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.





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