Edit Profile (opens in new tab) Zhou, Aihui Co-Author Distance Author ID: zhou.aihui Published as: Zhou, Aihui; Zhou, A.; Zhou, Ai-hui; Zhou, Ai Hui more...less Homepage: http://lsec.cc.ac.cn/~azhou/ External Links: Google Scholar · ResearchGate Documents Indexed: 149 Publications since 1984, including 3 Books and 11 Additional arXiv Preprints 1 Contribution as Editor Co-Authors: 72 Co-Authors with 130 Joint Publications 3,103 Co-Co-Authors all top 5 Co-Authors 18 single-authored 22 Ding, Jiu 20 Dai, Xiaoying 13 Chen, Huajie 11 Gong, Xingao 11 Lin, Qun 11 Liu, Fang 8 Gao, Xingyu 8 He, Lianhua 8 Xu, Jinchao 7 Shen, Lihua 5 Fang, Jun 4 Allegretto, Walter 4 Lin, Yanping 4 Ma, Xiuling 4 Xin, Jack X. 4 Yan, Ningning 4 Zhang, Dier 4 Zhang, Liwei 4 Zhou, Yuzhi 3 Mao, Dong 3 Shih, Tsimin 3 Stynes, Martin Joseph 3 Wang, Ting 3 Yang, Ying 3 Yang, Zhang 3 Zhang, Xin 2 Gu, Hong 2 He, Yinnian 2 Huang, Hung-Tsai 2 Jin, Congming 2 Li, Zi-Cai 2 Liang, Shengde 2 Liu, Zhuang 2 Lü, Tao 2 Wang, Qiao 2 Xu, Yuesheng 2 Yang, Bin 2 Zhou, Yunkai 2 Zhu, Jinwei 1 Bao, Gang 1 Chelikowsky, James R. 1 Chen, Zhongying 1 de Gironcoli, Stefano 1 Franz, Sebastian 1 1 Hou, Pengyu 1 Hu, Miao 1 Kuang, Xiong 1 Li, Jian 1 Li, Jichun 1 Li, Ronghua 1 Li, Tien-Yien 1 Liao, Xiaohai 1 Liem, Chinbo 1 Lü, Lao 1 Madden, Niall 1 Massatt, Daniel 1 Naga, Ahmed 1 Pan, Jianhua 1 Pan, Yan 1 Pflaum, Christoph 1 Reich, Nils 1 Ren, Zhongdao 1 Rhee, Noah H. 1 Roos, Hans-Görg 1 Rüde, Ulrich 1 Schneider, Reinhold 1 Shu, Shi 1 Sun, Jiguang 1 Tobiska, Lutz 1 Wang, Zheng 1 Wen, Zaiwen 1 Winter, Christoph 1 Zhang, Zhimin all top 5 Serials 8 Journal of Computational Mathematics 7 Advances in Computational Mathematics 6 Systems Science and Mathematical Sciences 5 Computer Methods in Applied Mechanics and Engineering 5 Numerische Mathematik 5 SIAM Journal on Scientific Computing 5 Multiscale Modeling & Simulation 4 Applied Mathematics and Computation 4 SIAM Journal on Numerical Analysis 4 Journal of Scientific Computing 4 Acta Mathematica Scientia 3 IMA Journal of Numerical Analysis 3 Journal of Computational Physics 3 Journal of Statistical Physics 3 Mathematical Methods in the Applied Sciences 3 BIT 3 Journal of Computational and Applied Mathematics 3 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 3 Natural Science Journal of Xiangtan University 3 Communications in Computational Physics 3 Science China. Mathematics 2 Nonlinearity 2 Mathematics of Computation 2 Applied Mathematics Letters 2 Journal of Integral Equations and Applications 2 International Journal of Numerical Analysis and Modeling 2 Numerical Mathematics: Theory, Methods and Applications 2 Scientia Sinica. Mathematica 2 Nonlinear Analysis. Theory, Methods & Applications 1 Journal of Mathematical Analysis and Applications 1 Physics Letters. A 1 Advances in Mathematics (Beijing) 1 Journal of Engineering Mathematics (Xi’an) 1 Physica D 1 Applied Numerical Mathematics 1 Journal of Systems Science and Mathematical Sciences 1 RAIRO. Modélisation Mathématique et Analyse Numérique 1 Acta Mathematicae Applicatae Sinica. English Series 1 Hunan Annals of Mathematics 1 Numerical Methods for Partial Differential Equations 1 Science in China. Series A 1 Applications of Mathematics 1 Journal of Partial Differential Equations 1 Electronic Journal of Differential Equations (EJDE) 1 Monte Carlo Methods and Applications 1 Discrete and Continuous Dynamical Systems 1 Journal of Mathematical Chemistry 1 Dynamics of Continuous, Discrete and Impulsive Systems 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Journal of Systems Science and Complexity 1 Communications on Pure and Applied Analysis 1 HERMIS-\(\mu\pi\). Hellenic European Research on Mathematics and Informatics Science 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Mathematical Modelling of Natural Phenomena 1 Advances in Applied Mathematics and Mechanics 1 Monographs and Research Notes in Mathematics all top 5 Fields 117 Numerical analysis (65-XX) 75 Partial differential equations (35-XX) 29 Quantum theory (81-XX) 15 Operator theory (47-XX) 14 Dynamical systems and ergodic theory (37-XX) 9 Integral equations (45-XX) 9 Statistical mechanics, structure of matter (82-XX) 8 Fluid mechanics (76-XX) 5 Measure and integration (28-XX) 5 Optics, electromagnetic theory (78-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 3 Functional analysis (46-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Operations research, mathematical programming (90-XX) 2 Mechanics