Field Solutions on Computers
Author - Stanley Humphries, Jr
Department of Electrical and Computer Engineering, University of
New Mexico,
Albuquerque
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How to use computer-based numerical methods for electromagnetic
analysis and design
Covers the full range of field applications from electrostatics
to electromagnetic
scattering
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.
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- Methods have broad applications, including simulation of
biological media, plasma
processing reactors, accelerators, solid state devices, and
rotating electrical equipment
- Hands-on approach to computer modeling
- Easier to understand than many other books on the market, making
it perfect for an
advanced undergraduate textbook
- Illustrates theoretical topics in the book with close to 100
real-world calculations
- Material will help readers to write their own programs
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- Physicists and electrical engineers who want to improve their
skills in computer-based numerical methods for electromagnetic
simulation and equipment design
- Undergraduate and graduate students in engineering and
physics in follow-up courses to basic electromagnetism
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- Chapter 1. Introduction
- Overview
- The Load Ahead
- Some Precautions
- Chapter 2. Finite-Element Electrostatic Equations
- Introduction
- Coulomb's law
- Gauss's law and charge density
- Differential equations for electrostatic fields
- Charge density distributions and dielectric materials
- Finite elements
- Coordinate relationships for triangles
- Gauss's law for elements at a vertex point
- Solution procedure and boundary conditions
- Electrostatics in cylindrical coordinates
- Exercises
- Chapter 3. Minimum-Energy Principles in Electrostatics
- Introduction
- Electrostatic field energy
- Elements of the calculus of variations
- Poisson equation as a condition of minimum energy
- Finite-element equations for two-dimensional electrostatics
- Three-dimensional finite-element electrostatics on arbitrary
meshes
- Higher-order finite element formulations
- Exercises
- Chapter 4. Finite-Difference Solutions and Regular Meshes
- Introduction
- Difference operators
- Initial value solutions of ordinary differential equations
- One-dimensional Poisson equation
- Solution of the Poisson equation by back-substitution
- Two-dimensional electrostatic solutions on a regular mesh
- Three-dimensional electrostatic solutions on a regular mesh
- Exercises
- Chapter 5. Techniques for Numerical Field Solutions
- Introduction
- Regular meshes in three dimensions
- Two-dimensional conformal triangular meshes
- Fitting triangular elements to physical boundaries
- Neumann boundaries in resistive media
- Boundary value solutions by successive over-relaxation
- Exercises
- Chapter 6. Matrix Methods for Field Solutions
- Introduction
- Gauss-Jordan elimination
- Solving tridiagonal matrices
- Matrix solutions for one-dimensional electrostatics
- Matrices for two-dimensional finite-element solutions
- Solving tridiagonal block matrix problems
- Exercises
- Chapter 7. Analyzing Numerical Solutions
- Introduction
- Locating elements
- Generalized least-square fits
- Field calculations on a two-dimensional triangular mesh
- Mesh and boundary plots
- Contour, element, elevation, and field line plots
- Exercises
- Chapter 8. Nonlinear and Anisotropic Materials
- Introduction
- Iterative solutions to boundary value problems
- Numerical data for material properties
- Finite-element equations for anisotropic materials
- Steady-state gas flow
- Exercises
- Chapter 9. Finite-Element Magnetostatic Solutions
- Introduction
- Differential and integral magnetostatic equations
- Vector potential and field equations in two dimensions
- Isotropic magnetic materials
- Finite-element magnetostatic equations
- Magnetic field solutions
- Properties of permanent magnet materials
- Magnetostatic solutions with permanent magnets
- Exercises
- Chapter 10. Static Field Analysis and Applications
- Introduction
- Volume and surface integrals on a finite-element mesh
- Electric and magnetic field energy
- Capacitance calculations
- Inductance calculations
- Electric and magnetic forces on materials
- Charged particle orbits
- Electron and ion guns
- Generalized Neumann boundaries - Hall effect devices
- Exercises
- Chapter 11. Low-Frequency Electric and Magnetic Fields
- Introduction
- Maxwell equations
- Complex numbers for harmonic quantities
- Electric field equations in resistive media
- Electric field solutions with complex number potentials
- Magnetic fields with eddy currents
- Exercises
- Chapter 12. Thermal Transport and Magnetic Field Diffusion
- Introduction
- Thermal transport equation
- Finite-difference solution of the diffusion equation
- Finite-element diffusion solutions
- Instabilities in finite-element diffusion solutions
- Magnetic field diffusion
- Exercises
- Chapter 13. Electromagnetic Fields in One Dimension
- Introduction
- Planar Electromagnetic waves
- Time-domain electromagnetism in one dimension
- Electromagnetic pulse solutions
- Frequency-domain equations
- Scattering solutions
- One-dimensional resonant modes
- Exercises
- Chapter 14. Two- and Three-Dimensional Electromagnetic
Simulations
- Introduction
- Time-domain equations on a conformal mesh
- Electromagnetic pulse solutions
- Frequency-domain equations
- Methods for scattering solutions
- Waveguides and resonant cavities
- Power losses and Q factors
- Finite-difference time-domain method in three dimensions
- Three-dimensional element-based time-domain equations
- Exercises
- Index
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CRC Catalog Number: 1668
December 1997, c. 448 pp., 6x9, ISBN: 0-8493-1668-5
$119.95
