Nonlinear Interpolation on Manifold of Reduced-Order Models in Magnetodynamic Problems

The proper orthogonal decomposition (POD) is an efficient model-order reduction (MOR) technique for linear problems in computational sciences, recently gaining popularity in electromagnetics. However, its efficiency has been shown to considerably degrade for nonlinear problems. In this paper, we propose a method to reduce nonlinear magnetodynamic problems by combining POD with an interpolation on manifolds, which interpolates the reduced bases to efficiently construct the appropriate reduced model. This method, new in electromagnetics, is applied on an inductor-core system and showed good results compared with the classical MOR approaches, e.g., direct POD reduction and a standard interpolation of pre-computed reduced bases (i.e., Lagrange interpolation).