Fast Lanczos Eigenvalue Solvers for Band Structures of Three Dimensional Photonic Crystals with Face-Centered Cubic Lattice

Content Provider	Semantic Scholar
Author	Huang, Tsung-Ming Hsieh, Han-En Lin, Wen-Wei Wang, Weichung
Copyright Year	2012
Abstract	To numerically determine the band structure of three-dimensional photonic crystals with face-centered cubic lattices, we study how the associated large-scale eigenvalue problems can be solved efficiently. Due to the complexity of the coefficient matrix and the fact that the desired eigenvalues are interior, a standard shift-and-invert Lanczos method (SILM) is usually not efficient. We first propose a new preconditioning scheme to accelerate the standard SILM. In addition, we consider the inverse projective Lanczos method (IPLM) that was proposed recently. The two approaches are compared theoretically and numerically. Our study suggests that the IPLM outperforms the accelerated SILM in timing and robustness. The IPLM is fast and promises to play an essential role in simulating photonic crystals.
File Format	PDF HTM / HTML
Alternate Webpage(s)	http://www.math.cts.nthu.edu.tw/download.php?dir=publish&filename=707_da9bb19e.pdf&title=prep2013-03-003
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article