Title: A hybrid Jacobi-Davidson method for interior cluster eigenvalues with large null-space in three dimensional lossless Drude dispersive metallic photonic crystals
Authors: Huang, Tsung-Ming
Lin, Wen-Wei
Wang, Weichung
Department of Applied Mathematics
Keywords: Three-dimensional dispersive metallic photonic crystals;Clustered eigenvalues;Zero eigenvalues;Hybrid Jacobi-Davidson method;Preconditioner
Issue Date: Oct-2016
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. (C) 2016 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.cpc.2016.06.017
ISSN: 0010-4655
DOI: 10.1016/j.cpc.2016.06.017
Volume: 207
Begin Page: 221
End Page: 231
Appears in Collections:Articles