Preconditioning bandgap eigenvalue problems in three-dimensional photonic crystals simulations

Tsung Ming Huang, Wei Jen Chang, Yin Liang Huang, Wen-Wei Lin, Wei Cheng Wang, Weichung Wang*

*Corresponding author for this work

研究成果: Article同行評審

11 引文 斯高帕斯(Scopus)

摘要

To explore band structures of three-dimensional photonic crystals numerically, we need to solve the eigenvalue problems derived from the governing Maxwell equations. The solutions of these eigenvalue problems cannot be computed effectively unless a suitable combination of eigenvalue solver and preconditioner is chosen. Taking eigenvalue problems due to Yee's scheme as examples, we propose using Krylov-Schur method and Jacobi-Davidson method to solve the resulting eigenvalue problems. For preconditioning, we derive several novel preconditioning schemes based on various preconditioners, including a preconditioner that can be solved by Fast Fourier Transform efficiently. We then conduct intensive numerical experiments for various combinations of eigenvalue solvers and preconditioning schemes. We find that the Krylov-Schur method associated with the Fast Fourier Transform based preconditioner is very efficient. It remarkably outperforms all other eigenvalue solvers with common preconditioners like Jacobi, Symmetric Successive Over Relaxation, and incomplete factorizations. This promising solver can benefit applications like photonic crystal structure optimization.

原文English
頁(從 - 到)8684-8703
頁數20
期刊Journal of Computational Physics
229
發行號23
DOIs
出版狀態Published - 1 一月 2010

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