Home Research Teaching Publications
List
of Publications
Submitted:
A pathway-based mean-field model for E. coli chemotaxis: Mathematical derivation and Keller-Segel limit (with Guangwei Si and Min Tang)
Computation of the Schrödinger equation in the semiclassical regime on unbounded domain (with Jiwei Zhang)
Accepted:
Seismic modeling using the frozen Gaussian approximation (with Jianfeng Lu and Sergey Fomel), to appear in the conference abstract of SEG International Exposition and Eighty-Third Annual Meeting.
Exponential Runge-Kutta methods for the multispecies Boltzmann equation (with Qin Li), Commun. Comput. Phys., to appear.
Asymptotic analysis of the quantum dynamics in crystals: The Bloch-Wigner transform, Bloch dynamics and Berry phase (with Weinan E and Jianfeng Lu), Acta Math. Appl. Sin. Engl. Ser., to appear.
In Refereed Journals:
2013
[22] Eulerian Gaussian beam method for high frequency wave propagation in the reduced momentum space (with Hao Wu), Wave Motion, 50, 1036--1049, 2013
2012
[21] Eulerian Gaussian beam method for high frequency wave propagation in heterogeneous media with discontinuities in one direction (with Dongming Wei), Commun. Math. Sci.,10, 1287--1299, 2012.
[20] Tailored finite cell method for computing Helmholtz equation in layered heterogeneous medium (with Zhongyi Huang), J. Comput. Math., 30, 381--391, 2012.
[19] Frozen Gaussian approximation for general linear strictly hyperbolic systems: Formulation and Eulerian methods (with Jianfeng Lu), Multiscale Model. Simul., 10, 451--472, 2012.
[18] Convergence of frozen Gaussian approximation for high frequency wave propagation (with Jianfeng Lu), Comm. Pure Appl. Math., 65, 759--789, 2012.
2011
[17] Tailored finite point methods for first order wave equation (with Zhongyi Huang), J. Sci. Comput., 49, 351--366, 2011.
[16] A hybrid phase-flow method for solving the Liouville equation in bounded domain (with Hao Wu), SIAM J. Numer. Anal., 49, 733--754, 2011.
[15] Frozen Gaussian approximation for high frequency wave propagation (with Jianfeng Lu), Commun. Math. Sci., 9, 663--683, 2011.
[14] Effective Maxwell equations from time-dependent density functional theory (with Weinan E and Jianfeng Lu), Acta Math. Sin., 27, 339--368, 2011.
[13] Semi-Eulerian and high order Gaussian beam methods for the Schrödinger equation in the semiclassical regime (with Shi Jin and Hao Wu), Commun. Comput. Phys., 9, 668--687, 2011.
2010
[12] A level set method for the semiclassical limit of the Schrödinger equation with discontinuous potentials (with Dongming Wei, Shi Jin and Richard Tsai), J. Comput. Phys., 229, 7440--7455, 2010.
[11] Bloch decomposition-based Gaussian beam method for the Schrödinger equation with periodic potentials (with Shi Jin, Hao Wu, and Zhongyi Huang), J. Comput. Phys., 229, 4869--4883, 2010.
[10] A numerical study of the Gaussian beam methods for one-dimensional Schrödinger-Poisson equations (with Shi Jin and Hao Wu), J. Comput. Math., 28, 261--272, 2010.
2008
[9] Gaussian beam methods for the Schrödinger equation in the semi-classical regime: Lagrangian and Eulerian formulations (with Shi Jin and Hao Wu), Commun. Math. Sci., 6, 995--1020, 2008.
[8] The Vlasov-Poisson equations as the semiclassical limit of the Schrödinger-Poisson equations: A numerical study (with Shi Jin and Xiaomei Liao), J. Hyperbolic Differ. Equ., 5, 569--587, 2008.
[7] Computation of the semiclassical limit of the Schrödinger equation with phase shift by a level set method (with Shi Jin), J. Sci. Comput., 35, 144--169, 2008.
[6] A simple model for biological aggregation with asymmetric sensing (with Paul A. Milewski), Commun. Math. Sci., 6, 397--416, 2008.
[5] Computation of interface reflection and regular or diffuse transmission of the planar symmetric radiative transfer equation with isotropic scattering and its diffusion limit (with Shi Jin and Xiaomei Liao), SIAM J. Sci. Comput., 30, 1992--2017, 2008.
[4] A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface (with Shi Jin and Guangwei Yuan), Kinet. Relat. Models, 1, 65--84, 2008.
2006
[3] Numerical study of a domain decomposition method for a two-scale linear transport equation (with Francois Golse, Zhongyi Huang and Shi Jin), Netw. Heterog. Media, 1, 143--166, 2006.
[2] On the forward and inverse displacement of spatial parallel manipulators (with Jingshan Zhao, Liang Zhu, Zhijing Feng and Kai Zhou), Int. J. Adv. Manuf. Technol., 29, 1284--1294, 2006.
[1] Wavelet-Galerkin method for reaction-diffusion equation (with Zhongyi Huang and Liang Zhu), J. Tsinghua Univ., 46, 392--395, 2006, (in Chinese).