
6.4.2 Implementation of Iterative Algorithms
227(2)
6.5 Krylov Subspace Iterations
229(10)
6.5.1 Conjugate Gradient Method
229(2)
6.5.2 Residual Error
231(1)
6.5.3 Condition Number
232(1)
6.5.4 CGNE Algorithm
232(1)
6.5.5 Other Krylov Subspace Methods
233(1)
6.5.6 Convergence of Krylov Subspace Iterations
234(4)
6.5.7 Preconditioners
238(1)
6.6 Multiscale Problems
239(5)
6.6.1 Fast Algorithms
241(2)
6.6.2 Reduced-Order Representations
243(1)
6.7 References
244(1)
6.8 Problems
245(2)
Chapter 7 Variational Methods and the Rayleigh-Ritz Procedure
247(12)
7.1 Operators and Functionals
248(1)
7.2 Variational Principles
249(6)
7.2.1 Variational Calculus
251(1)
7.2.2 Euler-Lagrange Equation
251(2)
7.2.3 Variational Principles for PDEs
253(1)
7.2.4 Variational Principles for Self-Adjoint, Positive Definite Operators
253(1)
7.2.5 Functionals in Mathematical Physics
253(2)
7.3 Rayleigh-Ritz Method
255(2)
7.4 References
257(1)
7.5 Problems
258(1)
Chapter 8 Finite Element Method
259(38)
8.1 Overview of the Finite Element Method
260(2)
8.1.1 Mesh
260(1)
8.1.2 Basis Functions
261(1)
8.1.3 Variational Principle and Rayleigh-Ritz Procedure
261(1)
8.1.4 Linear System Solution
262(1)
8.2 Laplace's Equation: 1-D FEM
262(10)
8.2.1 Functional Form of the Generalized Laplace Equation
263(1)
8.2.2 Mesh Representation
263(1)
8.2.3 Rayleigh-Ritz Procedure
264(1)
8.2.4 Element Stiffness Matrix
265(1)
8.2.5 Basis Functions and Shape Functions
265(2)
8.2.6 Evaluating the Element Stiffness Matrix
267(1)
8.2.7 Assembly of the Global Stiffness Matrix
268(1)
8.2.8 Example: Five-Element Mesh
269(2)
8.2.9 Comparison of FEM and FD
271(1)
8.2.10 Sparse Matrix and Dense Matrix Methods
271(1)
8.3 Boundary Conditions for FEM
272(2)
8.3.1 Boundary Terms in the Functional
273(1)
8.4 Helmholtz Equation: 2-D FEM
274(9)
8.4.1 Eigenvalue Problems (Unknown K)
276(1)
8.4.2 Scattering Problems (Known K)
276(1)
8.4.3 Triangular Mesh
277(2)
8.4.4 Basis Functions and Shape Functions
279(1)
8.4.5 Evaluating Element Matrices
280(2)
8.4.6 Matrix Assembly
282(1)
8.5 Finite Element Method-Boundary Element Method (FEM-BEM)
283(9)
8.5.1 Boundary Element Method
284(4)
8.5.2 Implementation
288(4)
8.6 Numerical Results
292(2)
8.7 References
294(1)
8.8 Problems
294(3)
Chapter 9 Optimization Methods
297(14)
9.1 Introduction
297(2)
9.1.1 Optimization Problems
298(1)
9.1.2 Local and Global Optimization
298(1)
9.2 Classes of Optimization Methods
299(4)
9.2.1 Common Optimization Algorithms
301(2)
9.2.2 Gradient and Gradient-Free Methods
303(1)
9.3 One-Dimensional Optimization
303(3)
9.3.1 Golden Section Search
304(1)
9.3.2 Tolerance Parameter
305(1)
9.3.3 Inverse Quadratic Interpolation
305(1)
9.3.4 Brent's Method
306(1)
9.4 Nelder-Mead Simplex Method
306(4)
9.4.1 Initial Simplex
306(1)
9.4.2 Simplex Transformations
307(1)
9.4.3 Termination
308(1)
9.4.4 Implementation Details
308(1)
9.4.5 Numerical Example
309(1)
9.5 References
310(1)
9.6 Problems
310(1)
Chapter 10 Inverse Problems
311(24)
10.1 Introduction
311(1)
10.2 Types of Inverse Problems
311(3)
10.2.1 Inverse Scattering
312(1)
10.2.2 Imaging
312(1)
10.2.3 Inverse Source Problems
312(1)
10.2.4 Design Synthesis
312(1)
10.2.5 Applications
313(1)
10.3 III-Posed Problems
314(4)
10.3.1 Regularization
315(1)
10.3.2 Resolution
316(1)
10.3.3 Types of Inverse Scattering Methods
316(2)
10.4 Born Approximation Methods
318(8)
10.4.1 Iterated Born Approximation
321(1)
10.4.2 Diffraction Tomography
321(1)
10.4.3 Holographic Backpropagation Tomography
322(2)
10.4.4 Implementation Details
324(1)
10.4.5 Numerical Results
325(1)
10.5 Regularized Sampling
326(5)
10.5.1 Discretization of the Regularized Sampling Equation
328(1)
10.5.2 Implementation Details
329(1)
10.5.3 Numerical Results
330(1)
10.6 References
331(1)
10.7 Problems
332(3)
Index 335
Karl F. Warnick is a faculty member in the Department of Electrical and Computer Engineering at BYU, where he is currently Associate Professor. Dr. Warnick has published many scientific articles and conference papers on electromagnetic theory, numerical methods, remote sensing, antenna applications, phased arrays, biomedical devices, and inverse scattering, and is the author of the books Problem Solving in Electromagnetics, Microwave Circuits, and Antenna Design for Communications Engineering (Artech House, 2006) with Peter Russer and Numerical Analysis for Electromagnetic Integral Equations (Artech House, 2008).