of deformable solids (74-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Approximations and expansions (41-XX) 1 Probability theory and stochastic processes (60-XX) 1 Statistics (62-XX) 1 Computer science (68-XX) 1 Mechanics of particles and systems (70-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Information and communication theory, circuits (94-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 109 Publications have been cited 1,867 times in 1,080 Documents Cited by ▼ Year ▼ A two-grid discretization scheme for eigenvalue problems. Zbl 0959.65119 Xu, Jinchao; Zhou, Aihui 162 2001 Local and parallel finite element algorithms based on two-grid discretizations. Zbl 0948.65122 Xu, Jinchao; Zhou, Aihui 143 2000 Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122 Lin, Qun; Tobiska, Lutz; Zhou, Aihui 143 2005 Local and parallel finite element algorithms for the Stokes problem. Zbl 1145.65097 He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian 88 2008 Convergence and optimal complexity of adaptive finite element eigenvalue computations. Zbl 1159.65090 Dai, Xiaoying; Xu, Jinchao; Zhou, Aihui 86 2008 Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Zbl 0990.65128 Xu, Jinchao; Zhou, Aihui 84 2001 Local and parallel finite element algorithms for the Navier-Stokes problem. Zbl 1093.76035 He, Yinnian; Xu, Jinchao; Zhou, Aihui 83 2006 A note on the optimal \(L^2\)-estimate of the finite volume element method. Zbl 0997.65122 Chen, Zhongying; Li, Ronghua; Zhou, Aihui 55 2002 Eigenvalues of rank-one updated matrices with some applications. Zbl 1139.15003 Ding, Jiu; Zhou, Aihui 53 2007 Local and parallel finite element algorithms for eigenvalue problems. Zbl 1015.65060 Xu, Jinchao; Zhou, Aihui 49 2002 Three-scale finite element discretizations for quantum eigenvalue problems. Zbl 1160.65060 Dai, Xiaoying; Zhou, Aihui 37 2008 A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions. Zbl 1188.65153 Liu, Fang; Madden, Niall; Stynes, Martin; Zhou, Aihui 36 2009 Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes. Zbl 0986.65098 Yan, Ningning; Zhou, Aihui 32 2001 Adaptive finite element approximations for Kohn-Sham models. Zbl 1316.35260 Chen, Huajie; Dai, Xiaoying; Gong, Xingao; He, Lianhua; Zhou, Aihui 32 2014 Finite element methods for eigenvalue problems. Zbl 1351.65085 Sun, Jiguang; Zhou, Aihui 32 2017 Finite approximations of Frobenius-Perron operators. A solution of Ulam’s conjecture to multi-dimensional transformations. Zbl 0890.58035 Ding, Jiu; Zhou, Aihui 29 1996 Symmetric finite volume discretizations for parabolic problems. Zbl 1038.65079 Ma, Xiuling; Shu, Shi; Zhou, Aihui 28 2003 Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates. Zbl 1103.65112 Mao, Dong; Shen, Lihua; Zhou, Aihui 28 2006 Finite element approximations of nonlinear eigenvalue problems in quantum physics. Zbl 1228.81026 Chen, Huajie; He, Lianhua; Zhou, Aihui 26 2011 Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh. Zbl 1221.81225 Zhang, Dier; Shen, Lihua; Zhou, Aihui; Gong, Xin-Gao 25 2008 Enhancing eigenvalue approximation by gradient recovery. Zbl 1148.65087 Naga, Ahmed; Zhang, Zhimin; Zhou, Aihui 24 2006 Numerical analysis of finite dimensional approximations of Kohn-Sham models. Zbl 1278.35225 Chen, Huajie; Gong, Xingao; He, Lianhua; Yang, Zhang; Zhou, Aihui 24 2013 An analysis of finite-dimensional approximations for the ground state solution of Bose-Einstein condensates. Zbl 1051.35094 Zhou, Aihui 23 2004 The full approximation accuracy for the stream function-vorticity- pressure method. Zbl 0823.65110 Zhou, Aihui; Li, Jichun 22 1994 A box scheme for coupled systems resulting from microsensor thermistor problems. Zbl 0979.78023 Allegretto, Walter; Lin, Yanping; Zhou, Aihui 21 1999 Gradient type optimization methods for electronic structure calculations. Zbl 1300.82006 Zhang, Xin; Zhu, Jinwei; Wen, Zaiwen; Zhou, Aihui 21 2014 Error analysis of the combination technique. Zbl 0942.65122 Pflaum, C.; Zhou, A. 19 1999 Piecewise linear Markov approximations of Frobenius-Perron operators associated with multi-dimensional transformations. Zbl 0907.47025 Ding, Jiu; Zhou, Ai Hui 19 1995 Finite element approximations for Schrödinger equations with applications to electronic structure computations. Zbl 1174.65047 Gong, Xingao; Shen, Lihua; Zhang, Dier; Zhou, Aihui 19 2008 Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model. Zbl 1194.35293 Chen, Huajie; Gong, Xingao; Zhou, Aihui 19 2010 A defect