Browsing by Author "Tian, Heng"

Now showing 1 - 4 of 4

Computing the full spectrum of large sparse palindromic quadratic eigenvalue problems arising from surface Green's function calculations
(2018-03-01)
Huang, Tsung-Ming
;
Lin, Wen-Wei
;
Tian, Heng
;
Chen, Guan-Hua
;
應用數學系
Full spectrum of a large sparse inverted perpendicular-palindromic quadratic eigenvalue problem inverted perpendicular-PQEP) is considered arguably for the first time in this article. Such a problem is posed by calculation of surface Green's functions SGFs) of mesoscopic transistors with a tremendous non-periodic cross-section. For this problem, general purpose eigensolvers are not efficient, nor is advisable to resort to the decimation method etc. to obtain the Wiener-Hopf factorization. After reviewing some rigorous understanding of SGF calculation from the perspective of inverted perpendicular-PQEP and nonlinear matrix equation, we present our new approach to this problem. In a nutshell, the unit disk where the spectrum of interest lies is broken down adaptively into pieces small enough that they each can be locally tackled by the generalized inverted perpendicular-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi G inverted perpendicular SHIRA) algorithm with suitable shifts and other parameters, and the eigenvalues missed by this divide-and-conquer strategy can be recovered thanks to the accurate estimation provided by our newly developed scheme. Notably the novel non-equivalence deflation is proposed to avoid as much as possible duplication of nearby known eigenvalues when a new shift of G inverted perpendicular SHIRA is determined. We demonstrate our new approach by calculating the SGF of a realistic nanowire whose unit cell is described by a matrix of size 4000 x 4000 at the density functional tight binding level, corresponding to a 8 x 8 nm(2) cross-section. We believe that quantum transport simulation of realistic nano-devices in the mesoscopic regime will greatly benefit from this work. (c) 2017 Elsevier Inc. All rights reserved.
Structure-Preserving Methods for Computing Complex Band Structures of Three Dimensional Photonic Crystals
(2020-05-06)
Huang, Tsung-Ming
;
Li, Tiexiang
;
Lin, Jia-Wei
;
Lin, Wen-Wei
;
Tian, Heng
This work is devoted to the numerical computation of complex band structure k=k(omega)is an element of C3, with omega being positive frequencies, of three dimensional isotropic dispersive or non-dispersive photonic crystals from the perspective of structured quadratic eigenvalue problems (QEPs). Our basic strategy is to fix two degrees of freedom in k and to view the remaining one as the eigenvalue of a complex gyroscopic QEP which stems from Maxwell's equations discretized by Yee's scheme. We reformulate this gyroscopic QEP into a T-palindromic QEP, which is further transformed into a structured generalized eigenvalue problem for which we have established a structure-preserving shift-and-invert Arnoldi algorithm. Moreover, to accelerate the inner iterations of the shift-and-invert Arnoldi algorithm, we propose an efficient preconditioner which makes most of the fast Fourier transforms. The advantage of our method is discussed in detail and corroborated by several numerical results.
Time-dependent density functional theory for quantum transport
(2010-09-21)
Zheng, Xiao
;
Chen, GuanHua
;
Mo, Yan
;
Koo, SiuKong
;
Tian, Heng
Based on our earlier works [X. Zheng , Phys. Rev. B 75, 195127 (2007); J. S. Jin , J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages. (c) 2010 American Institute of Physics. [doi:10.1063/1.3475566]
Time-dependent density functional theory for quantum transport
(2010-09-21)
Zheng, Xiao
;
Chen, GuanHua
;
Mo, Yan
;
Koo, SiuKong
;
Tian, Heng
Based on our earlier works [X. Zheng , Phys. Rev. B 75, 195127 (2007); J. S. Jin , J. Chem. Phys. 128, 234703 (2008)], we propose a rigorous and numerically convenient approach to simulate time-dependent quantum transport from first-principles. The proposed approach combines time-dependent density functional theory with quantum dissipation theory, and results in a useful tool for studying transient dynamics of electronic systems. Within the proposed exact theoretical framework, we construct a number of practical schemes for simulating realistic systems such as nanoscopic electronic devices. Computational cost of each scheme is analyzed, with the expected level of accuracy discussed. As a demonstration, a simulation based on the adiabatic wide-band limit approximation scheme is carried out to characterize the transient current response of a carbon nanotube based electronic device under time-dependent external voltages. (c) 2010 American Institute of Physics. [doi:10.1063/1.3475566]