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

作者：Huang Tsung Ming; Lin Wen Wei; Wang Weichung^*

来源：Computer Physics Communications, 2016, 207: 221-231.

DOI：10.1016/j.cpc.2016.06.017

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

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.

• 出版日期2016-10