correction scheme for finite element eigenvalues with applications to quantum Chemistry. Zbl 1104.65323 Shen, Lihua; Zhou, Aihui 17 2006 The projection method for computing multidimensional absolutely continuous invariant measures. Zbl 0972.28501 Ding, Jiu; Zhou, Aihui 16 1994 Statistical properties of deterministic systems. Zbl 1171.37001 Ding, Jiu; Zhou, Aihui 16 2009 Convergence and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues. Zbl 1332.65159 Dai, Xiaoying; He, Lianhua; Zhou, Aihui 16 2015 Multi-parameter extrapolation methods for boundary integral equations. Zbl 0922.65075 Rüde, Ulrich; Zhou, Aihui 14 1998 Convergence and complexity of adaptive finite element methods for elliptic partial differential equations. Zbl 1263.65103 He, Lianhua; Zhou, Aihui 14 2011 A Kohn-Sham equation solver based on hexahedral finite elements. Zbl 1245.82007 Fang, Jun; Gao, Xingyu; Zhou, Aihui 13 2012 Nonnegative matrices, positive operators, and applications. Zbl 1205.15048 Ding, Jiu; Zhou, Aihui 13 2009 Finite dimensional approximations for the electronic ground state solution of a molecular system. Zbl 1119.35095 Zhou, Aihui 12 2007 Orbital-free density functional theory for molecular structure calculations. Zbl 1174.81316 Chen, Huajie; Zhou, Aihui 12 2008 A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappings. Zbl 1231.37042 Ding, Jiu; Jin, Congming; Rhee, Noah H.; Zhou, Aihui 11 2011 Finite volume discretizations for eigenvalue problems with applications to electronic structure calculations. Zbl 1233.65082 Dai, Xiaoying; Gong, Xingao; Yang, Zhang; Zhang, Dier; Zhou, Aihui 11 2011 A symmetric finite volume scheme for selfadjoint elliptic problems. Zbl 1027.65150 Liang, Shengde; Ma, Xiuling; Zhou, Aihui 11 2002 Finite approximations of Markov operators. Zbl 1013.65140 Ding, Jiu; Li, Tien Yien; Zhou, Aihui 9 2002 Fast Boolean approximation methods for solving integral equations in high dimensions. Zbl 1085.65126 Xu, Yuesheng; Zhou, Aihui 8 2004 Three-scale finite element eigenvalue discretizations. Zbl 1157.65061 Gao, X.; Liu, F.; Zhou, A. 8 2008 A multi-parameter splitting extrapolation and a parallel algorithm. Zbl 0895.65058 Zhou, Aihui; Liem, Chin-bo; Shih, Tsi-min; Lü, Tao 8 1997 A conjugate gradient method for electronic structure calculations. Zbl 1378.65120 Dai, Xiaoying; Liu, Zhuang; Zhang, Liwei; Zhou, Aihui 8 2017 Two-scale Boolean Galerkin discretizations for Fredholm integral equations of the second kind. Zbl 1144.65087 Liu, Fang; Zhou, Aihui 7 2007 Multi-level adaptive corrections in finite dimensional approximations. Zbl 1224.65294 Zhou, Aihui 7 2010 A two-scale higher-order finite element discretization for Schrödinger equation. Zbl 1212.65432 Chen, Huajie; Liu, Fang; Zhou, Aihui 7 2009 An analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1099.65116 Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui 7 2006 Adaptive finite element approximations for a class of nonlinear eigenvalue problems in quantum physics. Zbl 1262.35187 Chen, Huajie; Gong, Xingao; He, Lianhua; Zhou, Aihui 7 2011 Characteristic polynomials of some perturbed matrices. Zbl 1154.15011 Ding, Jiu; Zhou, Aihui 6 2008 Error analysis on bi-parameter finite elements. Zbl 0945.65122 Zhou, Aihui; Liem, Chinbo; Shih, Tsimin; Lü, Lao 6 1998 Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation. Zbl 1121.65367 Yang, Ying; Zhou, Aihui 6 2006 Finite volume methods for eigenvalue problems. Zbl 0983.65124 Liang, Shengde; Ma, Xiuling; Zhou, Aihui 6 2001 A sparse finite element method with high accuracy. I. Zbl 0989.65134 Lin, Qun; Yan, Ningning; Zhou, Aihui 6 2001 Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions. Zbl 1167.65064 Dai, Xiaoying; Yang, Zhang; Zhou, Aihui 6 2008 Optimal and superconvergence estimates of the finite element method for a scalar hyperbolic equation. Zbl 0805.65099 Zhou, Aihui; Lin, Qun 6 1994 Hohenberg-Kohn theorem for Coulomb type systems and its generalization. Zbl 1308.81197 Zhou, Aihui 6 2012 Gradient flow based Kohn-Sham density functional theory model. Zbl 1459.37068 Dai, Xiaoying; Wang, Qiao; Zhou, Aihui 6 2020 A multi-parameter splitting extrapolation and a parallel algorithm for elliptic eigenvalue problem. Zbl 0905.65106 Liao, Xiaohai; Zhou, Aihui 5 1998 An analysis of some high accuracy finite element methods for hyperbolic problems. Zbl 1004.65100 Zhou, Aihui 5 2001 Long-time stability of finite element approximations for parabolic equations with memory. Zbl 0931.65136 