Numerical Techniques in Electromagnetics with MATLAB

Continuing in the bestselling tradition of the first edition, this second edition demonstrates how to pose, numerically analyze, and solve electromagnetic problems (EM). Significant updates include the transition of all FORTRAN code into the more widely used MATLAB format as well as improvements made to the standard algorithm for the finite difference time domain (FDTD) method and the treatment of absorbing boundary conditions in FDTD, the finite element method, and the transmission-line-matrix method. In addition to updated examples and new homework problems throughout, the second edition adds a chapter on the method of lines. An appendix on how to use MATLAB code also appears in the new edition.

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