Accurate magnetization modeling in multi-dimensional applications

Many natural substances in nature exhibit magnetism, which has a significant impact on human life. However, accurately predicting, analyzing, and manipulating magnetic fields requires the use of precise mathematical simulation techniques. One such method is numerical modeling with element matrices, which is crucial for simulating and analyzing complex physical models. In conventional mesh-based modeling, there is always a residual error, and the accuracy of the solution can be greatly affected by the mesh density. This work proposed a new numerical modeling theory for the field of magnetics, which is based on specially designed points within an element. With this new computational framework, the mesh-dependence feature of the element matrix can be significantly reduced, allowing for more efficient convergence to the theoretical value with minimal differences. This method can handle a wide range of extreme physical conditions in both three-dimensional and two-dimensional scenarios, which are beyond the capabilities of conventional methods, and can provide highly accurate computational solutions. The proposed method is demonstrated through the passive shielding design of a 9.4 T whole-body magnetic resonance imaging superconducting magnet, and the concept design of an extremely weak magnetic field scientific facility with cross-scale geometry was exemplified by the proposed method.