Allegretto, Walter; Lin, Yanping; Zhou, Aihui 5 1999 A local computational scheme for higher order finite element value approximation. Zbl 1168.65065 Dai, Xiaoying; Shen, Lihua; Zhou, Aihui 5 2008 A spectrum theorem for perturbed bounded linear operators. Zbl 1161.47004 Ding, Jiu; Zhou, Aihui 5 2008 Structure preserving finite element approximations of Markov operators. Zbl 1073.37091 Ding, Jiu; Zhou, Aihui 5 2002 Finite element computation of KPP front speeds in 3D cellular and ABC flows. Zbl 1416.65465 Shen, L.; Xin, J.; Zhou, A. 5 2013 Constructive approximations of Markov operators. Zbl 0991.37004 Ding, Jiu; Zhou, Aihui 4 2001 New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111 Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui 4 2006 Two-scale finite element discretizations for partial differential equations. Zbl 1100.65101 Liu, Fang; Zhou, Aihui 4 2006 On the “preconditioning” function used in planewave DFT calculations and its generalization. Zbl 1388.65195 Zhou, Yunkai; Chelikowsky, James R.; Gao, Xingyu; Zhou, Aihui 4 2015 Some open mathematical problems in electronic structure models and calculations. Zbl 1488.82029 Zhou, Aihui 4 2015 A parallel orbital-updating based optimization method for electronic structure calculations. Zbl 1528.81003 Dai, Xiaoying; Liu, Zhuang; Zhang, Xin; Zhou, Aihui 4 2021 The combination technique for a two-dimensional convection-diffusion problem with exponential layers. Zbl 1212.65443 Franz, Sebastian; Liu, Fang; Roos, Hans-Görg; Stynes, Martin; Zhou, Aihui 4 2009 Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation. Zbl 0858.73076 Zhou, Aihui 3 1996 Extrapolation for finite volume approximations. Zbl 1036.65091 Ma, Xiuling; Mao, Dong; Zhou, Aihui 3 2003 Analysis of finite dimensional approximations to a class of partial differential equations. Zbl 1064.65125 Bao, Gang; Zhou, Aihui 3 2004 Notes on superconvergence and its related topics. Zbl 0790.65095 Lin, Qun; Zhou, Aihui 3 1993 Localizations and parallelizations for two-scale finite element discretizations. Zbl 1141.65079 Liu, Fang; Zhou, Aihui 3 2007 Parallel mesh refinement of higher order finite elements for electronic structure calculations. Zbl 1364.65259 Zhang, Dier; Zhou, Aihui; Gong, Xin-Gao 3 2008 Finite element computation of KPP front speeds in cellular and cat’s eye flows. Zbl 1366.76055 Shen, Lihua; Xin, Jack; Zhou, Aihui 3 2013 Interpolation based local postprocessing for adaptive finite element approximations in electronic structure calculations. Zbl 1218.81044 Fang, Jun; Gao, Xingyu; Gong, Xingao; Zhou, Aihui 2 2011 The projection method for a class of Frobenius-Perron operators. Zbl 0943.47042 Ding, J.; Zhou, A. 2 1999 Parallel computation and domain decomposition for a class of hyperbolic problems. Zbl 0842.65070 Lin, Qun; Yan, Ningning; Zhou, Aihui 2 1995 Multi-parameter error resolution for the collocation method of Volterra integral equations. Zbl 0910.65110 Zhou, Aihui 2 1997 Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem. Zbl 0917.76042 Zhou, Aihui 2 1999 A finite element method for the Frobenius-Perron operator equation. Zbl 0977.65104 Ding, Jiu; Zhou, Aihui 2 1999 Extrapolation for collocation method of the first kind Volterra integral equations. Zbl 0755.65138 Zhou, Aihui 2 1991 Defect correction for finite element gradient. Zbl 0767.65001 Lin, Qun; Zhou, Aihui 2 1992 Accelerating large partial EVD/SVD calculations by filtered block Davidson methods. Zbl 1353.65029 Zhou, Yunkai; Wang, Zheng; Zhou, Aihui 2 2016 Plane wave methods for quantum eigenvalue problems of incommensurate systems. Zbl 1451.81243 Zhou, Yuzhi; Chen, Huajie; Zhou, Aihui 2 2019 A mathematical aspect of Hohenberg-Kohn theorem. Zbl 1409.81189 Zhou, Aihui 2 2019 A finite element recovery approach to eigenvalue approximations with applications to electronic structure calculations. Zbl 1272.65086 Fang, Jun; Gao, Xingyu; Zhou, Aihui 2 2013 Adaptive finite element analysis for semilinear elliptic problems. Zbl 1499.65665 He, Lianhua; Zhou, Aihui 2 2016 A posteriori error estimates for Markov approximations of Frobenius-Perron operators. Zbl 1119.41018 Ding, Jiu; Jin, Congming; Zhou, Aihui 1 2007 Absolutely continuous invariant measures for piecewise \(C^2\) and expanding mappings in higher dimensions. Zbl 1009.37012 Ding, Jiu; Zhou, Aihui 1 2000 Postprocessed two-scale finite element discretizations. I. Zbl 1241.65101 Liu, Fang; Stynes, Martin; Zhou, Aihui 1 2011 Two-scale finite element discretizations for integrodifferential