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報告題目：An efficient Fourier spectral eigensolver for computing the Bogoliubov-de Gennes excitations of spin-1 Bose-Einstein condensates

主講人：謝滿庭副教授（天津大學）

時間：2025年3月5日（周三）16:00 p.m.

地點：北院卓遠樓305會議室

主辦單位：統計與數學學院

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.

主講人簡介：

謝滿庭，天津大學應用數學中心副教授。博士畢業于中國科學院計算數學所。主要研究非線性微分方程、特征值問題的高效算法與理論分析等。相關研究成果發表在SIAM J. Sci. Comput., Sci. China Math.，J. Sci. Comput.，ESAIM M2NA，BIT等國際權威期刊。曾受邀在“第三屆京津冀計算數學學術交流會”做大會邀請報告。主持和參與多項國家級項目。曾榮獲中科院朱李月華優秀博士生獎。