Front Cover -- Numerical Methods in Electromagnetism -- Copyright Page -- Contents -- Foreword -- Preface -- CHAPTER 1. BASIC PRINCIPLES OF ELECTROMAGNETIC FIELDS -- 1.1 Introduction -- 1.2 Static Electric Fields -- 1.3 The Electric Potential -- 1.4 Electric Fields and Materials -- 1.5 Interface Conditions on the Electric Field -- 1.6 Laplace's and Poisson's Equations -- 1.7 Static Magnetic Fields -- 1.8 Energy in the Magnetic Field -- 1.9 Quasi-statics: Eddy Currents and Diffusion -- 1.10 The Wave Equation -- 1.11 Discussion of Choice of Variables -- 1.12 Classification of Differential Equations -- CHAPTER 2. OVERVIEW OF COMPUTATIONAL METHODS IN ELECTROMAGNETICS -- 2.1 Introduction and Historical Background -- 2.2 Graphical Methods -- 2.3 Conformal Mapping -- 2.4 Experimental Methods -- 2.5 ElectroConducting Analog -- 2.6 Resistive Analog -- 2.7 Closed Form Analytical Methods -- 2.8 Discrete Analytical Methods -- 2.9 Transformation Methods for Nonlinear Problems -- 2.10 Nonlinear Magnetic Circuit Analysis -- 2.11 Finite Difference Method -- 2.12 Integral Equation Method -- 2.13 The Finite Element Method -- CHAPTER 3. THE FINITE DIFFERENCE METHOD -- 3.1 Introduction -- 3.2 Difference Equations -- 3.3 Laplace's and Poisson's Equations -- 3.4 Interfaces Between Materials -- 3.5 Neumann Boundary Conditions -- 3.6 Treatment of Irregular Boundaries -- 3.7 Equivalent Circuit Representation -- 3.8 Formulas For High-Order Schemes -- 3.9 Finite Differences With Symbolic Operators -- 3.10 Diffusion Equation -- 3.11 Conclusions -- CHAPTER 4. VARIATIONAL AND GALERKIN METHODS -- 4.1 Introduction -- 4.2 The Variational Method -- 4.3 The Functional and its Extremum -- 4.4 Functional in more than one space variable and its extremum -- 4.5 Derivation of the Energy-Related Functional -- 4.6 Ritz's method -- 4.7 The Wave Equation.

4.8 Variational Method for Integral Equations -- 4.9 Introduction to The Galerkin Method -- 4.10 Example of the Galerkin Method -- CHAPTER 5. SHAPE FUNCTIONS -- 5.1 Introduction -- 5.2 Polynomial Interpolation -- 5.3 Deriving Shape Functions -- 5.4 Lagrangian Interpolation -- 5.5 Two-Dimensional Elements -- 5.6 High-Order Triangular Interpolation Functions -- 5.7 Rectangular Elements -- 5.8 Derivation of Shape Functions for Serendipity Elements -- 5.9 Three-Dimensional Finite Elements -- 5.10 Orthogonal Basis Functions -- CHAPTER 6. THE FINITE ELEMENT METHOD -- 6.1 Introduction -- 6.2 Functional minimization and global assembly -- 6.3 Solution to the nonlinear magnetostatic problem with first-order triangular finite elements -- 6.4 Application of the Newton-Raphson Method to a First-Order Element -- 6.5 Discretization of Time by the Finite Element Method -- 6.6 Axisymmetric Formulation for the Eddy Current Problem Using Vector Potential -- 6.7 Finite Difference and First-Order Finite Elements -- 6.8 Galerkin Finite Elements -- 6.9 Three-Element Magnetostatic Problem -- 6.10 Permanent Magnets -- 6.11 Numerical Example of Matrix Formation for Isoparametric Elements -- 6.12 Edge Elements -- CHAPTER 7. INTEGRAL EQUATIONS -- 7.1 Introduction -- 7.2 Basic Integral Equations -- 7.3 Method of Moments -- 7.4 The Charge Simulation Method -- 7.5 Boundary Element Equations for Poisson's Equation in Two Dimensions -- 7.6 Example of BEM Solution of a Two-Dimensional Potential Problem -- 7.7 Axisymmetric Integral Equations for Magnetic Vector Potential -- 7.8 Two-Dimensional Eddy Currents With T-Ω -- 7.9 BEM Formulation of The Scalar Poisson Equation in Three Dimensions -- 7.10 Green's functions for some typical electromagnetics applications -- CHAPTER 8. OPEN BOUNDARY PROBLEMS -- 8.1 Introduction -- 8.2 Hybrid Harmonic Finite Element Method.

8.3 Infinite Elements -- 8.4 Ballooning -- 8.5 Infinitesimal Scaling -- 8.6 Hybrid Finite Element-Boundary Element Method -- CHAPTER 9. HIGH-FREQUENCY PROBLEMS WITH FINITE ELEMENTS -- 9.1 Introduction -- 9.2 Finite Element Formulation in Two Dimensions -- 9.3 Boundary Element Formulation -- 9.4 Implementation of the Hybrid Method (HEM) -- 9.5 Evaluation of the Far-Field -- 9.6 Scattering Problems -- 9.7 Numerical Examples -- 9.8 Three Dimensional FEM Formulation for the Electric Field -- 9.9 Example -- CHAPTER 10. LOW-FREQUENCY APPLICATIONS -- 10.1 Time Domain Modeling of Electromechanical Devices -- 10.2 Modeling of Flow Electrification in Insulating Tubes -- 10.3 Coupled Finite Element and Fourier Transform Method for Transient Scalar Field Problems -- 10.4 Axiperiodic Analysis -- CHAPTER 11. SOLUTION OF EQUATIONS -- 11.1 Introduction -- 11.2 Direct Methods -- 11.3 LU Decomposition -- 11.4 Cholesky Decomposition -- 11.5 Sparse Matrix Techniques -- 11.6 The Preconditioned Conjugate Gradient Method -- 11.7 GMRES -- 11.8 Solution of Nonlinear Equations -- APPENDIX A. VECTOR OPERATORS -- APPENDIX B. TRIANGLE AREA IN TERMS OF VERTEX COORDINATES -- APPENDIX C. FOURIER TRANSFORM METHOD -- C.1 Computation of Element Coefficient Matrices and Forcing Functions -- APPENDIX D. INTEGRALS OF AREA COORDINATES -- APPENDIX E. INTEGRALS OF VOLUME COORDINATES -- APPENDIX F. GAUSS-LEGENDRE QUADRATURE FORMULAE, ABSCISSAE, AND WEIGHT COEFFICIENTS -- APPENDIX G. SHAPE FUNCTIONS FOR 1D FINITE ELEMENTS -- APPENDIX H. SHAPE FUNCTIONS FOR 2D FINITE ELEMENTS -- APPENDIX I. SHAPE FUNCTIONS FOR 3D FINITE ELEMENTS -- REFERENCES -- INDEX.