equations. Zbl 1238.65125 Chen, Huajie; Liu, Fang; Reich, Nils; Winter, Christoph; Zhou, Aihui 1 2011 A parallel orbital-updating based optimization method for electronic structure calculations. Zbl 1528.81003 Dai, Xiaoying; Liu, Zhuang; Zhang, Xin; Zhou, Aihui 4 2021 Layer-splitting methods for time-dependent Schrödinger equations of incommensurate systems. Zbl 1482.35188 Wang, Ting; Chen, Huajie; Zhou, Aihui; Zhou, Yuzhi 1 2021 Gradient flow based Kohn-Sham density functional theory model. Zbl 1459.37068 Dai, Xiaoying; Wang, Qiao; Zhou, Aihui 6 2020 Two-grid based adaptive proper orthogonal decomposition method for time dependent partial differential equations. Zbl 1448.65128 Dai, Xiaoying; Kuang, Xiong; Xin, Jack; Zhou, Aihui 1 2020 Plane wave methods for quantum eigenvalue problems of incommensurate systems. Zbl 1451.81243 Zhou, Yuzhi; Chen, Huajie; Zhou, Aihui 2 2019 A mathematical aspect of Hohenberg-Kohn theorem. Zbl 1409.81189 Zhou, Aihui 2 2019 Finite element methods for eigenvalue problems. Zbl 1351.65085 Sun, Jiguang; Zhou, Aihui 32 2017 A conjugate gradient method for electronic structure calculations. Zbl 1378.65120 Dai, Xiaoying; Liu, Zhuang; Zhang, Liwei; Zhou, Aihui 8 2017 Accelerating large partial EVD/SVD calculations by filtered block Davidson methods. Zbl 1353.65029 Zhou, Yunkai; Wang, Zheng; Zhou, Aihui 2 2016 Adaptive finite element analysis for semilinear elliptic problems. Zbl 1499.65665 He, Lianhua; Zhou, Aihui 2 2016 A singularity-based eigenfunction decomposition for Kohn-Sham equations. Zbl 1386.35316 Zhang, Xin; Zhou, Aihui 1 2016 Convergence and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues. Zbl 1332.65159 Dai, Xiaoying; He, Lianhua; Zhou, Aihui 16 2015 On the “preconditioning” function used in planewave DFT calculations and its generalization. Zbl 1388.65195 Zhou, Yunkai; Chelikowsky, James R.; Gao, Xingyu; Zhou, Aihui 4 2015 Some open mathematical problems in electronic structure models and calculations. Zbl 1488.82029 Zhou, Aihui 4 2015 Adaptive finite element approximations for Kohn-Sham models. Zbl 1316.35260 Chen, Huajie; Dai, Xiaoying; Gong, Xingao; He, Lianhua; Zhou, Aihui 32 2014 Gradient type optimization methods for electronic structure calculations. Zbl 1300.82006 Zhang, Xin; Zhu, Jinwei; Wen, Zaiwen; Zhou, Aihui 21 2014 Numerical analysis of finite dimensional approximations of Kohn-Sham models. Zbl 1278.35225 Chen, Huajie; Gong, Xingao; He, Lianhua; Yang, Zhang; Zhou, Aihui 24 2013 Finite element computation of KPP front speeds in 3D cellular and ABC flows. Zbl 1416.65465 Shen, L.; Xin, J.; Zhou, A. 5 2013 Finite element computation of KPP front speeds in cellular and cat’s eye flows. Zbl 1366.76055 Shen, Lihua; Xin, Jack; Zhou, Aihui 3 2013 A finite element recovery approach to eigenvalue approximations with applications to electronic structure calculations. Zbl 1272.65086 Fang, Jun; Gao, Xingyu; Zhou, Aihui 2 2013 A Kohn-Sham equation solver based on hexahedral finite elements. Zbl 1245.82007 Fang, Jun; Gao, Xingyu; Zhou, Aihui 13 2012 Hohenberg-Kohn theorem for Coulomb type systems and its generalization. Zbl 1308.81197 Zhou, Aihui 6 2012 Finite element approximations of nonlinear eigenvalue problems in quantum physics. Zbl 1228.81026 Chen, Huajie; He, Lianhua; Zhou, Aihui 26 2011 Convergence and complexity of adaptive finite element methods for elliptic partial differential equations. Zbl 1263.65103 He, Lianhua; Zhou, Aihui 14 2011 A maximum entropy method based on piecewise linear functions for the recovery of a stationary density of interval mappings. Zbl 1231.37042 Ding, Jiu; Jin, Congming; Rhee, Noah H.; Zhou, Aihui 11 2011 Finite volume discretizations for eigenvalue problems with applications to electronic structure calculations. Zbl 1233.65082 Dai, Xiaoying; Gong, Xingao; Yang, Zhang; Zhang, Dier; Zhou, Aihui 11 2011 Adaptive finite element approximations for a class of nonlinear eigenvalue problems in quantum physics. Zbl 1262.35187 Chen, Huajie; Gong, Xingao; He, Lianhua; Zhou, Aihui 7 2011 Interpolation based local postprocessing for adaptive finite element approximations in electronic structure calculations. Zbl 1218.81044 Fang, Jun; Gao, Xingyu; Gong, Xingao; Zhou, Aihui 2 2011 Postprocessed two-scale finite element discretizations. I. Zbl 1241.65101 Liu, Fang; Stynes, Martin; Zhou, Aihui 1 2011 Two-scale finite element discretizations for integrodifferential equations. Zbl 1238.65125 Chen, Huajie; Liu, Fang; Reich, Nils; Winter, Christoph; Zhou, Aihui 