Mathematical Models for Eddy Currents and Magnetostatics : With Selected Applications

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. - Springer eBooks. - Printed edition: 9789400702011