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Computational electromagnetics with MATLAB®
Sadiku, Matthew N. O.
اطلاعات کتابشناختی
Computational electromagnetics with MATLAB®
Author :
Sadiku, Matthew N. O.
Publisher :
CRC Press,
Pub. Year :
2019
Subjects :
MATLAB. Electromagnetism -- Mathematical models.
Call Number :
QC 760 .54 .S32 2019
جستجو در محتوا
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شماره صفحه
امتياز صفحه
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Cover
(1)
Half Title
(2)
Title Page
(4)
Copyright Page
(5)
Dedication
(6)
Contents
(8)
Preface
(14)
Acknowledgment
(16)
A Note to Students
(18)
Author
(20)
1. Fundamental Concepts
(22)
1.1 Introduction
(22)
1.2 Review of EM Theory
(24)
1.2.1 Electrostatic Fields
(24)
1.2.2 Magnetostatic Fields
(25)
1.2.3 Time-Varying Fields
(26)
1.2.4 Boundary Conditions
(28)
1.2.5 Wave Equations
(29)
1.2.6 Time-Varying Potentials
(30)
1.2.7 Time-Harmonic Fields
(32)
1.3 Classification of EM Problems
(36)
1.3.1 Classification of Solution Regions
(36)
1.3.2 Classification of Differential Equations
(36)
1.3.3 Classification of Boundary Conditions
(40)
1.4 Some Important Theorems
(42)
1.4.1 Superposition Principle
(42)
1.4.2 Uniqueness Theorem
(42)
References
(48)
2. Analytical Methods
(50)
2.1 Introduction
(50)
2.2 Separation of Variables
(50)
2.3 Separation of Variables in Rectangular Coordinates
(53)
2.3.1 Laplace’s Equation
(53)
2.3.2 Wave Equation
(57)
2.4 Separation of Variables in Cylindrical Coordinates
(63)
2.4.1 Wave Equation
(66)
2.5 Separation of Variables in Spherical Coordinates
(77)
2.5.1 Laplace’s Equation
(78)
2.5.2 Wave Equation
(82)
2.6 Some Useful Orthogonal Functions
(92)
2.7 Series Expansion
(101)
2.7.1 Poisson’s Equation in a Cube
(101)
2.7.2 Poisson’s Equation in a Cylinder
(103)
2.7.3 Strip Transmission Line
(106)
2.8 Practical Applications
(111)
2.8.1 Scattering by Dielectric Sphere
(111)
2.8.2 Scattering Cross Sections
(116)
2.9 Attenuation due to Raindrops
(119)
2.10 Concluding Remarks
(126)
References
(141)
3. Finite Difference Methods
(144)
3.1 Introduction
(144)
3.2 Finite Difference Schemes
(145)
3.3 Finite Differencing of Parabolic PDEs
(148)
3.4 Finite Differencing of Hyperbolic PDEs
(153)
3.5 Finite Differencing of Elliptic PDEs
(157)
3.5.1 Band Matrix Method
(158)
3.5.2 Iterative Methods
(158)
3.6 Accuracy and Stability of FD Solutions
(161)
3.7 Practical Applications I: Guided Structures
(168)
3.7.1 Transmission Lines
(168)
3.7.2 Waveguides
(174)
3.8 Practical Applications II: Wave Scattering (FDTD)
(177)
3.8.1 Yee’s Finite Difference Algorithm
(180)
3.8.2 Accuracy and Stability
(182)
3.8.3 Lattice Truncation Conditions
(183)
3.8.4 Initial Fields
(185)
3.8.5 Programming Aspects
(186)
3.9 Absorbing Boundary Conditions for FDTD
(194)
3.10 Advanced Applications of FDTD
(202)
3.10.1 Periodic Structures
(202)
3.10.2 Antennas
(203)
3.10.3 PSTD Techniques
(203)
3.10.4 Photonics
(203)
3.10.5 Metamaterials
(203)
3.10.6 MEEP
(204)
3.11 Finite Differencing for Nonrectangular Systems
(204)
3.11.1 Cylindrical Coordinates
(204)
3.11.2 Spherical Coordinates
(208)
3.12 Numerical Integration
(210)
3.12.1 Euler’s Rule
(211)
3.12.2 Trapezoidal Rule
(213)
3.12.3 Simpson’s Rule
(214)
3.12.4 Newton–Cotes Rules
(215)
3.12.5 Gaussian Rules
(217)
3.12.6 Multiple Integration
(218)
3.13 Concluding Remarks
(223)
References
(242)
4. Variational Methods
(250)
4.1 Introduction
(250)
4.2 Operators in Linear Spaces
(250)
4.3 Calculus of Variations
(253)
4.4 Construction of Functionals from PDEs
(257)
4.5 Rayleigh–Ritz Method
(260)
4.6 Weighted Residual Method
(267)
4.7 Collocation Method
(268)
4.7.1 Subdomain Method
(269)
4.7.2 Galerkin Method
(270)
4.7.3 Least Squares Method
(270)
4.8 Eigenvalue Problems
(276)
4.9 Practical Applications
(282)
4.10 Concluding Remarks
(289)
References
(297)
5. Moment Methods
(300)
5.1 Introduction
(300)
5.2 Differential Equations
(301)
5.3 Integral Equations
(303)
5.3.1 Classification of IEs
(304)
5.3.2 Connection between Differential and IEs
(305)
5.4 Green’s Functions
(308)
5.4.1 For Free Space
(309)
