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報(bào)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(xué)）

時(shí)間：2025年3月5日（周三）16:00 p.m.

地點(diǎn)：北院卓遠(yuǎn)樓305會(huì)議室

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)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(jiǎn)介：

謝滿庭,，天津大學(xué)應(yīng)用數(shù)學(xué)中心副教授,。博士畢業(yè)于中國(guó)科學(xué)院計(jì)算數(shù)學(xué)所,。主要研究非線性微分方程,、特征值問(wèn)題的高效算法與理論分析等,。相關(guān)研究成果發(fā)表在SIAM J. Sci. Comput., Sci. China Math.,，J. Sci. Comput.,，ESAIM M2NA，BIT等國(guó)際權(quán)威期刊,。曾受邀在“第三屆京津冀計(jì)算數(shù)學(xué)學(xué)術(shù)交流會(huì)”做大會(huì)邀請(qǐng)報(bào)告,。主持和參與多項(xiàng)國(guó)家級(jí)項(xiàng)目。曾榮獲中科院朱李月華優(yōu)秀博士生獎(jiǎng),。