Field Solutions on Computers

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Preface......Page 6
Author......Page 8
Table of Contents......Page 9
 1.1 Overview......Page 16
 1.2 The Load Ahead......Page 17
 1.3 Some Precautions......Page 22
Chapter 2: Finite-Element Electrostatic Solutions......Page 24
 2.1 Coulomb's Law......Page 25
 2.2 Gauss' Law and Charge Density......Page 27
 2.3 Differential Equations for Electrostatic Fields......Page 29
 2.4 Charge Density Distributions and Dielectric Materials......Page 34
 2.5 Finite Elements......Page 38
 2.6 Coordinate Relationships for Triangles......Page 40
 2.7 Gauss' Law for Elements at a Vertex Point......Page 43
 2.8 Solution Procedure and Boundary Conditions......Page 48
 2.9 Electrostatic Equations in Cylindrical Coordinates......Page 50
 Exercises......Page 53
Chapter 3: Minimum-Energy Principles in Electrostatics......Page 58
 3.1 Electrostatic Field Energy......Page 59
 3.2 Elements of the Calculus of Variations......Page 62
 3.3 Poisson Equation as a Condition of Minimum Energy......Page 64
 3.4 Finite-Element Equations for Two-Dimensional Electrostatics......Page 65
 3.5 Three-Dimensional Finite-Element Electrostatics on Arbitrary Meshes......Page 67
 3.6 High-Order Finite-Element Formulations......Page 71
 Exercises......Page 73
Chapter 4: Finite-Difference Solutions and Regular Meshes......Page 76
 4.1 Difference Operators......Page 77
 4.2 Initial Value Solutions of Ordinary Differential Equations......Page 84
 4.3 One-Dimensional Poisson Equation......Page 88
 4.4 Solution of the Poisson Equation by Back-Substitution......Page 90
 4.5 Two-Dimensional Electrostatic Solutions on a Regular Mesh......Page 92
 4.6 Three-Dimensional Electrostatic Solutions on a Regular Mesh......Page 96
 Exercises......Page 98
Chapter 5: Techniques for Numerical Field Solutions......Page 102
 5.1 Regular Meshes in Three Dimensions......Page 103
 5.2 Two-Dimensional Conformal Triangular Meshes......Page 107
 5.3 Fitting Triangular Elements to Physical Boundaries......Page 111
 5.4 Neumann Boundaries in Resistive Media......Page 117
 5.5 Boundary Value Solutions by Successive Over-Relaxation......Page 119
 Exercises......Page 122
Chapter 6: Matrix Methods for Field Solutions......Page 126
 6.1 Gauss-Jordan Elimination......Page 127
 6.2 Solving Tridiagonal Matrices......Page 130
 6.3 Matrix Solutions for One-Dimensional Electrostatics......Page 134
 6.4 Matrices for Two-Dimensional Finite-Element Solutions......Page 138
 6.5 Solving Tridiagonal Block Matrix Problems......Page 142
 Exercises......Page 145
Chapter 7: Analyzing Numerical Solutions......Page 148
 7.1 Locating Elements......Page 149
 7.2 Generalized Least-Squares Fits......Page 152
 7.3 Field Calculations on a Two-Dimensional Triangular Mesh......Page 156
 7.4 Mesh and Boundary Plots......Page 160
 7.5 Contour, Element, Elevation, and Field Line Plots......Page 163
 Exercises......Page 169
Chapter 8: Nonlinear and Anisotropic Materials......Page 174
 8.1 Iterative Solutions to Boundary Value Problems......Page 175
 8.2 Numerical Data for Material Properties......Page 178
 8.3 Finite-Element Equations for Anisotropic Materials......Page 184
 8.4 Steady-State Gas Flow......Page 188
 Exercises......Page 194
Chapter 9: Finite-Element Magnetostatic Solutions......Page 196
 9.1 Differential and Integral Magnetostatic Equations......Page 197
 9.2 Vector Potential and Field Equations in Two Dimensions......Page 204
 9.3 Isotropic Magnetic Materials......Page 208
 9.4 Finite-Element Magnetostatic Equations......Page 213
 9.5 Magnetic Field Solutions......Page 216
 9.6 Properties of Permanent Magnet Materials......Page 219
 9.7 Magnetostatic Solutions with Permanent Magnets......Page 223
 Exercises......Page 227
Chapter 10: Static Field Analysis and Applications......Page 232
 10.2 Electric and Magnetic Field Energy......Page 233
 10.3 Capacitance Calculations......Page 236
 10.4 Inductance Calculations......Page 238
 10.5 Electric and Magnetic Forces on Materials......Page 241
 10.6 Charged-Particle Orbits......Page 244
 10.7 Electron and Ion Guns......Page 248
 10.8 Generalized Neumann Boundaries — Hall-Effect Devices......Page 254
 Exercises......Page 259
Chapter 11: Low-Frequency Electric and Magnetic Fields......Page 266
 11.1 Maxwell Equations......Page 267
 11.2 Complex Numbers for Harmonic Quantities......Page 270
 11.3 Electric Field Equations in Resistive Media......Page 273
 11.4 Electric Field Solutions with Complex Number Potentials......Page 275
 11.5 Magnetic Fields with Eddy Currents......Page 278
 Exercises......Page 282
Chapter 12: Thermal Transport and Magnetic Field Diffusion......Page 288
 12.1 Thermal Transport Equation......Page 289
 12.2 Finite-Difference Solution of the Diffusion Equation......Page 292
 12.3 Finite-Element Diffusion Solutions......Page 295
 12.4 Instabilities in Finite-Element Diffusion Solutions......Page 297
 12.5 Magnetic Field Diffusion......Page 302
 Exercises......Page 308
Chapter 13: Electromagnetic Fields in One Dimension......Page 312
 13.1 Planar Electromagnetic Waves......Page 313
 13.2 Time-Domain Electromagnetism in One Dimension......Page 318
 13.3 Electromagnetic Pulse Solutions......Page 322
 13.4 Frequency-Domain Equations......Page 329
 13.5 Scattering Solutions......Page 332
 13.6 One-Dimensional Resonant Modes......Page 334
 Exercises......Page 340
Chapter 14: Two- and Three-Dimensional Electromagnetic Simulations......Page 344
 14.1 Time-Domain Equations on a Conformal Mesh......Page 345
 14.2 Electromagnetic Pulse Solutions......Page 349
 14.3 Frequency-Domain Equations......Page 355
 14.4 Methods for Scattering Solutions......Page 358
 14.5 Waveguides and Resonant Cavities......Page 363
 14.6 Power Losses and Q Factors......Page 365
 14.7 Finite-Difference Time-Domain Method in Three Dimensions......Page 371
 14.8 Three-Dimensional Element-Based Time-Domain Equations......Page 375
 Exercises......Page 381
Bibliography......Page 386
Index......Page 390