5.4.2 For Domain with Conducting Boundaries
(314)
5.4.2.1 Method of Images
(314)
5.4.2.2 Eigenfunction Expansion
(316)
5.5 Applications I: Quasi-Static Problems
(326)
5.6 Applications II: Scattering Problems
(331)
5.6.1 Scattering by Conducting Cylinder
(332)
5.6.2 Scattering by an Arbitrary Array of Parallel Wires
(335)
5.7 Applications III: Radiation Problems
(341)
5.7.1 Hallen’s IE
(343)
5.7.2 Pocklington’s IE
(344)
5.7.3 Expansion and Weighting Functions
(344)
5.8 Applications IV: EM Absorption in the Human Body
(355)
5.8.1 Derivation of IEs
(356)
5.8.2 Transformation to Matrix Equation (Discretization)
(359)
5.8.3 Evaluation of Matrix Elements
(360)
5.8.4 Solution of the Matrix Equation
(361)
5.9 Concluding Remarks
(372)
References
(387)
6. Finite Element Method
(392)
6.1 Introduction
(392)
6.2 Solution of Laplace’s Equation
(393)
6.2.1 Finite Element Discretization
(393)
6.2.2 Element Governing Equations
(394)
6.2.3 Assembling of All Elements
(398)
6.2.4 Solving the Resulting Equations
(400)
6.3 Solution of Poisson’s Equation
(406)
6.3.1 Deriving Element-Governing Equations
(408)
6.3.2 Solving the Resulting Equations
(411)
6.4 Solution of the Wave Equation
(413)
6.5 Automatic Mesh Generation I: Rectangular Domains
(416)
6.6 Automatic Mesh Generation II: Arbitrary Domains
(420)
6.6.1 Definition of Blocks
(421)
6.6.2 Subdivision of Each Block
(422)
6.6.3 Connection of Individual Blocks
(423)
6.7 Bandwidth Reduction
(423)
6.8 Higher-Order Elements
(429)
6.8.1 Pascal Triangle
(429)
6.8.2 Local Coordinates
(430)
6.8.3 Shape Functions
(432)
6.8.4 Fundamental Matrices
(434)
6.9 Three-Dimensional Elements
(441)
6.10 FEMs for Exterior Problems
(446)
6.10.1 Infinite Element Method
(446)
6.10.2 Boundary Element Method
(447)
6.10.3 Absorbing Boundary Condition
(448)
6.11 Finite-Element Time-Domain Method
(449)
6.12 Applications: Microstrip Lines
(451)
6.13 Concluding Remarks
(453)
References
(465)
7. Transmission-Line-Matrix Method
(472)
7.1 Introduction
(472)
7.2 Transmission-Line Equations
(474)
7.3 Solution of Diffusion Equation
(477)
7.4 Solution of Wave Equations
(481)
7.4.1 Equivalence between Network and Field Parameters
(482)
7.4.2 Dispersion Relation of Propagation Velocity
(485)
7.4.3 Scattering Matrix
(487)
7.4.4 Boundary Representation
(489)
7.4.5 Computation of Fields and Frequency Response
(490)
7.4.6 Output Response and Accuracy of Results
(491)
7.5 Inhomogeneous and Lossy Media in TLM
(496)
7.5.1 General 2-D Shunt Node
(496)
7.5.2 Scattering Matrix
(498)
7.5.3 Representation of Lossy Boundaries
(499)
7.6 3-D TLM Mesh
(504)
7.6.1 Series Nodes
(504)
7.6.2 3-D Node
(506)
7.6.3 Boundary Conditions
(510)
7.7 Error Sources and Correction
(518)
7.7.1 Truncation Error
(519)
7.7.2 Coarseness Error
(519)
7.7.3 Velocity Error
(519)
7.7.4 Misalignment Error
(520)
7.8 Absorbing Boundary Conditions
(520)
7.9 Concluding Remarks
(522)
References
(529)
8. Monte Carlo Methods
(534)
8.1 Introduction
(534)
8.2 Generation of Random Numbers and Variables
(535)
8.3 Evaluation of Error
(538)
8.4 Numerical Integration
(542)
8.4.1 Crude Monte Carlo Integration
(542)
8.4.2 Monte Carlo Integration with Antithetic Variates
(544)
8.4.3 Improper Integrals
(545)
8.5 Solution of Potential Problems
(547)
8.5.1 Fixed Random Walk
(547)
8.5.2 Floating Random Walk
(551)
8.5.3 Exodus Method
(554)
8.6 Markov Chain Regional MCM
(566)
8.7 MCMC for Poisson’s Equation
(573)
8.8 Time-Dependent Problems
(577)
8.9 Concluding Remarks
(583)
References
(593)
9. Method of Lines
(598)
9.1 Introduction
(598)
9.2 Solution of Laplace’s Equation
(599)
9.2.1 Rectangular Coordinates
(599)
9.2.2 Cylindrical Coordinates
(605)
9.3 Solution of Wave Equation
(609)
9.3.1 Planar Microstrip Structures
(611)
9.3.2 Cylindrical Microstrip Structures
(618)
9.4 Time-Domain Solution
(625)
9.5 Concluding Remarks
(627)
References
(630)
Selected Bibliography
(634)
Appendix A: Vector Relations
(638)
Appendix B: Programming in MATLAB
(642)
Appendix C: Solution of Simultaneous Equations
(656)
Appendix D: Computational Electromagnetic Codes
(676)
Appendix E: Answers to Odd-Numbered Problems
(678)
Index
(698)