1 2011 Numerical approximations of a nonlinear eigenvalue problem and applications to a density functional model. Zbl 1194.35293 Chen, Huajie; Gong, Xingao; Zhou, Aihui 19 2010 Multi-level adaptive corrections in finite dimensional approximations. Zbl 1224.65294 Zhou, Aihui 7 2010 A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions. Zbl 1188.65153 Liu, Fang; Madden, Niall; Stynes, Martin; Zhou, Aihui 36 2009 Statistical properties of deterministic systems. Zbl 1171.37001 Ding, Jiu; Zhou, Aihui 16 2009 Nonnegative matrices, positive operators, and applications. Zbl 1205.15048 Ding, Jiu; Zhou, Aihui 13 2009 A two-scale higher-order finite element discretization for Schrödinger equation. Zbl 1212.65432 Chen, Huajie; Liu, Fang; Zhou, Aihui 7 2009 The combination technique for a two-dimensional convection-diffusion problem with exponential layers. Zbl 1212.65443 Franz, Sebastian; Liu, Fang; Roos, Hans-Görg; Stynes, Martin; Zhou, Aihui 4 2009 A finite element recovery approach to Green’s function approximations with applications to electrostatic potential computation. Zbl 1157.78002 Yang, Ying; Zhou, Aihui 1 2009 Local and parallel finite element algorithms for the Stokes problem. Zbl 1145.65097 He, Yinnian; Xu, Jinchao; Zhou, Aihui; Li, Jian 88 2008 Convergence and optimal complexity of adaptive finite element eigenvalue computations. Zbl 1159.65090 Dai, Xiaoying; Xu, Jinchao; Zhou, Aihui 86 2008 Three-scale finite element discretizations for quantum eigenvalue problems. Zbl 1160.65060 Dai, Xiaoying; Zhou, Aihui 37 2008 Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh. Zbl 1221.81225 Zhang, Dier; Shen, Lihua; Zhou, Aihui; Gong, Xin-Gao 25 2008 Finite element approximations for Schrödinger equations with applications to electronic structure computations. Zbl 1174.65047 Gong, Xingao; Shen, Lihua; Zhang, Dier; Zhou, Aihui 19 2008 Orbital-free density functional theory for molecular structure calculations. Zbl 1174.81316 Chen, Huajie; Zhou, Aihui 12 2008 Three-scale finite element eigenvalue discretizations. Zbl 1157.65061 Gao, X.; Liu, F.; Zhou, A. 8 2008 Characteristic polynomials of some perturbed matrices. Zbl 1154.15011 Ding, Jiu; Zhou, Aihui 6 2008 Symmetric finite volume schemes for eigenvalue problems in arbitrary dimensions. Zbl 1167.65064 Dai, Xiaoying; Yang, Zhang; Zhou, Aihui 6 2008 A local computational scheme for higher order finite element value approximation. Zbl 1168.65065 Dai, Xiaoying; Shen, Lihua; Zhou, Aihui 5 2008 A spectrum theorem for perturbed bounded linear operators. Zbl 1161.47004 Ding, Jiu; Zhou, Aihui 5 2008 Parallel mesh refinement of higher order finite elements for electronic structure calculations. Zbl 1364.65259 Zhang, Dier; Zhou, Aihui; Gong, Xin-Gao 3 2008 Finite element computations of Kolmogorov-Petrovsky-Piskunov front speeds in random shear flows in cylinders. Zbl 1400.76096 Shen, Lihua; Xin, Jack; Zhou, Aihui 1 2008 Eigenvalues of rank-one updated matrices with some applications. Zbl 1139.15003 Ding, Jiu; Zhou, Aihui 53 2007 Finite dimensional approximations for the electronic ground state solution of a molecular system. Zbl 1119.35095 Zhou, Aihui 12 2007 Two-scale Boolean Galerkin discretizations for Fredholm integral equations of the second kind. Zbl 1144.65087 Liu, Fang; Zhou, Aihui 7 2007 Localizations and parallelizations for two-scale finite element discretizations. Zbl 1141.65079 Liu, Fang; Zhou, Aihui 3 2007 A posteriori error estimates for Markov approximations of Frobenius-Perron operators. Zbl 1119.41018 Ding, Jiu; Jin, Congming; Zhou, Aihui 1 2007 Local and parallel finite element algorithms for the Navier-Stokes problem. Zbl 1093.76035 He, Yinnian; Xu, Jinchao; Zhou, Aihui 83 2006 Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates. Zbl 1103.65112 Mao, Dong; Shen, Lihua; Zhou, Aihui 28 2006 Enhancing eigenvalue approximation by gradient recovery. Zbl 1148.65087 Naga, Ahmed; Zhang, Zhimin; Zhou, Aihui 24 2006 A defect correction scheme for finite element eigenvalues with applications to quantum Chemistry. Zbl 1104.65323 Shen, Lihua; Zhou, Aihui 17 2006 An analysis of discontinuous Galerkin methods for elliptic problems. Zbl 1099.65116 Schneider, Reinhold; Xu, Yuesheng; Zhou, Aihui 7 2006 Local averaging based a posteriori finite element error control for quasilinear elliptic problems with application to electrical potential computation. Zbl 1121.65367 Yang, Ying; Zhou, Aihui 6 2006 New error estimates of biquadratic Lagrange