Abstract 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.

中文翻译：

---

应用于 3D 微磁解算器的自适应几何积分

摘要 本文通过求解 Landau-Lifshitz-Gilbert (LLG) 方程，提出了一种 GPU 并行化 3D 微磁代码，用于有效计算磁性纳米结构的磁化动力学、平衡配置和静态磁滞回线。LLG 方程的时间积分是通过使用基于凯莱变换的技术进行的，这使我们能够满足对磁化幅度的约束。计算域用结构化的六面体网格重建。静磁场的空间积分是通过快速傅立叶变换 (FFT) 算法执行的，交换场是使用基于 26 节点的有限差分技术计算的。还通过与 OOMMF 和 MuMax3 的比较，对开发的求解器进行了仔细验证。然后，