报 告 人：邵美悦 研究员
报告题目：Structure-preserving algorithms for solving the Bethe--Salpeter eigenvalue problem and computing the absorption spectrum
报告时间：2023年7月20日（周四）上午10:30-11:30
报告地点：静远楼204学术报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
邵美悦，复旦大学大数据学院青年研究员。2014年毕业于瑞士洛桑联邦理工学院，获得计算数学博士学位。2014年至2019年在美国劳伦斯伯克利国家实验室从事研究工作，先后担任博士后研究员和项目科学家。2019年5月进入复旦大学大数据学院工作。其主要研究领域为数值线性代数和高性能计算。
报告摘要：
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.