Elsevier S & T

Numerical Methods in Electromagnetism

Salon, Sheppard; Chari, M. V.K.

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Table of contents
  • Cover
  • Contentsv
  • Forewordxi
  • Prefacexiii
  • CHAPTER 1. BASIC PRINCIPLES OF ELECTROMAGNETIC FIELDS1
  • 1.1 Introduction1
  • 1.2 Static Electric Fields1
  • 1.3 The Electric Potential3
  • 1.4 Electric Fields and Materials11
  • 1.5 Interface Conditions on the Electric Field13
  • 1.6 Laplace's and Poisson's Equations15
  • 1.7 Static Magnetic Fields24
  • 1.8 Energy in the Magnetic Field36
  • 1.9 Quasi-statics: Eddy Currents and Diffusion39
  • 1.10 The Wave Equation42
  • 1.11 Discussion of Choice of Variables44
  • 1.12 Classification of Differential Equations60
  • CHAPTER 2. OVERVIEW OF COMPUTATIONAL METHODS IN ELECTROMAGNETICS63
  • 2.1 Introduction and Historical Background63
  • 2.2 Graphical Methods65
  • 2.3 Conformal Mapping68
  • 2.4 Experimental Methods68
  • 2.5 ElectroConducting Analog69
  • 2.6 Resistive Analog70
  • 2.7 Closed Form Analytical Methods71
  • 2.8 Discrete Analytical Methods74
  • 2.9 Transformation Methods for Nonlinear Problems75
  • 2.10 Nonlinear Magnetic Circuit Analysis79
  • 2.11 Finite Difference Method80
  • 2.12 Integral Equation Method84
  • 2.13 The Finite Element Method96
  • CHAPTER 3. THE FINITE DIFFERENCE METHOD105
  • 3.1 Introduction105
  • 3.2 Difference Equations106
  • 3.3 Laplace's and Poisson's Equations108
  • 3.4 Interfaces Between Materials109
  • 3.5 Neumann Boundary Conditions111
  • 3.6 Treatment of Irregular Boundaries114
  • 3.7 Equivalent Circuit Representation115
  • 3.8 Formulas For High-Order Schemes117
  • 3.9 Finite Differences With Symbolic Operators122
  • 3.10 Diffusion Equation126
  • 3.11 Conclusions141
  • CHAPTER 4. VARIATIONAL AND GALERKIN METHODS143
  • 4.1 Introduction143
  • 4.2 The Variational Method144
  • 4.3 The Functional and its Extremum145
  • 4.4 Functional in more than one space variable and its extremum153
  • 4.5 Derivation of the Energy-Related Functional157
  • 4.6 Ritz's method170
  • 4.7 The Wave Equation176
  • 4.8 Variational Method for Integral Equations179
  • 4.9 Introduction to The Galerkin Method182
  • 4.10 Example of the Galerkin Method183
  • CHAPTER 5. SHAPE FUNCTIONS189
  • 5.1 Introduction189
  • 5.2 Polynomial Interpolation201
  • 5.3 Deriving Shape Functions207
  • 5.4 Lagrangian Interpolation211
  • 5.5 Two-Dimensional Elements214
  • 5.6 High-Order Triangular Interpolation Functions222
  • 5.7 Rectangular Elements227
  • 5.8 Derivation of Shape Functions for Serendipity Elements234
  • 5.9 Three-Dimensional Finite Elements240
  • 5.10 Orthogonal Basis Functions278
  • CHAPTER 6. THE FINITE ELEMENT METHOD283
  • 6.1 Introduction283
  • 6.2 Functional minimization and global assembly295
  • 6.3 Solution to the nonlinear magnetostatic problem with first-order triangular finite elements302
  • 6.4 Application of the Newton–Raphson Method to a First-Order Element306
  • 6.5 Discretization of Time by the Finite Element Method310
  • 6.6 Axisymmetric Formulation for the Eddy Current Problem Using Vector Potential313
  • 6.7 Finite Difference and First-Order Finite Elements320
  • 6.8 Galerkin Finite Elements322
  • 6.9 Three-Element Magnetostatic Problem326
  • 6.10 Permanent Magnets338
