Coupled Finite-Element Micromagnetic—Integral Equation Electromagnetic Simulator for Modeling Magnetization—Eddy Currents Dynamics

Abstract

A formulation for coupled Landau–Lifshitz–Gilbert (LLG) and magnetoquasistatic Maxwell equations (MEs) is reported. The formulation has no approximations apart from neglecting the displacement current, i.e., the magnetoquasistatic approximation, and is applicable for describing a broad range of magnetization and electromagnetic phenomena. The formulation is based on two parallel solvers: one for the non-linear LLG equation and the other for the MEs. These solvers are coupled at the computation of the magnetic field, which occurs during the process of solving the two equations. Solving the LLG equation is done through an implicit time integration scheme, and solving the MEs is done through a time-domain integral equations’ formulation. The framework was implemented as a part of the high-performance micromagnetic simulator FastMag, and it allows modeling magnetization and electromagnetic dynamics effects in highly complex magnetic materials and devices. Numerical results obtained for a test problem are compared with a known analytical solution to validate the solver and illustrate the interactions between eddy currents and magnetization dynamics. Moreover, simulation results for a non-linear problem, namely, the switching of a ferromagnetic disk, are presented, which illustrate the role that eddy currents can play in magnetization dynamics.