LOD-Homogenization of Multiscale Eddy Current Problem in Time Domain

Xiaotao Ren, Antti Hannukainen, Anouar Belahcen*, Yves Perriard

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review


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.

Original languageEnglish
Article number6302004
Number of pages4
JournalIEEE Transactions on Magnetics
Issue number6
Early online dateApr 2021
Publication statusPublished - Jun 2021
MoE publication typeA1 Journal article-refereed


  • Computational modeling
  • Eddy current problem
  • Eddy currents
  • Electric potential
  • Finite Element Method
  • homogenization
  • Magnetic domains
  • multiscale
  • Numerical models
  • orthogonal function space
  • Soft magnetic materials
  • Time-domain analysis


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