TY - JOUR
T1 - Modified edge finite elements for photonic crystals
AU - Boffi, Daniele
AU - Conforti, Matteo
AU - Gastaldi, Lucia
N1 - Generated from Scopus record by KAUST IRTS on 2020-05-05
PY - 2006/12/1
Y1 - 2006/12/1
N2 - 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.
AB - 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.
UR - http://link.springer.com/10.1007/s00211-006-0037-y
UR - http://www.scopus.com/inward/record.url?scp=33751184170&partnerID=8YFLogxK
U2 - 10.1007/s00211-006-0037-y
DO - 10.1007/s00211-006-0037-y
M3 - Article
SN - 0029-599X
VL - 105
SP - 249
EP - 266
JO - Numerische Mathematik
JF - Numerische Mathematik
IS - 2
ER -