Finite-difference time-domain/Landau-Lifshitz-Gilbert algorithm for modeling ferrites with hysteresis

The finite-difference time-domain (FDTD) method is a simple, robust tool for a variety of electromagnetic modeling scenarios. In order to model magnetic ferrite materials, the FDTD method is coupled with the Landau-Lifshitz-Gilbert (LLG) equation. The LLG equation is discretized by defining a magnetization vector at the center of each cell. The update at each time step then proceeds by (1) update the electric field with Ampere´s law, (2) update the magnetic flux density with Faraday´s law, (3) interpolate the magnetic field to the cell centers, (4) update the magnetization vector with the LLG equation, (5) interpolate the magnetization to the magnetic field locations on the Yee FDTD staggered grid, (6) update the magnetic field using B = μ₀ (H + M) where B is the magnetic flux density, μ₀ is the permeability of free space, H is the magnetic field, and M is the magnetization.