铁磁体中微波磁化率的预处理策略
A preconditioning strategy for microwave susceptibility in ferromagnets
AI总结：
针对大网格铁磁材料微波磁化率计算中的病态线性系统，提出一种结合投影与循环矩阵近似的预处理共轭梯度法。
摘要：
铁磁材料的3D数值模拟可以通过微波磁化率与实验结果进行比较。本文提出了一种针对大网格的微波磁化率优化计算方法。微波磁化率通过将Landau和Lifchitz方程在平衡态附近线性化得到，待求解的线性系统非常病态。使用正规方程的共轭梯度法（CGN方法）求解。开发了一种高效的预处理子，由投影和循环矩阵集中“精确”预处理子的近似组成。结果中展示了由于预处理导致的条件数控制以及奇异值分解的演化。
英文摘要：
3D numerical simulations of ferromagnetic materials can be compared with experimental results via microwave susceptibility. In this paper, an optimised computation of this microwave susceptibility for large meshes is proposed. The microwave susceptibility is obtained by linearisation of the Landau and Lifchitz equations near equilibrium states and the linear systems to be solved are very ill-conditionned. Solutions are computed using the Conjugate Gradient method for the Normal equation (CGN Method). An efficient preconditioner is developed consisting of a projection and an approximation of an ``exact'' preconditioner in the set of circulant matrices. Control of the condition number due to the preconditioning and evolution of the singular value decomposition are shown in the results.
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