Numerical Techniques in Electromagnetics, Second Edition

by Sadiku, Matthew N. O.

• ISBN13: 9780849313950
• ISBN10: 0849313953
• Edition: 2nd
• Format: Hardcover
• Copyright: 2000-07-12
• Publisher: CRC

Summary

As the availability of powerful computer resources has grown over the last three decades, the art of computation of electromagnetic (EM) problems has also grown - exponentially. Despite this dramatic growth, however, the EM community lacked a comprehensive text on the computational techniques used to solve EM problems. The first edition of Numerical Techniques in Electromagnetics filled that gap and became the reference of choice for thousands of engineers, researchers, and students.The Second Edition of this bestselling text reflects the continuing increase in awareness and use of numerical techniques and incorporates advances and refinements made in recent years. Most notable among these are the improvements made to the standard algorithm for the finite difference time domain (FDTD) method and treatment of absorbing boundary conditions in FDTD, finite element, and transmission-line-matrix methods. The author also added a chapter on the method of lines.Numerical Techniques in Electromagnetics continues to teach readers how to pose, numerically analyze, and solve EM problems, give them the ability to expand their problem-solving skills using a variety of methods, and prepare them for research in electromagnetism. Now the Second Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems.

Table of Contents

Fundamental Concepts	1	(26)
Introduction	1	(1)
Review of Electromagnetic Theory	2	(12)
Electrostatic Fields	3	(1)
Magnetostatic Fields	4	(1)
Time-varying Fields	5	(2)
Boundary Conditions	7	(1)
Wave Equations	7	(2)
Time-varying Potentials	9	(1)
Time-harmonic Fields	10	(4)
Classification of EM Problems	14	(6)
Classification of Solution Regions	14	(1)
Classification of Differential Equations	15	(3)
Classification of Boundary Conditions	18	(2)
Some Important Theorems	20	(7)
Superposition Principle	20	(1)
Uniqueness Theorem	21	(2)
References	23	(1)
Problems	23	(4)
Analytical Methods	27	(94)
Introduction	27	(1)
Separation of Variables	28	(2)
Separation of Variables in Rectangular Coordinates	30	(9)
Laplace's Equations	30	(4)
Wave Equation	34	(5)
Separation of Variables in Cylindrical Coordinates	39	(14)
Laplace's Equation	40	(2)
Wave Equation	42	(11)
Separation of Variables in Spherical Coordinates	53	(15)
Laplace's Equation	54	(5)
Wave Equation	59	(9)
Some Useful Orthogonal Functions	68	(10)
Series Expansion	78	(10)
Poisson's Equation in a Cube	78	(2)
Poisson's Equation in a Cylinder	80	(3)
Strip Transmission Line	83	(5)
Practical Applications	88	(7)
Scattering by Dielectric Sphere	88	(4)
Scattering Cross Sections	92	(3)
Attenuation Due to Raindrops	95	(10)
Concluding Remarks	105	(16)
References	106	(1)
Problems	107	(14)
Finite Difference Methods	121	(114)
Introduction	121	(1)
Finite Difference Schemes	122	(3)
Finite Differencing of Parabolic PDEs	125	(6)
Finite Differencing of Hyperbolic PDEs	131	(3)
Finite Differencing of Elliptic PDEs	134	(9)
Band Matrix Method	137	(1)
Iterative Methods	137	(6)
Accuracy and Stability of FD Solutions	143	(4)
Practical Applications I --- Guided Structures	147	(12)
Transmission Lines	148	(6)
Waveguides	154	(5)
Practical Applications II --- Wave Scattering (FDTD)	159	(18)
Yee's Finite Difference Algorithm	160	(3)
Accuracy and Stability	163	(1)
Lattice Truncation Conditions	164	(3)
Initial Fields	167	(1)
Programming Aspects	168	(9)
Absorbing Boundry Conditions for FDTD	177	(9)
Finite Differencing for Nonrectangular Systems	186	(7)
Cylindrical Coordinates	186	(4)
Spherical Coordinates	190	(3)
Numerical Integration	193	(15)
Euler's Rule	196	(1)
Trapezoidal Rule	197	(1)
Simpson's Rule	197	(1)
Newton-Cotes Rules	198	(2)
Gaussian Rules	200	(3)
Multiple Integration	203	(5)
Concluding Remarks	208	(27)
References	210	(9)
Problems	219	(16)
Variational Methods	235	(50)
Introduction	235	(1)
Operators in Linear Spaces	236	(2)
Calculus of Variations	238	(4)
Construction of Functionals from PDEs	242	(3)
Rayleigh-Ritz Method	245	(7)
Weighted Residual Method	252	(9)
Collocation Method	253	(1)
Subdomain Method	254	(1)
Galerkin Method	254	(1)
Least Squares Method	255	(6)
Eigenvalue Problems	261	(7)
Practical Applications	268	(6)
Concluding Remarks	274	(11)
References	275	(4)
Problems	279	(6)
Moment Methods	285	(92)
Introduction	285	(1)
Integral Equations	286	(4)
Classification of Integral Equations	286	(1)
