A hybrid Jacobi–Davidson method for interior cluster eigenvalues with large null-space in three dimensional lossless Drude dispersive metallic photonic crystals

Tsung Ming Huang, Wen-Wei Lin, Weichung Wang*

*Corresponding author for this work

Research output: Contribution to journalArticle

5 Scopus citations

Abstract

We study how to efficiently solve the eigenvalue problems in computing band structure of three-dimensional dispersive metallic photonic crystals with face-centered cubic lattices based on the lossless Drude model. The discretized Maxwell equations result in large-scale standard eigenvalue problems whose spectrum contains many zero and cluster eigenvalues, both prevent existed eigenvalue solver from being efficient. To tackle this computational difficulties, we propose a hybrid Jacobi–Davidson method (hHybrid) that integrates harmonic Rayleigh–Ritz extraction, a new and hybrid way to compute the correction vectors, and a FFT-based preconditioner. Intensive numerical experiments show that the hHybrid outperforms existed eigenvalue solvers in terms of timing and convergence behaviors.

Original languageEnglish
Pages (from-to)221-231
Number of pages11
JournalComputer Physics Communications
Volume207
DOIs
StatePublished - 1 Oct 2016

Keywords

  • Clustered eigenvalues
  • Hybrid Jacobi–Davidson method
  • Preconditioner
  • Three-dimensional dispersive metallic photonic crystals
  • Zero eigenvalues

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