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Two-dimensional finite-element solutions for charged-particle devices Finite-element Methods for Electromagnetics

Stanley Humphries
Professor Emeritus
University of New Mexico


Welcome to the Finite-element Methods for Electromagnetics download site. The text was originally published under the title Field Solutions on Computers (ISBN 0-8493-1668-5, QC760.54.H86) in 1997 by CRC Press (currently a division of Taylor and Francis). The unabridged book with all illustrations has been converted to PDF format with several corrections. Composition of the original work was partially supported by a sabbtical leave from the University of New Mexico. Taylor and Francis generously gave permission to create and to distribute the electronic text. The conversion was supported by Field Precision LLC. Please send any comments to humphriess@fieldp.com.

-Stan Humphries



Description

Finite-element Methods for Electromagnetics 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 167 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 plotting routines.




Restrictions

The copyright of the electronic document (U.S. TX 7-175-613) is held by Stanley Humphries, Jr. The author grants all persons the right to download a single copy of the book in digital format for their personal use. A single copy of the book or selected pages may be made using print features of PDF readers for personal use. Other modes of reproduction, translation and distribution of any part of this work are unlawful. The PDF file may not be distributed to other individuals or posted on the Internet for download. Extracts from the book may not be used in other works without permission from the author.

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Table of contents

Chapter 1. Introduction
Overview
Summary of material
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