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dc.contributor.authorHuang, Tsung-Mingen_US
dc.contributor.authorHsieh, Han-Enen_US
dc.contributor.authorLin, Wen-Weien_US
dc.contributor.authorWang, Weichungen_US
dc.date.accessioned2019-04-02T06:00:08Z-
dc.date.available2019-04-02T06:00:08Z-
dc.date.issued2014-12-15en_US
dc.identifier.issn0377-0427en_US
dc.identifier.urihttp://dx.doi.org/10.1016/j.cam.2014.02.016en_US
dc.identifier.urihttp://hdl.handle.net/11536/147782-
dc.description.abstractTo 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.en_US
dc.language.isoen_USen_US
dc.subjectMaxwell's equationsen_US
dc.subjectThree-dimensional photonic crystalsen_US
dc.subjectFace-centered cubic latticeen_US
dc.subjectNull space free eigenvalue problemen_US
dc.subjectShift-invert residual Arnoldi methoden_US
dc.subjectFast Fourier transform matrix-vector multiplicationsen_US
dc.titleEigenvalue solvers for three dimensional photonic crystals with face-centered cubic latticeen_US
dc.typeArticleen_US
dc.identifier.doi10.1016/j.cam.2014.02.016en_US
dc.identifier.journalJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICSen_US
dc.citation.volume272en_US
dc.citation.spage350en_US
dc.citation.epage361en_US
dc.contributor.department應用數學系zh_TW
dc.contributor.departmentDepartment of Applied Mathematicsen_US
dc.identifier.wosnumberWOS:000340336600027en_US
dc.citation.woscount7en_US
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