DocumentCode :
1428921
Title :
Calculating the Band Structure of Photonic Crystals Through the Meshless Local Petrov-Galerkin (MLPG) Method and Periodic Shape Functions
Author :
Nicomedes, Williams ; Mesquita, Renato ; Moreira, Fernando
Author_Institution :
Dept. of Electron. Eng., Fed. Univ. of Minas Gerais, Belo Horizonte, Brazil
Volume :
48
Issue :
2
fYear :
2012
Firstpage :
551
Lastpage :
554
Abstract :
This paper illustrates how to determine the bandgap structure of photonic crystals through MLPG. This method is akin to the Finite Element Method (FEM), as it also deals with the discretization of weak forms and produces sparse global matrices. The major difference is the complete absence of any kind of mesh. We concentrate in a particular version of it, the MLPG4, also known as Local Boundary Integral Equation Method (LBIE). Since the boundary conditions governing the electromagnetic field are periodic in a unit cell, we develop a special scheme to embed this feature on the shape functions used in the discretization process. As a result, boundary conditions do not need to be imposed on the unit cell.
Keywords :
Galerkin method; band structure; electromagnetic fields; electromagnetic wave propagation; finite element analysis; integral equations; photonic crystals; FEM; Finite Element Method; LBIE; Local Boundary Integral Equation Method; MLPG4; band structure; bandgap structure; boundary conditions; electromagnetic field; meshless local Petrov-Galerkin method; periodic shape functions; photonic crystals; sparse global matrices; weak form discretization; Boundary conditions; Dielectrics; Finite element methods; Indexes; Photonic crystals; Shape; Vectors; Electromagnetic wave propagation; finite element methods; integral equations; photonic crystals;
fLanguage :
English
Journal_Title :
Magnetics, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9464
Type :
jour
DOI :
10.1109/TMAG.2011.2175206
Filename :
6136753
Link To Document :
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