Numerische Mathematik

, Volume 105, Issue 2, pp 249–266

Modified edge finite elements for photonic crystals

Authors

    • Dipartimento di Matematica “F. Casorati”Università di Pavia
  • Matteo Conforti
    • Dipartimento di MatematicaUniversità di Brescia
  • Lucia Gastaldi
    • Dipartimento di MatematicaUniversità di Brescia
Article

DOI: 10.1007/s00211-006-0037-y

Cite this article as:
Boffi, D., Conforti, M. & Gastaldi, L. Numer. Math. (2006) 105: 249. doi:10.1007/s00211-006-0037-y

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.

Mathematics Subject Classification

65N3065N2535Q6078M10

Copyright information

© Springer-Verlag 2006