Adaptive geometric integration applied to a 3D micromagnetic solver

This paper presents a GPU-parallelized 3D micromagnetic code for the efficient calculation of the magnetization dynamics, equilibrium configuration and static hysteresis loops of magnetic nanostructures, by solving the Landau-Lifshitz-Gilbert (LLG) equation. The time-integration of the LLG equation is carried out by using a technique based on the Cayley transform, which allows us to fulfil the constraint on the magnetization amplitude. The computational domain is reconstructed with a structured hexahedral mesh. The spatial-integration of the magnetostatic field is performed via a Fast Fourier Transform (FFT) algorithm, and the exchange field is computed with a 26-node-based finite difference technique. A careful validation of the developed solver was carried out, also by comparison to OOMMF and MuMax3. Then, we analysed the computational efficiency of the geometrical time-integrator and of its time-adaptive variant, investigating the role of the numerical damping introduced by the Cayley transform-based time-discretization.