Dai, Xiaoying; de Gironcoli, Stefano; Yang, Bin; Zhou, Aihui Mathematical analysis and numerical approximations of density functional theory models for metallic systems. (English) Zbl 1518.65072 Multiscale Model. Simul. 21, No. 3, 777-803 (2023). MSC: 65K10 65N25 49S05 35P30 PDFBibTeX XMLCite \textit{X. Dai} et al., Multiscale Model. Simul. 21, No. 3, 777--803 (2023; Zbl 1518.65072) Full Text: DOI arXiv
Dai, Xiaoying; Zhang, Liwei; Zhou, Aihui Convergent and orthogonality preserving schemes for approximating the Kohn-Sham orbitals. (English) Zbl 1524.37076 Numer. Math., Theory Methods Appl. 16, No. 1, 1-25 (2023). MSC: 37M15 37M21 65M12 65N25 81Q05 PDFBibTeX XMLCite \textit{X. Dai} et al., Numer. Math., Theory Methods Appl. 16, No. 1, 1--25 (2023; Zbl 1524.37076) Full Text: DOI arXiv
Dai, Xiaoying; Liu, Zhuang; Zhang, Xin; Zhou, Aihui A parallel orbital-updating based optimization method for electronic structure calculations. (English) Zbl 1528.81003 J. Comput. Phys. 445, Article ID 110622, 17 p. (2021). MSC: 81-08 65N25 49M20 PDFBibTeX XMLCite \textit{X. Dai} et al., J. Comput. Phys. 445, Article ID 110622, 17 p. (2021; Zbl 1528.81003) Full Text: DOI arXiv
Dai, Xiaoying; Wang, Qiao; Zhou, Aihui Gradient flow based Kohn-Sham density functional theory model. (English) Zbl 1459.37068 Multiscale Model. Simul. 18, No. 4, 1621-1663 (2020). MSC: 37M05 37N40 65N25 70G60 81Q05 PDFBibTeX XMLCite \textit{X. Dai} et al., Multiscale Model. Simul. 18, No. 4, 1621--1663 (2020; Zbl 1459.37068) Full Text: DOI
Zhou, Yuzhi; Chen, Huajie; Zhou, Aihui Plane wave methods for quantum eigenvalue problems of incommensurate systems. (English) Zbl 1451.81243 J. Comput. Phys. 384, 99-113 (2019). MSC: 81Q35 65F15 65N25 65Z05 PDFBibTeX XMLCite \textit{Y. Zhou} et al., J. Comput. Phys. 384, 99--113 (2019; Zbl 1451.81243) Full Text: DOI arXiv
Zhou, Aihui A mathematical aspect of Hohenberg-Kohn theorem. (English) Zbl 1409.81189 Sci. China, Math. 62, No. 1, 63-68 (2019). MSC: 81V70 PDFBibTeX XMLCite \textit{A. Zhou}, Sci. China, Math. 62, No. 1, 63--68 (2019; Zbl 1409.81189) Full Text: DOI arXiv
Dai, Xiaoying; Liu, Zhuang; Zhang, Liwei; Zhou, Aihui A conjugate gradient method for electronic structure calculations. (English) Zbl 1378.65120 SIAM J. Sci. Comput. 39, No. 6, A2702-A2740 (2017). MSC: 65K05 81Q05 90C30 81V55 PDFBibTeX XMLCite \textit{X. Dai} et al., SIAM J. Sci. Comput. 39, No. 6, A2702--A2740 (2017; Zbl 1378.65120) Full Text: DOI arXiv
Chen, Huajie; Dai, Xiaoying; Gong, Xingao; He, Lianhua; Zhou, Aihui Adaptive finite element approximations for Kohn-Sham models. (English) Zbl 1316.35260 Multiscale Model. Simul. 12, No. 4, 1828-1869 (2014). MSC: 35Q55 65N15 65N25 65N30 81Q05 35P30 PDFBibTeX XMLCite \textit{H. Chen} et al., Multiscale Model. Simul. 12, No. 4, 1828--1869 (2014; Zbl 1316.35260) Full Text: DOI arXiv
Zhang, Xin; Zhu, Jinwei; Wen, Zaiwen; Zhou, Aihui Gradient type optimization methods for electronic structure calculations. (English) Zbl 1300.82006 SIAM J. Sci. Comput. 36, No. 3, C265-C289 (2014). MSC: 82-08 65N25 65N30 65N50 90C30 81V70 90C52 PDFBibTeX XMLCite \textit{X. Zhang} et al., SIAM J. Sci. Comput. 36, No. 3, C265--C289 (2014; Zbl 1300.82006) Full Text: DOI arXiv
