20190425 數學系專題演講田恆 (Tian Heng) 博士

20190425 數學系專題演講田恆 (Tian Heng) 博士 (01:00:04)

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影片標題:	20190425 數學系專題演講田恆 (Tian Heng) 博士
影片說明:	Large Sparse Palindromic Quadratic Eigenvalue Problems Arising from Computing Complete Complex Band Structure of 1D Nanowires 演講公告：https://tinyurl.com/yxpqteyz 演講投影片：演講摘要： Complete spectrum of a large sparse T-palindromic quadratic eigenvalue problem (T-PQEP) is needed in the calculation of surface Green’s functions (SGFs) of nanowires with a tremendous non-periodic cross-section. Equivalently, complete complex band structure of quasi-1D nanowires is required. 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 nonlinear matrix equation, we present our own approach to this problem. In brief, the unit disk where the spectrum of interest lies is broken down adaptively into small pieces so that they each can be locally tackled by the generalized T-skew-Hamiltonian implicitly restarted shift-and-invert Arnoldi (GTSHIRA) 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 in this process, the novel non-equivalence deflation of the T-PQEP greatly accelerates the computation. We will demonstrate the new approach by one realistic example. If possible, we will discuss our recent application of this new approach to the computation of partial complex band structure of 3D photonic crystals/metamaterials. 成大數學演講公告連結：https://tinyurl.com/ybjxmujm
影片分類:	研討會議/教育訓練
演講者:	田恆 (Tian Heng) 博士（交通大學應用數學系）
活動時間:	2019-04-25
主辦單位:	數學系
上傳時間:	2019-04-29 18:00:55
上傳者:	陳旻宏
觀看次數:	2