標題: | Eigenvalue solvers for three dimensional photonic crystals with face-centered cubic lattice |
作者: | Huang, Tsung-Ming Hsieh, Han-En Lin, Wen-Wei Wang, Weichung 應用數學系 Department of Applied Mathematics |
關鍵字: | Maxwell's equations;Three-dimensional photonic crystals;Face-centered cubic lattice;Null space free eigenvalue problem;Shift-invert residual Arnoldi method;Fast Fourier transform matrix-vector multiplications |
公開日期: | 15-Dec-2014 |
摘要: | To numerically determine the band structure of three-dimensional photonic crystals with face-centered cubic lattices, we study how the associated large-scale generalized eigenvalue problem (GEP) can be solved efficiently. The main computational challenge is due to the complexity of the coefficient matrix and the fact that the desired eigenvalues are interior. For solving the GEP by the shift-and-invert Lanczos method, we propose a preconditioning for the associated linear system therein. Recently, a way to reformat the GEP to the null space free eigenvalue problem (NFEP) is proposed. For solving the NFEP, we analyze potential advantages and disadvantages of the null space free inverse Lanczos method, the shift-invert residual Arnoldi method, and the Jacobi-Davidson method from theoretical viewpoints. These four approaches are compared numerically to find out their properties. The numerical results suggest that the shift-invert residual Arnoldi method with an initialization scheme is the fastest and the most robust eigensolver for the target eigenvalue problems. Our findings promise to play an essential role in simulating photonic crystals. (C) 2014 Elsevier B.V. All rights reserved. |
URI: | http://dx.doi.org/10.1016/j.cam.2014.02.016 http://hdl.handle.net/11536/25017 |
ISSN: | 0377-0427 |
DOI: | 10.1016/j.cam.2014.02.016 |
期刊: | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS |
Volume: | 272 |
Issue: | |
起始頁: | 350 |
結束頁: | 361 |
Appears in Collections: | Articles |
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