Field Solutions on Computers covers a broad range of practical applications involving electric and magnetic fields. The text emphasizes finite-element techniques to solve real-world problems in research and industry. After introducing numerical methods with a thorough treatment of electrostatics, the book moves in a structured sequence to advanced topics. These include magnetostatics with non-linear materials, permanent magnet devices, RF heating, eddy current analysis, electromagnetic pulses, microwave structures, and wave scattering. The mathematical derivations are supplemented with chapter exercises and comprehensive reviews of the underlying physics. The book also covers essential supporting techniques such as mesh generation, interpolation, sparse matrix inversions, and advanced plotting routines.
Author(s): Stanley Humphries Jr.
Edition: draft
Publisher: CRC
Year: 1998
Language: English
Pages: 327
Contents......Page 3
1.1 Overview......Page 6
1.2 Summary of material......Page 7
1.3 Some precautions......Page 11
2 Finite-element Electrostatic Solutions......Page 14
2.1 Coulomb’s law......Page 15
2.2 Gauss’ law and charge density......Page 17
2.3 Differential equations for electrostatic fields......Page 18
2.4 Charge density distributions and dielectric materials......Page 22
2.5 Finite elements......Page 26
2.6 Coordinate relationships for triangles......Page 28
2.7 Gauss’s law for elements at a vertex point......Page 31
2.8 Solution procedure and boundary conditions......Page 35
2.9 Electrostatic equations in cylindrical coordinates......Page 37
3.1 Electrostatic field energy......Page 42
3.2 Elements of the calculus of variations......Page 45
3.3 Poisson equation as a condition of minimum energy......Page 47
3.4 Finite-element equations for two-dimensional electrostatics......Page 48
3.5 Three-dimensional finite-element electrostatics on arbitrary meshes......Page 50
3.6 High-order finite-element formulations......Page 53
4 Finite-difference Solutions and Regular Meshes......Page 56
4.1 Difference operators......Page 57
4.2 Initial value solutions of ordinary differential equations......Page 63
4.3 One-dimensional Poisson equation......Page 66
4.4 Solving the Poisson equation by back-substitution......Page 68
4.5 Two dimensional electrostatic solutions on a regular mesh......Page 69
4.6 Three-dimensional electrostatic solutions on a regular mesh......Page 73
5 Techniques for Numerical Field Solutions......Page 78
5.1 Regular meshes in three dimensions......Page 79
5.2 Two-dimensional conformal triangular meshes......Page 82
5.3 Fitting triangular elements to physical boundaries......Page 88
5.4 Neumann boundaries in resistive media......Page 92
5.5 The method of successive over-relaxation......Page 94
6 Matrix Methods for Field Solutions......Page 98
6.1 Gauss-Jordan elimination......Page 99
6.2 Solving tridiagonal matrices......Page 101
6.3 Matrix solutions for one-dimensional electrostatics......Page 103
6.4 Matrices for two-dimensional finite-element solutions......Page 106
6.5 Solving Tridiagonal Block Matrix Problems......Page 108
7.1 Locating elements......Page 112
7.2 Generalized least-squares fits......Page 115
7.3 Field calculations on a two-dimensional triangular mesh......Page 118
7.4 Mesh and boundary plots......Page 121
7.5 Contour, element, elevation and field line plots......Page 124
8.1 Iterative solutions to boundary value problems......Page 134
8.2 Numerical data for material properties......Page 137
8.3 Finite-element equations for anisotropic materials......Page 143
9 Finite-element Magnetostatic Solutions......Page 148
9.1 Differential and integral magnetostatic equations......Page 149
9.2 Vector potential and field equations in two dimensions......Page 155
9.3 Isotropic magnetic materials......Page 158
9.4 Finite-element magnetostatic equations......Page 163
9.5 Magnetic field solutions......Page 166
9.6 Properties of permanent magnet materials......Page 168
9.7 Magnetostatic solutions with permanent magnets......Page 172
10.1 Volume and surface integrals on a finite-element mesh......Page 180
10.2 Electric and magnetic field energy......Page 181
10.3 Capacitance calculations......Page 183
10.4 Inductance calculations......Page 185
10.5 Electric and magnetic forces on materials......Page 188
10.6 Charged particle orbits......Page 191
10.7 Electron and ion guns......Page 193
10.8 Generalized Neumann boundaries - Hall effect devices......Page 200
11 Low-frequency Electric and Magnetic Fields......Page 210
11.1 Maxwell equations......Page 211
11.2 Complex numbers for harmonic quantities......Page 214
11.3 Electric field equations in resistive media......Page 216
11.4 Electric field solutions with complex number potentials......Page 218
11.5 Magnetic fields with eddy currents......Page 221
12 Thermal Transport and Magnetic Field Diffusion......Page 228
12.1 Thermal transport equation......Page 229
12.2 Finite-difference solution of the diffusion equation......Page 231
12.3 Finite-element diffusion solutions......Page 234
12.4 Instabilities in finite-element diffusion solutions......Page 237
12.5 Magnetic field diffusion......Page 240
13 Electromagnetic Fields in One Dimension......Page 248
13.1 Planar electromagnetic waves......Page 249
13.2 Time-domain electromagnetism in one dimension......Page 253
13.3 Electromagnetic pulse solutions......Page 256
13.4 Frequency-domain equations......Page 262
13.5 Scattering solutions......Page 265
13.6 One-dimensional resonant modes......Page 268
14 Two and Three-dimensional Electromagnetic Simulations......Page 276
14.1 Time-domain equations on a conformal mesh......Page 277
14.2 Electromagnetic pulse solutions......Page 280
14.3 Frequency-domain equations......Page 286
14.4 Methods for scattering solutions......Page 288
14.5 Waveguides and resonant cavities......Page 292
14.6 Power losses and Q factors......Page 294
14.7 Finite-difference time-domain method in three dimensions......Page 298
14.8 Three-dimensional element-based time-domain equations......Page 302
References......Page 312
Index......Page 317
