Optimum partitioning strategies in partitioned finite element analysis of electromechanical devices
A partitioned finite element method (PFEM) has recently been set forth and applied to the solution of magnetic fields in electromechanical systems. Therein, the solution space is divided into sub-regions that are initially solved separately. These sub-regions can be further divided creating a hierarchical solution strategy. The results are then reassembled to form the overall solution. Optimal partitioning strategies implementing the PFEM for electromechanical systems including rotation and nonlinearities are studied. Desirable choices of hierarchical tree structure, partition geometry, and leaf size are investigated. In addition, the development of reduced-dimension equations for torque and back-EMF calculations are set forth. ^ The PFEM shifts the computational expense of the FEM from the solution or field update stage to the calculation of Jacobian matrices and gradient vectors. At the same time, when only a portion of the problem domain is nonlinear, or when only limited areas involve motion, it allows for much of the computational expense of updating Jacobian matrices to be reused. In addition, reduced-dimension equations for torque and back-EMF calculations eliminate the need to solve for all but a small set of the total number of node potentials. These advantages combined result in significant reductions in computation time. Application of the PFEM to the calculation of the cogging torque and back-EMF of a permanent-magnet synchronous machine resulted in a greater than 10-fold reduction in computation time with no reduction in accuracy as compared to the conventional FEM.^
Oleg Wasynczuk, Purdue University.
Engineering, Electronics and Electrical|Physics, Electricity and Magnetism