Modeling and Numerical Methods for the Study of Nonlinear Electromagnetic Problems

Abstract

The main objective of the PhD thesis is the study of mathematical problems that arise in low frequency electromagnetics, mainly oriented to the numerical simulation of industrial processes. Specifically, we focus on both eddy currents and transient magnetic problems. In Part I, we first perform the mathematical and numerical analysis of a 3D harmonic formulation with sources given in terms of the current through or the potential drop on surfaces located at the domain boundary, and then we describe a finite element method for the numerical simulation of magnetization processes in ferromagnetic pieces presenting hysteresis. In Part II we deal with problems related to electrical machines. Firstly, we perform the mathematical analysis of a basic transient magnetic formulation, next next we study an optimal control problem on a synchronous machine, and we finally present a novel method for accelerating the steady-state computation in induction motors with squirrel-cage rotor.