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

List of Contents

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