  • 6.11 Numerical Example of Matrix Formation for Isoparametric Elements342
  • 6.12 Edge Elements353
  • CHAPTER 7. INTEGRAL EQUATIONS359
  • 7.1 Introduction359
  • 7.2 Basic Integral Equations359
  • 7.3 Method of Moments362
  • 7.4 The Charge Simulation Method370
  • 7.5 Boundary Element Equations for Poisson's Equation in Two Dimensions374
  • 7.6 Example of BEM Solution of a Two-Dimensional Potential Problem381
  • 7.7 Axisymmetric Integral Equations for Magnetic Vector Potential389
  • 7.8 Two-Dimensional Eddy Currents With T–Ω393
  • 7.9 BEM Formulation of The Scalar Poisson Equation in Three Dimensions403
  • 7.10 Green's functions for some typical electromagnetics applications409
  • CHAPTER 8. OPEN BOUNDARY PROBLEMS413
  • 8.1 Introduction413
  • 8.2 Hybrid Harmonic Finite Element Method413
  • 8.3 Infinite Elements417
  • 8.4 Ballooning427
  • 8.5 Infinitesimal Scaling433
  • 8.6 Hybrid Finite Element–Boundary Element Method437
  • CHAPTER 9. HIGH-FREQUENCY PROBLEMS WITH FINITE ELEMENTS451
  • 9.1 Introduction451
  • 9.2 Finite Element Formulation in Two Dimensions452
  • 9.3 Boundary Element Formulation459
  • 9.4 Implementation of the Hybrid Method (HEM)467
  • 9.5 Evaluation of the Far-Field471
  • 9.6 Scattering Problems481
  • 9.7 Numerical Examples488
  • 9.8 Three Dimensional FEM Formulation for the Electric Field494
  • 9.9 Example517
  • CHAPTER 10. LOW-FREQUENCY APPLICATIONS519
  • 10.1 Time Domain Modeling of Electromechanical Devices519
  • 10.2 Modeling of Flow Electrification in Insulating Tubes550
  • 10.3 Coupled Finite Element and Fourier Transform Method for Transient Scalar Field Problems561
  • 10.4 Axiperiodic Analysis570
  • CHAPTER 11. SOLUTION OF EQUATIONS591
  • 11.1 Introduction591
  • 11.2 Direct Methods595
  • 11.3 LU Decomposition598
  • 11.4 Cholesky Decomposition605
  • 11.5 Sparse Matrix Techniques607
  • 11.6 The Preconditioned Conjugate Gradient Method627
  • 11.7 GMRES645
  • 11.8 Solution of Nonlinear Equations658
  • APPENDIX A. VECTOR OPERATORS707
  • APPENDIX B. TRIANGLE AREA IN TERMS OF VERTEX COORDINATES709
  • APPENDIX C. FOURIER TRANSFORM METHOD711
  • C.1 Computation of Element Coefficient Matrices and Forcing Functions714
  • APPENDIX D. INTEGRALS OF AREA COORDINATES719
  • APPENDIX E. INTEGRALS OF VOLUME COORDINATES721
  • APPENDIX F. GAUSS–LEGENDRE QUADRATURE FORMULAE, ABSCISSAE, AND WEIGHT COEFFICIENTS723
  • APPENDIX G. SHAPE FUNCTIONS FOR 1D FINITE ELEMENTS725
  • APPENDIX H. SHAPE FUNCTIONS FOR 2D FINITE ELEMENTS727
  • APPENDIX I. SHAPE FUNCTIONS FOR 3D FINITE ELEMENTS735
  • REFERENCES749
  • INDEX759
Book details
  • Vendor Elsevier S & T
  • SKU 9780126157604
  • ISBN-13 9780080512891
  • Author Salon, Sheppard; Chari, M. V.K.
  • Category Mathematics
  • Subject Mathematical Analysis

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Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. This book will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students.


* Comprehensive descriptions of numerical methods
* In-depth introduction to finite differences, finite elements, and integral equations
* Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis
* Numerical examples to facilitate understanding of the methods
* Appendices for quick reference of mathematical and numerical methods employed