Model Order Reduction Algorithms in the Design of Electric Machines

Abstract

Although model order reduction techniques based on searching for a solution in a low-rank subspace are researched well for the case of linear differential equations, it is still questionable if such model order reduction techniques would work well for nonlinear PDEs. In this work, model order reduction via POD-DEIM (Proper Orthogonal Decomposition via Discrete Empirical Interpolation) method is applied to a particular nonlinear parametric PDE that is used for the modeling of electric machines. The idea of the POD-DEIM algorithm is to use statistical data about ‘typical solutions’ that correspond to ‘typical’ parameter values, to approximate solutions for other parameter values. Practical POD-DEIM application to the particular PDE has met a number of difficulties, and several improvements to the selection of initial approximation, selection of interpolation nodes, selection of interpolation basis and handling moving physical entities were made to make the method to work. These improvements, along with some numerical experiments, are presented.