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

Research output: Contribution to journalArticle

2 Citations (Scopus)

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
Publication statusPublished - 2016 Oct 1

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Maxwell equations
Photonic crystals
Crystal lattices
Fast Fourier transforms
Band structure
eigenvalues
photonics
crystals
Experiments
face centered cubic lattices
fast Fourier transformations
Maxwell equation
time measurement
harmonics

Keywords

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

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Hardware and Architecture

Cite this

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

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