Modified edge finite elements for photonic crystals

Daniele Boffi, Matteo Conforti, Lucia Gastaldi

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We consider Maxwell's equations with periodic coefficients as it is usually done for the modeling of photonic crystals. Using Bloch/Floquet theory, the problem reduces in a standard way to a modification of the Maxwell cavity eigenproblem with periodic boundary conditions. Following [8], a modification of edge finite elements is considered for the approximation of the band gap. The method can be used with meshes of tetrahedrons or parallelepipeds. A rigorous analysis of convergence is presented, together with some preliminary numerical results in 2D, which fully confirm the robustness of the method. The analysis uses well established results on the discrete compactness for edge elements, together with new sharper interpolation estimates. © Springer-Verlag 2006.
Original languageEnglish (US)
Pages (from-to)249-266
Number of pages18
JournalNumerische Mathematik
Volume105
Issue number2
DOIs
StatePublished - Dec 1 2006
Externally publishedYes

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