報 告 人：邵美悅 研究員
報告題目：Structure-preserving algorithms for solving the Bethe--Salpeter eigenvalue problem and computing the absorption spectrum
報告時間：2023年7月20日（周四）上午10:30-11:30
報告地點：靜遠樓204學術報告廳
主辦單位：數學與統計學院、數學研究院、科學技術研究院
報告人簡介：
邵美悅，復旦大學大數據學院青年研究員。2014年畢業于瑞士洛桑聯邦理工學院，獲得計算數學博士學位。2014年至2019年在美國勞倫斯伯克利國家實驗室從事研究工作，先后擔任博士后研究員和項目科學家。2019年5月進入復旦大學大數據學院工作。其主要研究領域為數值線性代數和高性能計算。
報告摘要：
In a molecular system the excitation of an electron is obtained by solving the so-called Bethe--Salpeter equation (BSE). Discretization of the Bethe--Salpeter equation leads to a dense non-Hermitian matrix eigenvalue problem with a special 2-by-2 block structure. In principle all excitation energies, i.e., all positive eigenvalues of the BSE Hamiltonian, are of interest. This is challenging in practice because the dimension of the BSE Hamiltonian depends quadratically on the number of electrons in the system. We present a parallel structure preserving algorithm that computes all eigenpairs of the BSE Hamiltonian efficiently and accurately. In some circumstances, instead of computing each individual eigenpair, we need to compute the optical absorption spectrum, which is a frequency dependent matrix functional of the BSE Hamiltonian. We develop a Lanczos-type algorithm to efficiently compute the absorption spectrum without diagonalizing the BSE Hamiltonian. Parallel implementations of these algorithms are available in the software package BSEPACK.