標題: Matrix representation of the double-curl operator for simulating three dimensional photonic crystals
作者: Huang, Tsung-Ming
Hsieh, Han-En
Lin, Wen-Wei
Wang, Weichung
應用數學系
Department of Applied Mathematics
關鍵字: Photonic crystals;Face centered cubic lattice;The Maxwell equations;Yee's scheme;Double-curl operator;Matrix representation
公開日期: 1-七月-2013
摘要: Three dimensional photonic crystals can be modeled by the Maxwell equations as a generalized eigenvalue problem (GEVP). Simulations based on the numerical solutions of the GEVP are used to reveal physical properties and boost innovative applications of photonic crystals. However, to solve these GEVP remains a computational challenge in both timing and accuracy. The GEVP corresponding to the photonic crystals with face centered cubic (FCC) lattice is one of the challenging eigenvalue problems. From a viewpoint of matrix computation, we demonstrate how such obstacles can be overcome. Our main contribution is an explicit matrix representation of the double-curl operator associated with the photonic crystal with FCC lattice. This particular matrix represents the degenerate coefficient matrix of the discrete GEVP obtained by Yee's scheme. The explicit matrix leads to an eigendecomposition of the degenerate coefficient matrix and then a fast eigenvalue solver. Promising numerical results in terms of timing and accuracy are reported for solving the discrete GEVP arising in three dimensional photonic crystals with various geometric parameters. (C) 2012 Elsevier Ltd. All rights reserved.
URI: http://dx.doi.org/10.1016/j.mcm.2012.11.008
http://hdl.handle.net/11536/22256
ISSN: 0895-7177
DOI: 10.1016/j.mcm.2012.11.008
期刊: MATHEMATICAL AND COMPUTER MODELLING
Volume: 58
Issue: 1-2
起始頁: 379
結束頁: 392
顯示於類別:期刊論文


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  1. 000320601000039.pdf