Touzani R., Rappaz J. Mathematical Models for Eddy Currents and Magnetostatics: With Selected Applications

Springer, 2014. — 309 p. — Scientifi c Computation. — ISBN: 978-94-007-0202-8.This monograph addresses fundamental aspects of mathematical modeling and numerical solution methods of electromagnetic problems involving low frequencies, i.e. magnetostatic and eddy current problems which are rarely presented in the applied mathematics literature. In the first part, the authors introduce the mathematical models in a realistic context in view of their use for industrial applications. Several geometric configurations of electric conductors leading to different mathematical models are carefully derived and analyzed, and numerical methods for the solution of the obtained problems are given. Related issues such as convergence of the approximations and error estimates are discussed. The second part of the monograph presents various coupled problems that involve eddy current or magnetostatic problems, in particular magneto-hydrodynamic problems and magnetic shaping problems concerning the melt flow of electrically conducting metals, induction heating processes, inductively coupled plasmas and ferromagnetic screening modeling. The presentation of each model comes with numerical illustration from industrial applications.Mathematical Framework
Maxwell and Eddy Current Equations
Two-Dimensional Models
Three-Dimensional Models
Axisymmetric Models
Eddy Current Models with Thin Inductors
Numerical Methods
Induction Heating Processes
Magnetohydrodynamics and Magnetic Shaping
Inductively Coupled Plasma Torches
Ferromagnetic Shielding
The Electrolytic Process for Aluminium Production