Department of Mathematics, Penn State University, Sep. 2008--Oct. 2008; Max Planck Institute for Mathematics in the Sciences at Leipzig, March 2006--May 2006; PACM, Princeton University, Feb. 2003--Dec. 2003 and Dec. 2004.-Feb. 2005; Ruhr-University, Bochum (Alexander von Humboldt Research Fellow) Nov. 2000-
Mar. 2002; Alexander von Humboldt Foundation; Hong Kong University of Science and Technology, Sep.-Oct. 2000, Oct.-Dec. 2004 and Feb.-Mar. 2006
Research Interests
Multiscale modeling and simulation
Numerical homogenization and optimal design
Numerical analysis and scientific computing
Selected Publications
Heterogeneous multiscale finite element method with novel numerical integration schemes (with R. Du)
Comm. Math. Sci., to appear,
pdf
Shear Locking in a plane elasticity problem and the enhanced assumed strain method (with D. Braess and Z.-C. Shi)
SIAM J. Numer. Anal., Vol. 47, 4473--4491,
pdf
Analysis of a one-dimensional nonlocal quasicontinuum method (with Zhijian Yang)
Multiscale Model. Simul., 2009, Vol. 7, 1838--1875,
pdf
Error estimate of force-based quasicontinuum method Comm. Math. Sci., 2008, Vol. 5 1089--1095,
pdf
Cascadic multigrid methods for parabolic problems (with Q. Du), Sci. in China Ser. A: Math. 2008, Vol. 51 1415--1439
pdf
A generalized Peierls-Nabarro model for curved dislocations and
core structures of dislocation loops in Al and Cu (with Yang Xiang, He Wei and W. E), Acta Materialia, 2008, Vol 56, 1447--1460
pdf
A generalized Peierls-Nabarro model for
curved dislocations with discrete Fourier transform (with He Wei and Yang Xiang), Commun. Comput. Phys. 2008, Vol 4, 275--293,pdf
Ab initio calculation of ideal strength and phonon instability of
graphene in tension (with F. Liu and J. Li) Phy. Rev. B 2007, Vol. 76, 064120
pdf
Cauchy-Born rule and the stability of the crystalline solids: dynamic problems(with W. E)
Acta Math. Appl. Sin. Engl. Ser., 2007, Vol. 23, 529--550
pdf
Cauchy-Born rule and the stability of the crystalline solids: static problems(with W. E)
Arch. Rational Mech. Anal., 2007, Vol. 183, 241-297
pdf
Analysis of the heterogeneous multiscale method for parabolic homogenization problems
(with P.-W. Zhang) Math. Comp., 2007, Vol. 76, 153-177
pdf
Analysis of some low order quadrilateral Reissner-Mindlin plate elements
(with Z.-C. Shi) Math. Comp., 2006, Vol. 75, 1043-1065
pdf
Numerical methods for multiscale elliptic problems
(with Xingye Yue) J. Comput. Phys., 2006, Vol. 214, 421-445
pdf
Analysis of the local quasicontinuum methods
(with W. E) In Frontiers and
Prospects of Contemporary Applied Mathematics, Tatisen Li and Pingwen Zhang eds, Higher
Education Press, World Scientific, Singapore, 2005, pp. 18-32.
pdf
Two nonconforming quadrilateral elements for the Reissner-Mindlin plate
(with Z.-C. Shi) Math. Model Meth.
Appl. Sci., 2005, Vol. 15, 1503-1518
pdf
Analysis of the heterogeneous multiscale method for elliptic homogenization problems
(with W. E and P.-W. Zhang) J. AMS., 2005, Vol. 18, 121-156
pdf
A finite element method for nearly incompressible elasticity problem
(with D. Braess) Math. Comp., 2005, Vol. 74, 25-52.
pdf
Analysis of multiscale problem (with W. E) J. Comput. Math., 2004 Vol. 22, 210-219.pdf
