Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren*, Antti Hannukainen, Anouar Belahcen

*Corresponding author for this work

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A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with the help of a projection operator acting between the coarse space and a space of rapidly oscillating functions. A Helmholtz decomposition is applied to treat the null-space of the curl operator so that the projection can be locally calculated. The results are illustrated in a 2-D numerical example.

Original languageEnglish
Article number7500204
Number of pages4
JournalIEEE Transactions on Magnetics
Issue number9
Publication statusPublished - Sep 2019
MoE publication typeA1 Journal article-refereed


  • Homogenization
  • Orthogonal projection
  • Quasi-static Maxwell's equations

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