Integral Methods in Low-Frequency Electromagnetics
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More About This Title Integral Methods in Low-Frequency Electromagnetics


A modern presentation of integral methods in low-frequency electromagnetics

This book provides state-of-the-art knowledge on integral methods in low-frequency electromagnetics. Blending theory with numerous examples, it introduces key aspects of the integral methods used in engineering as a powerful alternative to PDE-based models. Readers will get complete coverage of:

  • The electromagnetic field and its basic characteristics

  • An overview of solution methods

  • Solutions of electromagnetic fields by integral expressions

  • Integral and integrodifferential methods

  • Indirect solutions of electromagnetic fields by the boundary element method

  • Integral equations in the solution of selected coupled problems

  • Numerical methods for integral equations

All computations presented in the book are done by means of the authors' own codes, and a significant amount of their own results is included. At the book's end, they also discuss novel integral techniques of a higher order of accuracy, which are representative of the future of this rapidly advancing field.

Integral Methods in Low-Frequency Electromagnetics is of immense interest to members of the electrical engineering and applied mathematics communities, ranging from graduate students and PhD candidates to researchers in academia and practitioners in industry.


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.



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.


Topic Index.