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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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Finite-element Methods for Electromagnetics (9.4 MB).
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
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