Connection Between Differential and Integral Equations	287	(3)
Green's Functions	290	(18)
For Free Space	292	(3)
For Domain with Conducting Boundaries	295	(13)
Applications I --- Quasi-Static Problems	308	(5)
Applications II --- Scattering Problems	313	(12)
Scattering by Conducting Cylinder	314	(3)
Scattering by an Arbitrary Array of Parallel Wires	317	(8)
Applications III --- Radiation Problems	325	(13)
Hallen's Integral Equation	326	(1)
Pocklington's Integral Equation	327	(1)
Expansion and Weighting Functions	327	(11)
Applications IV --- EM Absorption in the Human Body	338	(9)
Derivation of Integral Equations	339	(3)
Transformation to Matrix Equation (Discretization)	342	(1)
Evaluation of Matrix Elements	343	(2)
Solution of the Matrix Equation	345	(2)
Concluding Remarks	347	(30)
References	357	(6)
Problems	363	(14)
Finite Element Method	377	(90)
Introduction	377	(1)
Solution of Laplace's Equation	378	(19)
Finite Element Discretization	378	(2)
Element Governing Equations	380	(3)
Assembling of All Elements	383	(3)
Solving the Resulting Equations	386	(11)
Solution of Poisson's Equation	397	(3)
Deriving Element-governing Equations	397	(2)
Solving the Resulting Equations	399	(1)
Solution of the Wave Equation	400	(7)
Automatic Mesh Generation I --- Rectangular Domains	407	(3)
Automatic Mesh Generation II --- Arbitrary Domains	410	(10)
Definition of Blocks	411	(1)
Subdivision of Each Block	412	(1)
Connection of Individual Blocks	413	(7)
Bandwidth Reduction	420	(4)
Higher Order Elements	424	(15)
Pascal Triangle	425	(1)
Local Coordinates	426	(1)
Shape Functions	427	(3)
Fundamental Matrices	430	(9)
Three-Dimensional Elements	439	(5)
Finite Element Methods for Exterior Problems	444	(4)
Infinite Element Method	444	(2)
Boundary Element Method	446	(1)
Absorbing Boundary Conditions	446	(2)
Concluding Remarks	448	(19)
References	449	(9)
Problems	458	(9)
Transmission-line-matrix Method	467	(70)
Introduction	467	(2)
Transmission-line Equations	469	(4)
Solution of Diffusion Equation	473	(4)
Solution of Wave Equations	477	(16)
Equivalence Between Network and Field Parameters	477	(4)
Dispersion Relation of Propagation Velocity	481	(2)
Scattering Matrix	483	(3)
Boundary Representation	486	(1)
Computation of Fields and Frequency Response	487	(1)
Output Response and Accuracy of Results	487	(6)
Inhomogeneous and Lossy Media in TLM	493	(6)
General Two-Dimensional Shunt Node	494	(2)
Scattering Matrix	496	(1)
Representation of Lossy Boundaries	497	(2)
Three-Dimensional TLM Mesh	499	(18)
Series Nodes	499	(5)
Three-Dimensional Node	504	(3)
Boundary Conditions	507	(10)
Error Sources and Correction	517	(2)
Truncation Error	518	(1)
Coarseness Error	518	(1)
Velocity Error	519	(1)
Misalignment Error	519	(1)
Absorbing Boundary Conditions	519	(2)
Concluding Remarks	521	(16)
References	523	(6)
Problems	529	(8)
Monte Carlo Methods	537	(60)
Introduction	537	(1)
Generation of Random Numbers and Variables	538	(4)
Evaluation of Error	542	(4)
Numerical Integration	546	(4)
Crude Monte Carlo Integration	546	(2)
Monte Carlo Integration with Antithetic Variates	548	(1)
Improper Integrals	549	(1)
Solution of Potential Problems	550	(24)
Fixed Random Walk	552	(5)
Floating Random Walk	557	(2)
Exodus Method	559	(15)
Regional Monte Carlo Methods	574	(7)
Concluding Remarks	581	(16)
References	582	(6)
Problems	588	(9)
Method of Lines	597	(42)
Introduction	597	(1)
Solution of Laplace's Equation	598	(11)
Rectangular Coordinates	598	(7)
Cylindrical Coordinates	605	(4)
Solution of Wave Equation	609	(18)
Planar Microstrip Structures	612	(7)
Cylindrical Microstrip Structures	619	(8)
Time-Domain Solution	627	(2)
Concluding Remarks	629	(10)
References	629	(6)
Problems	635	(4)
A Vector Relations	639	(4)
A.1 Vector Identities	639	(1)
A.2 Vector Theorems	639	(1)
A.3 Orthogonal Coordinates	640	(3)
B Solving Electromagnetic Problems Using C++	643	(34)
B.1 Introduction	643	(1)
B.2 A Brief Description of C++	643	(18)
B.3 Object-Orientation	661	(4)
B.4 C++ Object-Oriented Language Features	665	(9)
B.5 A Final Note	674	(3)
References	675	(2)
C Numerical Techniques in C++	677	(24)
D Solution of Simultaneous Equations	701	(24)
D.1 Elimination Methods	701	(5)
D.1.1 Gauss's Method	702	(1)
D.1.2 Cholesky's Method	703	(3)
D.2 Iterative Methods	706	(7)
D.2.1 Jacobi's Method	706	(2)
D.2.2 Gauss-Seidel Method	708	(1)
D.2.3 Relaxation Method	708	(2)
D.2.4 Gradient Methods	710	(3)
D.3 Matrix Inversion	713	(1)
D.4 Eigenvalue Problems	714	(11)
D.4.1 Iteration (or Power) Method	716	(1)
D.4.2 Jacobi's Method	717	(8)
E Answers to Odd-Numbered Problems	725	(16)
Index	741