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Tsung-Ming Huang Wei-Jen Chang Yin-Liang Huang Wen-Wei Lin Wei-Cheng Wang Weichung Wang 《Journal of computational physics》2010,229(23):8684-8703
To explore band structures of three-dimensional photonic crystals numerically, we need to solve the eigenvalue problems derived from the governing Maxwell equations. The solutions of these eigenvalue problems cannot be computed effectively unless a suitable combination of eigenvalue solver and preconditioner is chosen. Taking eigenvalue problems due to Yee’s scheme as examples, we propose using Krylov–Schur method and Jacobi–Davidson method to solve the resulting eigenvalue problems. For preconditioning, we derive several novel preconditioning schemes based on various preconditioners, including a preconditioner that can be solved by Fast Fourier Transform efficiently. We then conduct intensive numerical experiments for various combinations of eigenvalue solvers and preconditioning schemes. We find that the Krylov–Schur method associated with the Fast Fourier Transform based preconditioner is very efficient. It remarkably outperforms all other eigenvalue solvers with common preconditioners like Jacobi, Symmetric Successive Over Relaxation, and incomplete factorizations. This promising solver can benefit applications like photonic crystal structure optimization. 相似文献
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We propose a structure-preserving doubling algorithm for a quadratic eigenvalue problem arising from the stability analysis of time-delay systems. We are particularly interested in the eigenvalues on the unit circle, which are difficult to estimate. The convergence and backward error of the algorithm are analyzed and three numerical examples are presented. Our experience shows that our algorithm is efficient in comparison to the few existing approaches for small to medium size problems. 相似文献
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A simple and efficient FFT-based fast direct solver for Poisson-typeequations on 3D cylindrical and spherical geometries is presented.The solver relies on the truncated Fourier series expansion,where the differential equations of Fourier coefficients aresolved using second-order finite difference discretizationswithout pole conditions. Three different boundary conditions(Dirichlet, Neumann and Robin conditions) can be handled withoutsubstantial differences. 相似文献
99.
Qi-Ying Xia Deng-Xue Ma Dong-Jiao Li Bao-Hui Li Wen-Wei Zhao Guang-Fu Ji 《Structural chemistry》2016,27(3):793-800
In an attempt to find single-source precursors, a series of small clusters of inorganic azides of indium (Br2InN3) n (n = 1–6) were studied using the dispersion correction density functional theory (wB97XD). The obtained (Br2InN3) n (n = 2–6) clusters have the core structures of 2n-membered ring with alternating indium and α-nitrogen atoms. The influences of cluster size (oligomerization degree n) on the structures, energies, IR spectra, and thermodynamic properties of clusters were discussed. The computed binding energies indicate the stability: 3A > 3B, 4B > 4C > 4A > 4D, 5E > 5D > 5B = 5C > 5A and 6I > 6C > 6D > 6G ≥ 6H > 6F > 6E > 6B > 6A. It is also found that (Br2InN3)2 and (Br2InN3)4 clusters possess higher stability than their neighbor sizes judged by the calculated second-order difference of energies (Δ2 E). Meanwhile, thermodynamic properties for (Br2InN3) n (n = 1–6) clusters increase with the increasing temperature and oligomerization degree n, and the oligomerizations are thermodynamically favorable at temperatures up to 800 K. 相似文献
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In this paper, we propose an inverse inexact iteration method for the computation of the eigenvalue with the smallest modulus and its associated eigenvector for a large sparse matrix. The linear systems of the traditional inverse iteration are solved with accuracy that depends on the eigenvalue with the second smallest modulus and iteration numbers. We prove that this approach preserves the linear convergence of inverse iteration. We also propose two practical formulas for the accuracy bound which are used in actual implementation. © 1997 John Wiley & Sons, Ltd. 相似文献