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(yuǎn)樓204學(xué)術(shù)報告廳
主辦單位：數(shù)學(xué)與統(tǒng)計學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院
報告人簡介：
邵美悅，復(fù)旦大學(xué)大數(shù)據(jù)學(xué)院青年研究員。2014年畢業(yè)于瑞士洛桑聯(lián)邦理工學(xué)院，獲得計算數(shù)學(xué)博士學(xué)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(dān)任博士后研究員和項目科學(xué)家。2019年5月進(jìn)入復(fù)旦大學(xué)大數(shù)據(jù)學(xué)院工作。其主要研究領(lǐng)域為數(shù)值線性代數(shù)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.