Chen, Huajie; Zhou, Aihui Chapter 8: Finite element approximations in orbital-free density functional theory. (English) Zbl 1378.82006 Wesolowski, Tomasz A. (ed.) et al., Recent progress in orbital-free density functional theory. Hackensack, NJ: World Scientific (ISBN 978-981-4436-72-4/hbk; 978-981-4436-74-8/ebook). Recent Advances in Computational Chemistry 6, 251-271 (2013). MSC: 82-08 82B10 81Q05 65N30 65N25 35R09 35Q82 90C52 65K10 PDFBibTeX XMLCite \textit{H. Chen} and \textit{A. Zhou}, Recent Adv. Comput. Chem. 6, 251--271 (2013; Zbl 1378.82006) Full Text: DOI
Chen, Huajie; Gong, Xingao; He, Lianhua; Yang, Zhang; Zhou, Aihui Numerical analysis of finite dimensional approximations of Kohn-Sham models. (English) Zbl 1278.35225 Adv. Comput. Math. 38, No. 2, 225-256 (2013). MSC: 35Q55 65N15 65N25 65N30 81Q05 PDFBibTeX XMLCite \textit{H. Chen} et al., Adv. Comput. Math. 38, No. 2, 225--256 (2013; Zbl 1278.35225) Full Text: DOI arXiv
Zhou, Aihui Hohenberg-Kohn theorem for Coulomb type systems and its generalization. (English) Zbl 1308.81197 J. Math. Chem. 50, No. 10, 2746-2754 (2012). MSC: 81V70 49S05 81V55 82D20 PDFBibTeX XMLCite \textit{A. Zhou}, J. Math. Chem. 50, No. 10, 2746--2754 (2012; Zbl 1308.81197) Full Text: DOI arXiv
Fang, Jun; Gao, Xingyu; Zhou, Aihui A Kohn-Sham equation solver based on hexahedral finite elements. (English) Zbl 1245.82007 J. Comput. Phys. 231, No. 8, 3166-3180 (2012). MSC: 82B10 35Q55 82-08 65N30 65N50 PDFBibTeX XMLCite \textit{J. Fang} et al., J. Comput. Phys. 231, No. 8, 3166--3180 (2012; Zbl 1245.82007) Full Text: DOI
Ding, Jiu; Jin, Congming; Rhee, Noah H.; Zhou, Aihui A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappings. (English) Zbl 1231.37042 J. Stat. Phys. 145, No. 6, 1620-1639 (2011). MSC: 37M25 37C30 65H10 37E05 PDFBibTeX XMLCite \textit{J. Ding} et al., J. Stat. Phys. 145, No. 6, 1620--1639 (2011; Zbl 1231.37042) Full Text: DOI
Chen, Huajie; He, Lianhua; Zhou, Aihui Finite element approximations of nonlinear eigenvalue problems in quantum physics. (English) Zbl 1228.81026 Comput. Methods Appl. Mech. Eng. 200, No. 21-22, 1846-1865 (2011). MSC: 81-08 65N25 65N30 PDFBibTeX XMLCite \textit{H. Chen} et al., Comput. Methods Appl. Mech. Eng. 200, No. 21--22, 1846--1865 (2011; Zbl 1228.81026) Full Text: DOI
Chen, Huajie; Gong, Xingao; Zhou, Aihui Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model. (English) Zbl 1194.35293 Math. Methods Appl. Sci. 33, No. 14, 1723-1742 (2010). MSC: 35P30 35Q55 65N15 65N25 65N30 81Q05 PDFBibTeX XMLCite \textit{H. Chen} et al., Math. Methods Appl. Sci. 33, No. 14, 1723--1742 (2010; Zbl 1194.35293) Full Text: DOI
Chen, Huajie; Zhou, Aihui Orbital-free density functional theory for molecular structure calculations. (English) Zbl 1174.81316 Numer. Math., Theory Methods Appl. 1, No. 1, 1-28 (2008). MSC: 81Q05 65N22 35Q55 65N25 65N30 81V45 81V55 PDFBibTeX XMLCite \textit{H. Chen} and \textit{A. Zhou}, Numer. Math., Theory Methods Appl. 1, No. 1, 1--28 (2008; Zbl 1174.81316) Full Text: Link