Optimal Segmentation of Three-Dimensional Permanent-Magnet Assemblies

The optimal design of permanent-magnet systems is crucial for applications such as electric motors and generators, accelerator magnets, and MRI scanners. One challenge in achieving best performance is to compute the optimal segmentation into uniformly magnetized blocks, but typical numerical techniques cannot handle three-dimensional (3D) problems. The authors demonstrate a versatile analytical method, using a surprising connection to the problem of tessellating a 2D spherical surface to study 3D problems. This insight is of interest beyond the development of permanent magnets, bringing geometric methods to bear on a widely studied problem in magnetostatics.