A two-dimensional time-domain finite element formulation for periodic structures

L. E.Rickard Petersson, Jian Ming Jin

Research output: Contribution to journalArticlepeer-review


A formulation is presented for a two-dimensional time-domain finite-element method (FEM-TD) that incorporates periodic boundaries. The specifics of the method are shown for scattering problems, but it should be straightforward to extend it to radiation problems. The method solves for a transformed field variable (instead of solving directly for the electric field) in order to easily enable periodic boundary conditions in the time domain. The accuracy and stability of the method is demonstrated by a series of examples where the new formulation is compared with reference solutions. Very accurate results are obtained when the excitation (frequency range) and the geometry are such that no higher order Floquet modes are present. The accuracy is degraded in the presence of higher order modes due to the rather simple absorbing boundary condition that is used with the present formulation. The method is found to be stable even for angles of incidence close to grazing.

Original languageEnglish (US)
Pages (from-to)1480-1488
Number of pages9
JournalIEEE Transactions on Antennas and Propagation
Issue number4
StatePublished - Apr 2005


  • Electromagnetic scattering by periodic structures
  • Finite element methods
  • Time domain analysis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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