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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.

Eddy currents (Electric) --- Harmonic analysis. --- Time-series analysis. --- Mathematical models. --- Eddy currents (Electric) -- Mathematical models. --- Mathematics. --- Computer mathematics. --- Physics. --- Applied mathematics. --- Engineering mathematics. --- Computational Science and Engineering. --- Numerical and Computational Physics. --- Appl.Mathematics/Computational Methods of Engineering. --- Analysis of time series --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Probabilities --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Electric currents --- Computer science. --- Numerical and Computational Physics, Simulation. --- Mathematical and Computational Engineering. --- Engineering --- Engineering analysis --- Informatics --- Science --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Computer mathematics --- Electronic data processing