Books and Special Issues
- Numerical Analysis, Higher Education Press,
Beijing, 2023(in Chinese)
- Finite Element Methods for Eigenvalue Problems,
Monographs and Research Notes in Mathematics, CRC Press,
Boca Raton, 2017 (with J. Sun)
- Special Issue Dedicated to the 80th Birthday of Professor Qun Lin,
Sci. Sin. Math., 45 (2015), 829-1360
(with Z. Chen and J. Xu)(in Chinese)
- Nonnegative Matrices, Positive Operators, and Applications,
World Scientific, New Jersey, 2009(with J. Ding)
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Statistical Properties of Deterministic Systems, Springer-Verlag, Berlin;
Tsinghua University Press, Beijing, 2009(with J. Ding)
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Statistical Properties of Deterministic Systems, Tsinghua
University Press, Beijing, 2006(with J. Ding)(in Chinese)
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A Posteriori Error Estimation and Adaptive Computational
Methods, Advances in Computational Mathematics,
15(2001), 1-404
Selected Articles
- Mathematical analysis and numerical approximations of density functional theory models for metallic systems,
Multiscale Model. Simul., 21 (2023), 777-803 (with X. Dai, S. de Gironcoli, and B. Yang)
- Gradient flow based discretized Kohn-Sham density functional theory, Multiscale Model. Simul., 18(2020), 1621-1663
(with X. Dai and Q. Wang)
- Plane wave methods for quantum eigenvalue problems of incommensurate systems, J. Comput. Phys., 384
(2019), 99-113 (with Y. Zhou and H. Chen)
- A conjugate gradient method for electronic structure calculations, SIAM J. Sci. Comput., 39 (2017),
A2702-A2740 (with X. Dai, Z. Liu, and L. Zhang)
- A parallel orbital-updating approach for electronic structure calculations, arXiv:1405.0260
(with X. Dai, X. Gong, and J. Zhu)
- Convergence and quasi-optimal complexity of adaptive finite element computations for multiple eigenvalues,
IMA J. Numer. Anal.,35(2015), 1934-1977, arXiv:1210.1846 (with X. Dai and L. He)
- Adaptive finite element approximations for Kohn-Sham models,
Multiscale Model. Simul., 12(2014), 1828-1869, arXiv:1302.6896
(with H. Chen, X. Dai, X. Gong, and L.He)
- Accuracy of generalized gradient approximation functionals for density
functional perturbation theory calculations, Phys. Rev. B., 89(2014), 064305-064320
(with L. He, F. Liu, G. Hautier, M. J. T. Oliveira, M. A. L. Marques,
F. D. Vila, J. J. Rehr, and G.-M. Rignanese)
- Gradient type optimization methods for electronic structure calculations, SIAM J. Sci.
Comput., 36(2014), C265-C289 (with X. Zhang, J. Zhu, and Z. Wen)
- A symmetry-based decomposition approach to eigenvalue problems, J. Sci. Comput., 57(2013), 638-669
(with J. Fang and X. Gao)
- Numerical analysis of finite dimensional approximations of Kohn-Sham models, Adv. Comput. Math.,
38(2013),225-256, arXiv:1108.1891 (with H. Chen, X. Gong, L. He, and Z. Yang)
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Hohenberg-Kohn theorem for Coulomb type systems and its generalization, J. Math. Chem., 50(2012),2746-2754
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Finite element approximations of nonlinear eigenvalue problems
in quantum physics, Comput. Meth. Appl. Mech. Engrg.,
200(2011), 1846-1865 ( with H. Chen and L. He)
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Finite volume discretizations for eigenvalue problems with
applications to electronic structure calculations, Multiscale
Model. Simul., 9(2011), 208-240 (with X. Dai, X. Gong, Z. Yang, and D. Zhang)
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Convergence and complexity of adaptive finite element methods for elliptic
partial differential equations, Int. J. Numer. Anal. Model., 8(2011), 615-640 (with L. He)
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Numerical approximations of a nonlinear eigenvalue problem and
applications to a density functional model, Math. Methods Applied Sci.,
33(2010), 1723-1742 (with H. Chen and X. Gong)
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Convergence and optimal complexity of adaptive finite element
eigenvalue computations, Numer. Math., 110(2008), 313-355 (with
X. Dai and J. Xu)
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Three-scale finite element discretizations for quantum eigenvalue
problems, SIAM J. Numer. Anal., 46(2008), 295-324 (with X. Dai)
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Two-scale Boolean Galerkin discretizations for Fredholm integral
equations of the second kind, SIAM J. Numer. Anal., 45(2007),
296-312 (with F. Liu)
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Finite dimensional approximations for the electronic ground state
solution of a molecular system, Math. Methods Applied Sci.,
30(2007), 429-447
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A defect correction scheme for finite element eigenvalues
with applications to quantum chemistry, SIAM J. Sci. Comput.,
28(2006), 321-338 (with L. Shen)
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An analysis for finite dimensional approximations for the
ground state solution of Bose-Einstein condensates,
Nonlinearity, 17(2004), 541-550
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Local and parallel finite element algorithms based on two-grid
discretizations, Math. Comp., 69(2000), 881-909 (with J. Xu)
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Error analysis of the combination technique, Numer. Math., 84(1999),
327-350 (with C. Pflaum)
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Error analysis on bi-parameter finite elements, Comput. Meth. Appl.
Mech. Engrg., 158(1998), 329-339 (with C. Liem, T.-M. Shih and T. Lu)
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Finite approximations of Frobenius-Perron operators--a solution of
Ulam's conjecture to multi-dimensional transformations, Phys. D,
92(1996), 61-68(with J. Ding)
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Optimal and superconvergence estimates of the finite element
approximation for a scalar hyperbolic equation, Acta Math. Sci.,
14(1994), 90-94 (with Q. Lin)