Despite the dramatic growth in the availability of powerful computer resources, the EM community lacks 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.
This third edition of the 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 has added a chapter on the method of lines.
Numerical Techniques in Electromagnetics with MATLAB®, Third Edition continues to teach readers how to pose, numerically analyze, and solve EM problems, to give them the ability to expand their problem-solving skills using a variety of methods, and to prepare them for research in electromagnetism. Now the Third Edition goes even further toward providing a comprehensive resource that addresses all of the most useful computation methods for EM problems and includes MATLAB code instead of FORTRAN.
Fundamental Concepts
Introduction
Review of Electromagnetic Theory
Classification of EM Problems
Some Important Theorems
Analytical Methods
Introduction
Separation of Variables
Separation of Variables in Rectangular Coordinates
Separation of Variables in Cylindrical Coordinates
Separation of Variables in Spherical Coordinates
Some Useful Orthogonal Functions
Series Expansion
Practical Applications
Attenuation Due to Raindrops
Concluding Remarks
Finite Difference Methods
Introduction
Finite Difference Schemes
Finite Differencing of Parabolic PDEs
Finite Differencing of Hyperbolic PDEs
Finite Differencing of Elliptic PDEs
Accuracy and Stability of FD Solutions
Practical Applications I — Guided Structures
Practical Applications II — Wave Scattering (FDTD)
Absorbing Boundary Conditions for FDTD
Finite Differencing for Nonrectangular Systems
Numerical Integration
Concluding Remarks
Variational Methods
Introduction
Operators in Linear Spaces
Calculus of Variations
Construction of Functionals from PDEs
Rayleigh–Ritz Method
Weighted Residual Method
Eigenvalue Problems
Practical Applications
Concluding Remarks
Moment Methods
Introduction
Integral Equations
Green’s Functions
Applications I — Quasi-Static Problems
Applications II — Scattering Problems
Applications III— Radiation Problems
Applications IV — EM Absorption in the Human Body
Concluding Remarks
Finite Element Method
Introduction
Solution of Laplace’s Equation
Solution of Poisson’s Equation
Solution of the Wave Equation
Automatic Mesh Generation I — Rectangular Domains
Automatic Mesh Generation II — Arbitrary Domains
Bandwidth Reduction
Higher Order Elements
Three-Dimensional Elements
Finite Element Methods for Exterior Problems
Finite-Element Time-Domain Method
Concluding Remarks
Transmission-line-matrix Method
Introduction
Transmission-line Equations
Solution of Diffusion Equation
Solution of Wave Equations
Inhomogeneous and Lossy Media in TLM
Three-Dimensional TLM Mesh
Error Sources and Correction
Absorbing Boundary Conditions
Concluding Remarks
Monte Carlo Methods
Introduction
Generation of Random Numbers and Variables
Evaluation of Error
Numerical Integration
Solution of Potential Problems
Regional Monte Carlo Methods
Time-Dependent Problems
Concluding Remarks
Method of Lines
Introduction
Solution of Laplace’s Equation
Solution of Wave Equation
Time-Domain Solution
Concluding Remarks
References
Problems
APPENDICES
Vector Relations
Vector Identities
Vector Theorems
Orthogonal Coordinates
Programming in MATLAB
MATLAB Fundamentals
Using MATLAB to Plot
Programming with MATLAB
Functions
Solving Equations
Programming Hints
Other Useful MATLAB Commands
Solution of Simultaneous Equations
Elimination Methods
Iterative Methods
Matrix Inversion
Eigenvalue Problems
Answers to Odd-Numbered Problems
