A hybrid Jacobi-Davidson method for interior cluster eigenvalues with large null-space in three dimensional lossless drude dispersive metallic photonic crystals. (English) Zbl 1375.78044
Summary: 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.
MSC:
| 78M25 | Numerical methods in optics (MSC2010) |
| 65F15 | Numerical computation of eigenvalues and eigenvectors of matrices |
| 65Z05 | Applications to the sciences |
| 82D25 | Statistical mechanics of crystals |
Keywords:
three-dimensional dispersive metallic photonic crystals; clustered eigenvalues; zero eigenvalues; hybrid Jacobi-Davidson method; preconditionerReferences:
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