Computational Electromagnetics with Matlab, Fourth Edition

709 Pages·2019·131.38 MB·English

by  Matthew N O Sadiku

Computational
Electromagnetics
with MATLAB®
Fourth Edition

Computational
Electromagnetics
with MATLAB®
Fourth Edition
Matthew N.O. Sadiku
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the
accuracy of the text or exercises in this book. This book’s use or discussion of MATLAB® software or related products
does not constitute endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particu-
lar use of the MATLAB® software.
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To my teacher
Carl A. Ventrice
and my parents
Ayisat and Solomon Sadiku

Contents
Preface ...........................................................................................................................................xiii
Acknowledgment ..........................................................................................................................xv
A Note to Students .....................................................................................................................xvii
Author ...........................................................................................................................................xix
1. Fundamental Concepts ..........................................................................................................1
1.1 Introduction ...................................................................................................................1
1.2 Review of EM Theory ...................................................................................................3
1.2.1 Electrostatic Fields ...........................................................................................3
1.2.2 Magnetostatic Fields ........................................................................................4
1.2.3 Time-Varying Fields ........................................................................................5
1.2.4 Boundary Conditions ......................................................................................7
1.2.5 Wave Equations ................................................................................................8
1.2.6 Time-Varying Potentials .................................................................................9
1.2.7 Time-Harmonic Fields ..................................................................................11
1.3 Classification of EM Problems ..................................................................................15
1.3.1 Classification of Solution Regions ...............................................................15
1.3.2 Classification of Differential Equations ......................................................15
1.3.3 Classification of Boundary Conditions .......................................................19
1.4 Some Important Theorems ........................................................................................21
1.4.1 Superposition Principle .................................................................................21
1.4.2 Uniqueness Theorem .....................................................................................21
References ...............................................................................................................................27
2. Analytical Methods ..............................................................................................................29
2.1 Introduction .................................................................................................................29
2.2 Separation of Variables ...............................................................................................29
2.3 Separation of Variables in Rectangular Coordinates .............................................32
2.3.1 Laplace’s Equation .........................................................................................32
2.3.2 Wave Equation ................................................................................................36
2.4 Separation of Variables in Cylindrical Coordinates...............................................42
2.4.1 Wave Equation ................................................................................................45
2.5 Separation of Variables in Spherical Coordinates ..................................................56
2.5.1 Laplace’s Equation .........................................................................................57
2.5.2 Wave Equation ................................................................................................61
2.6 Some Useful Orthogonal Functions .........................................................................71
2.7 Series Expansion .........................................................................................................80
2.7.1 Poisson’s Equation in a Cube ........................................................................80
2.7.2 Poisson’s Equation in a Cylinder .................................................................82
2.7.3 Strip Transmission Line ................................................................................85
2.8 Practical Applications .................................................................................................90
2.8.1 Scattering by Dielectric Sphere ....................................................................90
2.8.2 Scattering Cross Sections ..............................................................................95
2.9 Attenuation due to Raindrops ...................................................................................98
vii
viii Contents
2.10 Concluding Remarks ................................................................................................105
References .............................................................................................................................120
3. Finite Difference Methods ...............................................................................................123
3.1 Introduction ...............................................................................................................123
3.2 Finite Difference Schemes .......................................................................................124
3.3 Finite Differencing of Parabolic PDEs ....................................................................127
3.4 Finite Differencing of Hyperbolic PDEs ................................................................132
3.5 Finite Differencing of Elliptic PDEs .......................................................................136
3.5.1 Band Matrix Method ...................................................................................137
3.5.2 Iterative Methods .........................................................................................137
3.6 Accuracy and Stability of FD Solutions .................................................................140
3.7 Practical Applications I: Guided Structures ..........................................................147
3.7.1 Transmission Lines ......................................................................................147
3.7.2 Waveguides ...................................................................................................153
3.8 Practical Applications II: Wave Scattering (FDTD) ..............................................156
3.8.1 Yee’s Finite Difference Algorithm .............................................................159
3.8.2 Accuracy and Stability ................................................................................161
3.8.3 Lattice Truncation Conditions ...................................................................162
3.8.4 Initial Fields ..................................................................................................164
3.8.5 Programming Aspects ................................................................................165
3.9 Absorbing Boundary Conditions for FDTD .........................................................173
3.10 Advanced Applications of FDTD............................................................................181
