Integral Methods in Low-Frequency Electromagnetics

Ivo Dolezel is Full Professor at the Czech Technical University (CTU) in Prague and Senior Researcher at the Institute of Thermomechanics of the Academy of Sciences of the Czech Republic. His professional interests are in the numerical simulation of electromagnetic fields with particular emphasis on power applications, coupled problems, special electrical machines, and electromagnetic compatibility. Pavel Karban is Assistant Professor at the Department of Theory of Electrical Engineering at the University of West Bohemia in Pilsen. His research interests include computational electromagnetics, particularly differential and integral models of low-frequency magnetic fields and coupled problems. Pavel Solin is Associate Professor at the University of Nevada, Reno, and Senior Researcher at the Institute of Thermomechanics of the Academy of Sciences of the Czech Republic, Prague. His professional interests are aimed at modern adaptive higher-order finite element methods (hp-FEM) and higher-order methods for integral equations, with applications to multi-scale multi-physics-coupled problems in various areas of engineering and science.

List of Figures. List of Tables.

Preface.

Acknowledgments.

1 Electromagnetic Field and their Basic Characteristics.

1.1 Fundamentals.

1.2 Potentials.

1.3 Mathematical models of electromagnetic fields.

1.4 Energy and forces in electromagnetic fields.

1.5 Power balance in electromagnetic fields. 

2 Overview of Solution Methods.

2.1 Continuous models in electromagnetism.

2.2 Methods of solution of the continuous models.

2.3 Classification of the analytical methods.

2.4 Numerical methods and their classification.

2.5 Differential methods.

2.6 Finite element method.

2.7 Integral and integrodifferential methods.

2.8 Important mathematical aspects of numerical methods.

2.9 Numerical schemes for parabolic equations.

3 Solution of Electromagnetic Fields by Integral Expressions.

3.1 Introduction.

3.2 1D integration area.

3.3 2D integration area.

3.4 Forces acting in the system of long massive conductors.

3.5 3D integration area.

4 Integral and Integrodifferential Methods.

4.1 Integral versus differential models.

4.2 Theoretical foundations.

4.3 Static and harmonic problems in one dimension.

4.4 Static and harmonic problems in two dimensions.

4.5 Static problems in three dimensions.

4.6 Time-dependent eddy current problems in one dimension and two dimensions.

4.7 Static and 2D eddy current problems with motion.

5 Indirect Solution of Electromagnetic Fields by the Boundary Element Method.

5.1 Introduction.

5.2 BEM-based solution of differential equations.

5.3 Problems with 1D integration area.

6 Integral Equations in Solution of Selected Coupled Problems.

6.1 Continual induction heating of nonferrous cylindrical bodies.

6.2 Induction heating of a long nonmagnetic cylindrical billet rotating in uniform magnetic field.

6.3 Pulsed Induction Accelerator.

7 Numerical Methods for Integral Equations.

7.1 Introduction.

7.2 Collocation methods.

7.3 Galerkin methods.

7.4 Numerical example.

Appendix A: Basic Mathematical Tools.

A.1 Vectors, matrices, systems of linear equations.

A.2 Vector analysis.

Appendix B: Special Functions.

B.1 Bessel functions.

B.2 Elliptic integrals.

B.3 Special polynomials.

Appendix C: Integration Techniques.

C.1 Analytical calculations of some integrals over typical elements.

C.2 Techniques of numerical integration.

References.

Topic Index.