Mathematical Models for Eddy Currents and Magnetostatics

Part I Eddy Current Models.- Mathematical framework.- Introduction.- Preliminaries.- The Three-Dimensional Case.- The Two-Dimensional Case.- Maxwell and eddy current equations.- Introduction.- Maxwell equations.- Low frequency approximation.- Static cases.- Time{Harmonic Regime.- Eddy Current Equations.- Two-dimensional models.- Introduction.- A solenoidal two-dimensional model.- A transversal model.- Three-dimensional models.- A current density formulation.- A magnetic field formulation.- An electric field model.- Axisymmetric models.- Axisymmetric setting.- A magnetic field model.- A scalar potential model.- Eddy current models with thin inductors.- The two-dimensional solenoidal model.- The two-dimensional transversal model.- Three-dimensional models.- Numerical Methods.- Introduction and main notations.- Standard (H1) finite element method.- A finite element method for the 2-D solenoidal model.- Finite elements for the axisymmetric model.- Finite elements in H(curl){spaces.- Finite elements in H(div){spaces.- The boundary element method for boundary integral equations.- Approximation of a domain integral equation.- Coupled finite element/boundary element methods.- Part II Selected Applications.- Induction Heating Processes.- A mathematical model.- Bibliographical comments.- A 2-D stationary problem.- A 2-D time dependent problem.- Numerical experiments.- An optimal control problem.- Magnetohydrodynamics and Magnetic Shaping.- Incompressible Magnetohydrodynamics.- Eddy current free boundary problems.- An Electromagnetic Casting problem.- Inductively coupled plasma torches.- The model.- Numerical approximation.- A numerical simulation.- Ferromagnetic Shielding.- Mathematical analysis.- An iterative procedure.- Solution of the linear problem by a domain decomposition method.- An iterative procedure for the discrete nonlinear problem.- Numerical results.- The electrolytic process for aluminium production.-Introduction.- The model.- Numerical approximation.- Numerical results.- Mathematical Symbols.- References.- Index