The subregion method in magnetic field analysis and design optimization

A method that subdivides the finite element solution region into subregions is introduced for the efficient synthesis of magnetic devices. The coefficient matrices of the different subregions are assembled separately and reduced only to those degrees of freedom that are associated with the nodes at subregion interfaces. The reduced matrices of all subregions are used to assemble the final global matrix, which is solved for the reduced system. It is in this repeated analysis of similar field problems that the subregion method is applied with significant computational savings: in synthesis only those subregions that enclose changes in the design have to be assembled and reduced for the modified design. Thus, the computational effort for reanalysis is reduced to the area of design modifications. The subregion approach is successfully applied to the procedure of device synthesis, where a large number of field computations is required in the iterative search for the optimal design. The subregion method is extended to the calculation of the potential gradient directly from the finite element equations