elements for Poisson’s equation. Zbl 1091.65111 Huang, Hung-Tsai; Li, Zi-Cai; Zhou, Aihui 4 2006 Two-scale finite element discretizations for partial differential equations. Zbl 1100.65101 Liu, Fang; Zhou, Aihui 4 2006 Superconvergence and extrapolation of non-conforming low order finite elements applied to the Poisson equation. Zbl 1068.65122 Lin, Qun; Tobiska, Lutz; Zhou, Aihui 143 2005 An analysis of finite-dimensional approximations for the ground state solution of Bose-Einstein condensates. Zbl 1051.35094 Zhou, Aihui 23 2004 Fast Boolean approximation methods for solving integral equations in high dimensions. Zbl 1085.65126 Xu, Yuesheng; Zhou, Aihui 8 2004 Analysis of finite dimensional approximations to a class of partial differential equations. Zbl 1064.65125 Bao, Gang; Zhou, Aihui 3 2004 Symmetric finite volume discretizations for parabolic problems. Zbl 1038.65079 Ma, Xiuling; Shu, Shi; Zhou, Aihui 28 2003 Extrapolation for finite volume approximations. Zbl 1036.65091 Ma, Xiuling; Mao, Dong; Zhou, Aihui 3 2003 A note on the optimal \(L^2\)-estimate of the finite volume element method. Zbl 0997.65122 Chen, Zhongying; Li, Ronghua; Zhou, Aihui 55 2002 Local and parallel finite element algorithms for eigenvalue problems. Zbl 1015.65060 Xu, Jinchao; Zhou, Aihui 49 2002 A symmetric finite volume scheme for selfadjoint elliptic problems. Zbl 1027.65150 Liang, Shengde; Ma, Xiuling; Zhou, Aihui 11 2002 Finite approximations of Markov operators. Zbl 1013.65140 Ding, Jiu; Li, Tien Yien; Zhou, Aihui 9 2002 Structure preserving finite element approximations of Markov operators. Zbl 1073.37091 Ding, Jiu; Zhou, Aihui 5 2002 A two-grid discretization scheme for eigenvalue problems. Zbl 0959.65119 Xu, Jinchao; Zhou, Aihui 162 2001 Local and parallel finite element algorithms based on two-grid discretizations for nonlinear problems. Zbl 0990.65128 Xu, Jinchao; Zhou, Aihui 84 2001 Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes. Zbl 0986.65098 Yan, Ningning; Zhou, Aihui 32 2001 Finite volume methods for eigenvalue problems. Zbl 0983.65124 Liang, Shengde; Ma, Xiuling; Zhou, Aihui 6 2001 A sparse finite element method with high accuracy. I. Zbl 0989.65134 Lin, Qun; Yan, Ningning; Zhou, Aihui 6 2001 An analysis of some high accuracy finite element methods for hyperbolic problems. Zbl 1004.65100 Zhou, Aihui 5 2001 Constructive approximations of Markov operators. Zbl 0991.37004 Ding, Jiu; Zhou, Aihui 4 2001 On estimating absolutely continuous invariant measures. Zbl 1031.37004 Ding, Jiu; Zhou, Aihui 1 2001 Local and parallel finite element algorithms based on two-grid discretizations. Zbl 0948.65122 Xu, Jinchao; Zhou, Aihui 143 2000 Absolutely continuous invariant measures for piecewise \(C^2\) and expanding mappings in higher dimensions. Zbl 1009.37012 Ding, Jiu; Zhou, Aihui 1 2000 A box scheme for coupled systems resulting from microsensor thermistor problems. Zbl 0979.78023 Allegretto, Walter; Lin, Yanping; Zhou, Aihui 21 1999 Error analysis of the combination technique. Zbl 0942.65122 Pflaum, C.; Zhou, A. 19 1999 Long-time stability of finite element approximations for parabolic equations with memory. Zbl 0931.65136 Allegretto, Walter; Lin, Yanping; Zhou, Aihui 5 1999 The projection method for a class of Frobenius-Perron operators. Zbl 0943.47042 Ding, J.; Zhou, A. 2 1999 Multi-parameter asymptotic error resolution of the mixed finite element method for the Stokes problem. Zbl 0917.76042 Zhou, Aihui 2 1999 A finite element method for the Frobenius-Perron operator equation. Zbl 0977.65104 Ding, Jiu; Zhou, Aihui 2 1999 Multi-parameter extrapolation methods for boundary integral equations. Zbl 0922.65075 Rüde, Ulrich; Zhou, Aihui 14 1998 Error analysis on bi-parameter finite elements. Zbl 0945.65122 Zhou, Aihui; Liem, Chinbo; Shih, Tsimin; Lü, Lao 6 1998 A multi-parameter splitting extrapolation and a parallel algorithm for elliptic eigenvalue problem. Zbl 0905.65106 Liao, Xiaohai; Zhou, Aihui 5 1998 Invariant measures and their computation. Zbl 1054.37500 Ding, Jiu; Zhou, Aihui 1 1998 A multi-parameter splitting extrapolation and a parallel algorithm. Zbl 0895.65058 Zhou, Aihui; Liem, Chin-bo; Shih, Tsi-min; Lü, Tao 8 1997 Multi-parameter error resolution for the collocation method of Volterra integral equations. Zbl 0910.65110 Zhou, Aihui 2 1997 Finite approximations of Frobenius-Perron operators. A solution of Ulam’s conjecture to multi-dimensional transformations. Zbl 0890.58035 Ding, Jiu; Zhou, Aihui 29 1996 Global