3.10.1 Periodic Structures ......................................................................................181
3.10.2 Antennas .......................................................................................................182
3.10.3 PSTD Techniques .........................................................................................182
3.10.4 Photonics .......................................................................................................182
3.10.5 Metamaterials ...............................................................................................182
3.10.6 MEEP .............................................................................................................183
3.11 Finite Differencing for Nonrectangular Systems .................................................183
3.11.1 Cylindrical Coordinates ..............................................................................183
3.11.2 Spherical Coordinates .................................................................................187
3.12 Numerical Integration ..............................................................................................189
3.12.1 Euler’s Rule ...................................................................................................190
3.12.2 Trapezoidal Rule ..........................................................................................192
3.12.3 Simpson’s Rule .............................................................................................193
3.12.4 Newton–Cotes Rules ...................................................................................194
3.12.5 Gaussian Rules .............................................................................................196
3.12.6 Multiple Integration .....................................................................................197
3.13 Concluding Remarks ................................................................................................202
References .............................................................................................................................221
4. Variational Methods ..........................................................................................................229
4.1 Introduction ...............................................................................................................229
4.2 Operators in Linear Spaces ......................................................................................229
4.3 Calculus of Variations ..............................................................................................232
4.4 Construction of Functionals from PDEs ................................................................236
4.5 Rayleigh–Ritz Method ..............................................................................................239
4.6 Weighted Residual Method .....................................................................................246
Contents ix
4.7 Collocation Method ..................................................................................................247
4.7.1 Subdomain Method .....................................................................................248
4.7.2 Galerkin Method ..........................................................................................249
4.7.3 Least Squares Method .................................................................................249
4.8 Eigenvalue Problems ................................................................................................255
4.9 Practical Applications ...............................................................................................261
4.10 Concluding Remarks ................................................................................................268
References .............................................................................................................................276
5. Moment Methods................................................................................................................279
5.1 Introduction ...............................................................................................................279
5.2 Differential Equations ..............................................................................................280
5.3 Integral Equations .....................................................................................................282
5.3.1 Classification of IEs ......................................................................................283
5.3.2 Connection between Differential and IEs ................................................284
5.4 Green’s Functions ......................................................................................................287
5.4.1 For Free Space ...............................................................................................288
5.4.2 For Domain with Conducting Boundaries ..............................................293
5.4.2.1 Method of Images.........................................................................293
5.4.2.2 Eigenfunction Expansion ............................................................295
5.5 Applications I: Quasi-Static Problems ....................................................................305
5.6 Applications II: Scattering Problems ......................................................................310
5.6.1 Scattering by Conducting Cylinder...........................................................311
5.6.2 Scattering by an Arbitrary Array of Parallel Wires ................................314
5.7 Applications III: Radiation Problems .....................................................................320
5.7.1 Hallen’s IE .....................................................................................................322
5.7.2 Pocklington’s IE ............................................................................................323
5.7.3 Expansion and Weighting Functions ........................................................323
5.8 Applications IV: EM Absorption in the Human Body ........................................334
5.8.1 Derivation of IEs ..........................................................................................335
5.8.2 Transformation to Matrix Equation (Discretization) ..............................338
5.8.3 Evaluation of Matrix Elements ...................................................................339
5.8.4 Solution of the Matrix Equation.................................................................340
5.9 Concluding Remarks ................................................................................................351
References .............................................................................................................................366
6. Finite Element Method ......................................................................................................371
6.1 Introduction ...............................................................................................................371
6.2 Solution of Laplace’s Equation ................................................................................372
6.2.1 Finite Element Discretization .....................................................................372
6.2.2 Element Governing Equations ...................................................................373
6.2.3 Assembling of All Elements .......................................................................377
6.2.4 Solving the Resulting Equations ...............................................................379
6.3 Solution of Poisson’s Equation ................................................................................385
6.3.1 Deriving Element-Governing Equations ..................................................387
6.3.2 Solving the Resulting Equations ...............................................................390
6.4 Solution of the Wave Equation ................................................................................392
6.5 Automatic Mesh Generation I: Rectangular Domains ........................................395
6.6 Automatic Mesh Generation II: Arbitrary Domains ............................................399