极速体育,极速体育直播

报告题目：An efficient Fourier spectral eigensolver for computing the Bogoliubov-de Gennes excitations of spin-1 Bose-Einstein condensates

主讲人：谢满庭副教授（天津大学）

时间：2025年3月5日（周三）16:00 p.m.

地点：北院卓远楼305会议室

主办单位：统计与数学学院

摘要：In this talk, we propose a spectrally accurate solver for computing the elementary/collective excitations of spin-1 Bose-Einstein condensates (BEC), which is governed by the Bogoliubov-de Gennes (BdG) equation, around the mean-field ground state. The BdG equation is essentially a constrained eigen-system. Firstly, we investigate its analytical properties, including exact eigenpairs, generalized nullspace, and bi-orthogonality of eigenspaces. Secondly, by combining the standard Fourier spectral method for spatial discretization and a stable Gram-Schmidt bi-orthogonal algorithm, we develop a subspace iterative eigensolver for such a large-scale dense eigenvalue problem, and it proves to be numerically stable, efficient, and accurate. Our solver is matrix-free and the operator-function evaluation is accelerated by discrete Fast Fourier Transform (FFT) with almost optimal efficiency. Therefore, it is memory-friendly and efficient for large-scale problems. Finally, we present extensive numerical examples to illustrate the spectral accuracy and efficiency, and investigate the excitation spectrum and Bogoliubov amplitudes around the ground state in 1-3 spatial dimensions.

主讲人简介：

谢满庭，天津大学应用数学中心副教授。博士毕业于中国科学院计算数学所。主要研究非线性微分方程、特征值问题的高效算法与理论分析等。相关研究成果发表在SIAM J. Sci. Comput., Sci. China Math.，J. Sci. Comput.，ESAIM M2NA，BIT等国际权威期刊。曾受邀在“第三届京津冀计算数学学术交流会”做大会邀请报告。主持和参与多项国家级项目。曾荣获中科院朱李月华优秀博士生奖。