superconvergence approximations of the mixed finite element method for the Stokes problem and the linear elasticity equation. Zbl 0858.73076 Zhou, Aihui 3 1996 Piecewise linear Markov approximations of Frobenius-Perron operators associated with multi-dimensional transformations. Zbl 0907.47025 Ding, Jiu; Zhou, Ai Hui 19 1995 ...and 9 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,222 Authors 72 Shi, Dongyang 50 Yang, Yidu 48 Zhou, Aihui 46 Ding, Jiu 36 Shang, Yueqiang 36 Xie, Hehu 34 Bi, Hai 32 Xu, Fei 29 Huang, Yunqing 24 Du, Guangzhi 22 Chen, Yanping 21 Zhang, Zhimin 20 He, Yinnian 19 Huang, Qiumei 18 Rhee, Noah H. 16 Han, Jiayu 15 Li, Jian 15 Lin, Qun 14 Li, Yonghai 14 Yan, Ningning 13 Chen, Huajie 13 Hu, Jun 12 Carstensen, Carsten 12 Guan, Hongbo 12 Hu, Guanghui 12 Sun, Jiguang 12 Zuo, Liyun 11 Ma, Hongkun 11 Zhang, Yu 10 Chen, Chuanjun 10 Hou, Yanren 10 Jia, Shanghui 10 Li, Jichun 10 Zhao, Yanmin 9 Dai, Xiaoying 9 Demlow, Alan 9 Jin, Congming 9 Li, Zi-Cai 9 Xie, ManTing 9 Xu, Yuesheng 8 Bi, Chunjia 8 Feng, Xinlong 8 Gong, Wei 8 Hu, Hanzhang 8 Liu, Huipo 8 Shu, Shi 8 Zhang, Tie 7 Chen, Luoping 7 Huang, Jin 7 Madden, Niall 7 Shi, Zhongci 7 Wang, Fenling 7 Wang, Yang 7 Xu, Jinchao 7 Yang, Ying 7 Yue, Meiling 7 Zhang, Houchao 7 Zhang, Shuhua 7 Zheng, Haibiao 6 Bollt, Erik M. 6 Chen, Zhangxin 6 Chien, Cheng-Sheng 6 Gao, Xingyu 6 Gavini, Vikram 6 Gedicke, Joscha 6 Guo, Hailong 6 Huang, Hung-Tsai 6 Stynes, Martin Joseph 6 Tang, Qili 6 Wang, Cheng 6 Wang, Shixi 6 Wang, Xiang 6 Weng, Zhifeng 6 Xu, Chao 6 Yang, Huaijun 6 Yang, Min 6 Zhang, Shuo 6 Zhang, Tong 5 Bao, Gang 5 Cancès, Eric 5 Chen, Hongtao 5 Fang, Jun 5 Froyland, Gary 5 Giani, Stefano 5 Gong, Bo 5 Guo, Yukun 5 He, Xiaoming 5 Lin, Lin 5 Luo, Fusheng 5 Lv, Junliang 5 Mao, Shipeng 5 Meng, XiangYun 5 Motamarri, Phani 5 Ovall, Jeffrey S. 5 Pei, Lifang 5 Perotto, Simona 5 Shanthi, Vembu 5 Shiromani, Ram 5 Si, Zhiyong 5 Temizer, Ilker ...and 1,122 more Authors all top 5 Cited in 163 Serials 76 Journal of Scientific Computing 73 Computers & Mathematics with Applications 56 Applied Mathematics and Computation 55 Journal of Computational and Applied Mathematics 43 Journal of Computational Physics 41 Advances in Computational Mathematics 40 Applied Numerical Mathematics 36 Mathematics of Computation 30 Numerische Mathematik 28 Numerical Methods for Partial Differential Equations 27 Numerical Algorithms 25 Computer Methods in Applied Mechanics and Engineering 22 Advances in Applied Mathematics and Mechanics 22 Science China. 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Commentarii Mathematici ...and 63 more Serials all top 5 Cited in 50 Fields 908 Numerical analysis (65-XX) 487 Partial differential equations (35-XX) 178 Fluid mechanics (76-XX) 64 Dynamical systems and ergodic theory (37-XX) 45 Mechanics of deformable solids (74-XX) 42 Linear and multilinear algebra; matrix theory (15-XX) 42 Quantum theory (81-XX) 39 Calculus of variations and optimal control; optimization (49-XX) 38 Optics, electromagnetic theory (78-XX) 35 Integral equations (45-XX) 33 Operator theory (47-XX) 32 Statistical mechanics, structure of matter (82-XX) 19 Probability theory and stochastic processes (60-XX) 19 Operations research, mathematical programming (90-XX) 15 Approximations and expansions (41-XX) 15 Statistics (62-XX) 13 Computer science (68-XX) 10 Combinatorics (05-XX) 10 Biology and other natural sciences (92-XX) 9 Ordinary differential equations (34-XX) 9 Systems theory; control (93-XX) 7 Measure and integration (28-XX) 6 Potential theory (31-XX) 5 Classical thermodynamics, heat transfer (80-XX) 5 Information and communication theory, circuits (94-XX) 4 Real functions (26-XX) 4 Global analysis, analysis on manifolds (58-XX) 4 Mechanics of particles and systems (70-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 3 Number theory (11-XX) 3 Difference and functional equations (39-XX) 3 Geophysics (86-XX) 2 Commutative algebra (13-XX) 2 Associative rings and algebras (16-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Functional analysis (46-XX) 2 Convex and discrete geometry (52-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Nonassociative rings and algebras (17-XX) 1 Group theory and generalizations (20-XX) 1 Functions of a complex variable (30-XX) 1 Special functions (33-XX) 1 Integral transforms, operational calculus (44-XX) 1 General topology (54-XX) 1 Algebraic topology (55-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) Citations by Year