Accelerating algorithm of micromagnetic simulation by interpolating magnetization vectors

It is widely known that coercivity of permanent magnets depends on crystal grain size, temperature, the properties of grain boundaries, and so on. Nevertheless, the detailed mechanism has not been well understood. Recently, micromagnetic simulation attracts much attention to elucidate the coercivity mechanism of permanent magnets
¹
. However, to avoid creating “artificial pinning” in the simulation, the edge length of numerical mesh elements has to be smaller than the exchange length (1.7 nm in Nd-Fe-B phase)
²
. On the other hand, typical grain size of sintered Nd-Fe-B magnets is measured from 100 nm to 10 μm. To simulate the pinning and nucleation process in the realistic grain structures, therefore, the number of finite elements involved in the numerical calculations exceeds millions. This means that realistic micromagnetic simulation takes an immense amount of time. This is a great issue to be resolved in micromagnetics, since even large-scale simulation should be completed within a practical period of time. To realize such calculations, there are two possible approaches: one is the improvement of the calculation speed itself, and the other is the reduction of the number of mesh elements. In this study, we focused our attention on the latter. Reduction of the number of mesh elements correspond to increase of the mesh size. However, as previously mentioned, it is difficult to simply increase the mesh size beyond the exchange length while dealing with domain walls precisely. Thus, a method which can treat a domain wall accurately even with large mesh elements is eagerly desired to solve such a problem and to accelerate numerical studies of various types of magnets. Here, we discussed how to treat a domain wall accurately with large mesh size.