This work is concerned with the important connection that exists between micromagnetism and high frequency electromagnetism. As micromagnetic solvers have become important tools in the study and engineering of magnetic devices, and as these devices are increasingly operated at high frequencies, it is important to understand both how micromagnetic simulations can be used in the modeling of magnetic materials for high-frequency applications and how micromagnetic models can be impacted by high-frequency electromagnetic effects.

After an introduction to the theory behind micromagnetism and micromagnetic solvers, the dissertation is divided into two main themes. The first one is the modeling and characterization through micromagnetic simulations of ferromagnetic materials for high frequency applications. A particular class of materials, namely ferromagnetic nano-granular materials, are studied since they have important technological applications as soft magnetic materials which also exhibit high saturation magnetizations and low electrical resistivities. The extraction of properties such as the hysteresis loop and frequency dependent permeability tensor from micromagnetic simulations is examined. Also, the anisotropy averaging mechanism responsible for the soft magnetic properties of this class of materials is studied and some theoretical results are obtained and presented, such as a derivation of the residual exchange energy between groups of exchange coupled nano-particles and a generalized Stoner-Wohlfarth hysteresis model which accounts for exchange interactions between ferromagnetic particles with random uniaxial anisotropies.

The second theme is the modeling of eddy currents in micromagnetic simulations. Eddy currents, also known as Foucault currents, arise in conductive materials due to rapid variations of the magnetic field and magnetization. A method coupling the Landau-Lifshitz-Gilbert equation of micromagnetics with the magnetoquasistatic Maxwell equations is presented. Based on this method, two coupled micromagnetic-electromagnetic solvers are presented, one based on an integral equation formulation, the other based on the finite element method. A test problem with a known analytical solution is suggested and used to validate the implemented solvers. Also, results concerning the bounds of validity for the magnetostatic approximation to theMaxwell equations, in which case eddy currents are neglected, as well as for the magnetoquasistatic Maxwell equations, where eddy currents are accounted for but electromagnetic wave propagation is neglected, are given. It is found that the magnetoquasistatic approximation is excellent for the vast majority of micromagnetic simulations that are executed today.