LOD Homogenization of Multiscale Eddy Current Problem in Time Domain

Abstract

Devices fabricated from Soft Magnetic Composites (SMCs) are gaining popularity in research and application. The multiscale characteristics require special attention. Solving the quasi-statics Maxwell's equations on such devices consumes huge time and memory if the granular scale of SMCs is resolved. We have proposed a Localized Orthogonal Decomposition (LOD) homogenization strategy which allows us to compute the problem on a middle scale while retrieving the material dimension. The LOD projector has a localization property so that it can be accurately approximated on a local patch. In this work, we explore the localization characteristic further to show that the projector can be reused at different time steps. The requirement for computational time and memory can be greatly reduced. A numerical example in two dimensions is provided to show the feasibility and advantage of this approach. This technique is applied to a domain of SMCs with randomly distributed polygon-shaped granules. Finally, error analysis is provided to show the validation of the LOD projector.