Exploring the boundary element method for optimization-based machine design

To meet demands for ever greater efficiency and torque-density, the design of electric machinery through optimization techniques is increasingly common. Such approaches may involve the evaluation of millions of candidate designs and therefore their rapid assessment is paramount. Such emphasis on computational performance is problematic for modern machine design in which many cutting-edge topologies rely on the Finite Element Method (FEM) for evaluation. The Boundary Element Method (BEM) is an alternative numerical technique for solving partial differential equations that avoids the main computational expense of the FEM: one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated numerically to populate the full system matrix. Recently, however, the need for numerical integration was eliminated for the 2-D Galerkin BEM, greatly enhancing its computational performance with no trade-off in accuracy, and a toolbox was developed including these gains. The performance of the BEM toolbox is compared with a similar implementation of the FEM, in which it is shown that the computation time of the BEM from meshing through post-processing is two orders of magnitude less than that needed just to generate the FEM mesh. Finally, the BEM toolbox is employed to analyze a wound rotor synchronous machine design, and the results are validated with commercial software. The path to realizing the BEM as a valuable tool in the machine design toolbox is discussed.