MOR for the MSFEM of the Eddy Current Problem in Linear Laminated Media

Abstract

The simulation of the eddy currents in electrical devices with the finite element method (FEM) is satisfactory. However, the large systems to be solved result in high computational costs, i.e. memory requirement and computation time. Although the multiscale finite element method (MSFEM) can be exploited to simulate eddy currents in laminted iron more efficiently the complexity of the problems are still too large to solve them conveniently. The computational costs are a multiple of the costs of anisotropic models in brute force methods according to the components used in the multiscale formulation, compare with Hollaus and Schöberl (2017). Model order reduction (MOR) has proven to be a powerful methodology to reduce the costs and is well established for linear problems. MOR with proper orthogonal decompsition (POD) has been applied to solve large scale linear problems in computational electromagnetics very successful. Strategies to select an optimal number of snapshots except those with the largest singular values can be found in Sato and Igarashi (2013) and Klis et al. (2016).