Numerical Techniques in Electromagnetics

Preface. A Note to Students. FUNDAMENTAL CONCEPTS. Introduction. Review of Electromagnetic Theory. Electrostatic Fields. Magnetostatic Fields. Time-Varying Fields. Boundary Conditions. Wave Equations. Time-Varying Potentials. Time-Harmonic Fields. Classification of EM Problems. Classification of Solution Region. Classification of Differential Equations. Classification of Boundary Conditions. Some Important Theorems. Superposition Principle. Uniqueness Theorem. References. Problems. 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. Concluding Remarks. References. Problems. 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 (FD-TD). Finite Differencing of Nonrectangular Systems. Numerical Integration. Concluding Remarks. References. Problems. VARIATIONAL METHODS. Introduction. Operators in Linear Space. Calculus of Variation. Construction of Functional from PDEs. Rayleigh-Ritz Methods. Weighted Residual Method. Eigenvalue Problems. Practical Application. Concluding Remarks. References. Problems. MOMENT METHODS. Introduction. Integral Equations. Green's Functions. Applications I-Quasi-Static Problems. Applications II-Scattering Problems. Applications III-Radiation Problems. Hallen's Integral Equation. Pocklington's Integral Equation. Applications IV-EM Absorption in Human Body. Concluding Remarks. References. Problems. FINITE ELEMENT METHOD. Introduction. Solution of Laplace's Equation. Solution of Poisson's Equations. Solution of the Wave Equation. Automatic Mesh Generation. Bandwidth Reduction. Higher-Order Elements. Three-Dimensional Elements. Hybrid Finite Elements Methods. Concluding Remarks. References. Problems. TRANSMISSION-LINE MODELING. Introduction. Transmission-Line Equations. Solution of Diffusion Equation. Solution of Wave Equation. Scattering Problem in Three Dimensions. Errors in TLM. Concluding Remarks. References. Problems. MONTE CARLO METHODS. Introduction. Generation of Random Numbers and Variables. Estimation of Error. Solution Potential Problems. Scattering of EM Waves by Randomly Rough Surfaces. Monte Carlo Integration. Concluding Remarks. References. Problems. APPENDICES. Vector Relations. Review of FORTRAN Language. How to Write a Good Program. Solution of Simultaneous Equations. Answers to Odd-Numbered Problems.