天元名家讲座|An intermediate eigenvalue problem in electronic structure calculation
报 告 人: 张绍良 教授
所在单位: 日本名古屋大学
报告地点: 腾讯会议
报告时间: 2022-09-13 09:00:00
报告简介:

腾讯会议 ID:722-811-073

会议链接:https://meeting.tencent.com/dm/qNV403RKKtel

We consider the generalized eigenvalue problem A x = λB x where A is a real symmetric matrix and B is a real symmetric positive definite matrix. A property of this problem is that all the eigenvalues are real, and it is often needed to compute a number of eigenvalues which are important for applications. In the field of electronic structure calculation, there has emerged a need to find the eigenvalues related to luminescence of organic materials. The targets are small in number, and from the atomic configuration of the material it is determined which eigenvalues need to be computed. In this talk, we present a bisection approach to obtaining the eigenvalues related to the luminescence. By iteratively searching and narrowing the interval within which the target eigenvalues exist, we can find them without computing unrelated eigenvalues.

 

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主讲人简介:
张绍良教授于吉林大学数学系计算算数学专业获学士学位,于日本筑波大学获理工学硕士学位及工学博士学位。曾任职于日本名古屋大学工学部、日本筑波大学电子情报工学系、日本东京大学工学系等。张绍良教授曾/现任日本应用数理学会理事, 日本应用数理学会理事会监事,East Asia SIAM的秘书,以及包括 International Journal of Numerical Analysis and Modeling,East Asian Journal on Applied Mathematics, Journal of Mathematical Research and Exposition, 及Journal of Information and Computational Science等杂志编委。张绍良教授在近年国际热门研究课题“乘积型迭代法”方面,开拓了一个新的研究方向。在改良著名迭代法 Bi-CGSTAB的同时,根据 Lanczos 三阶递推公式,成功地建立了线性方程组求解的乘积迭代法的统一模型。由此统一模型,可简单地推导出著名的 CGS法,Bi-CGSTAB法,Bi-CGSTAB2法,并可推导出新⽅法:GPBi-CG法。设计出的算法GPBi-CG法在理论上有独特的见解,在实际问题的应用上可解上百万线性形方程组。各种计算结果表明GPBi-CG法是国际上现有的迭代法中精度最高,迭代速度最快,计算效率最有效的算法之一。