Hierarchical Multilevel Surrogate Model Based on POD Combined With RBF Interpolation of Nonlinear Magnetostatic FE Model

From solutions of finite element (FE) simulations depending on parameters, a surrogate model of the FE solution can be built based on the proper orthogonal decomposition (POD) combined with the radial basis functions (RBFs) interpolation. Then, a fast approximation of an FE solution can be computed for any parameter set. In order to optimize the number of FE solutions required for the construction of the surrogate model and to control the error between the FE and surrogate models, a hierarchical multilevel approach based on an iterative algorithm is investigated. In this article, a hierarchical multilevel (H-POD-RBF) approach is developed for a nonlinear magnetostatic problem. In terms of application, a 3-D three-phase inductance is considered. The results obtained from the surrogate model are compared with those given from the FE model for a current or voltage supply.