Structure-Preserving Methods for Computing Complex Band Structures of Three Dimensional Photonic Crystals

Tsung Ming Huang, Tiexiang Li*, Jia Wei Lin, Wen Wei Lin, Heng Tian

*此作品的通信作者

研究成果: 雜誌貢獻期刊論文同行評審

2 引文 斯高帕斯(Scopus)

摘要

This work is devoted to the numerical computation of complex band structure k= k(ω) ∈ C3, with ω being positive frequencies, of three dimensional isotropic dispersive or non-dispersive photonic crystals from the perspective of structured quadratic eigenvalue problems (QEPs). Our basic strategy is to fix two degrees of freedom in k and to view the remaining one as the eigenvalue of a complex gyroscopic QEP which stems from Maxwell’s equations discretized by Yee’s scheme. We reformulate this gyroscopic QEP into a ⊤-palindromic QEP, which is further transformed into a structured generalized eigenvalue problem for which we have established a structure-preserving shift-and-invert Arnoldi algorithm. Moreover, to accelerate the inner iterations of the shift-and-invert Arnoldi algorithm, we propose an efficient preconditioner which makes most of the fast Fourier transforms. The advantage of our method is discussed in detail and corroborated by several numerical results.

原文英語
文章編號35
期刊Journal of Scientific Computing
83
發行號2
DOIs
出版狀態已發佈 - 2020 5月 1

ASJC Scopus subject areas

  • 軟體
  • 理論電腦科學
  • 數值分析
  • 一般工程
  • 計算機理論與數學
  • 計算數學
  • 應用數學

指紋

深入研究「Structure-Preserving Methods for Computing Complex Band Structures of Three Dimensional Photonic Crystals」主題。共同形成了獨特的指紋。

引用此