# Numerical Computation of Electric and Magnetic Fields, 2nd ed.

## Charles W. Steele

1996

xv + 260 pages

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1996

xv + 260 pages

This new edition reports on the advances in the state-of-the-art of field computation since the book's first edition in 1987. The book provides:

- Field Properties
- Introduction
- Maxwell's Equations in the Dynamic, Quasi-Static, and Static Cases
- Polarization and Magnetization
- Laws for Static Fields in Unbounded Regions
- Integral Representations for Quasi-Static Fields Using the Helmholtz Theorem
- Equivalent Configurations
- Steady-State Dynamic Problems and Phasor Field Representations
- Continuity Conditions of Fields at a Medium Discontinuity References
- Problem Definition
- Introduction
- Field Problem Domains, Source Problem Domains, Interior Problems, and Exterior Problems
- Is the Problem Static, Quasi-Static, or Dynamic?
- What Field Is To Be Computed?
- Is the Problem Two-Dimensional or Three-Dimensional?
- The Medium
- Boundary Conditions and Uniqueness of Solutions
- References
- Linear Spaces in Field Computations
- Introduction
- Basis Functions
- Shape Functions
- Finite Elements and Shape Functions of Global Coordinates in Two-Dimensional Problem Domains
- Isoparametric Shape Functions in Two Dimensions
- Finite Elements and Shape Functions of Global Coordinates in Three-Dimensional Problem Domains
- References
- Projection Methods in Field Computations
- Introduction
- Special Spaces in Field Computations
- Operators in Field Calculations
- Approaches Used in Obtaining Approximate Solutions to Field Problems
- Finite Element Method for Interior Problems
- Integral Equation Method
- Projection Methods
- Orthogonal Projection Methods References
- Finite Element Method for Interior Problems
- Introduction
- Formulation of Finite Element Method for Interior Problems
- Computation of Linear System for Finite Element Method
- Sample Problem
- References
- Finite Element Method for Exterior Problems
- Introduction
- McDonald-Wexler Algorithm
- Silvester et al. Algorithm
- Mapping Algorithms
- References
- Automatic and Adaptive Mesh Generation
- Introduction
- Preliminary Mesh Generation
- Delaunay Tesselation
- An Algorithm for Local and Global Error Estimation
- Mesh Refinement Algorithm References
- Integral Equation Method
- Introduction
- Linear and Uniform Media in Continuity Subdomains
- Saturable, Nonlinear, and Nonuniform Media in Continuity Subdomains
- Numerical Solution of Integral Equations General Approach
- Finite Elements and Basis Functions Used in the Integral Equation Method
- Integral Equation Numerical Solution by the Collocation Method
- Integral Equation Numerical Solution by the Galerkin Method
- Numerical Integration
- Sample Problem
- References
- Static Magnetic Problem
- Introduction
- Interior Static Field Problems
- Exterior Static Problems Approximated by Interior Problems
- Exterior Magnetic Field Static Problem
- Static Magnetic Field in a Saturable Medium
- References
- Eddy Current Problem
- Introduction
- Commonly Used Basic Formulations for the Eddy Current Problem
- Two-Dimensional Eddy Current Problem
- Three-Dimensional Steady-State Eddy Current Problem
- Transient Eddy Current Problem
- References
- Derivation of the Helmholtz Theorem
- Properties of the Magnetic Vector Potential, A Proof Regarding Split of Quadrangle into Two Triangles
- Derivation of Formulations Used in the Cendes-Shenton Adaptive Mesh Algorithm
- Integral Expressions for Scalar Potential from Green' s Theorem