NAV
Shi Jin（金石）

Publications

Google Scholar Citation data

Most Cited Mathematicians by Years of Ph.D. Degree (based on citation data from MathSciNet)

In refereed journals

Submitted

[252] Shi Jin, Nana Liu, Yue Yu, Quantum Circuits for the heat equation with physical boundary conditions via Schrodingerisation, preprint.

[251] Tian-ai Zhang, Shi Jin, AP-MIONet: Asymptotic-preserving multiple-input neural operators for capturing the high-field limits of collisional kinetic equations, preprint.

[250] Weihang Gao, Teng Zhao, Yongfa Guo, Jiuyang Liang, Huan Liu, Maoying Luo, Zedong Luo, Wei Qin, Yichao Wang, Qi Zhou, Shi Jin, Zhenli Xu,RBMD: A molecular dynamics package enabling to simulate 10 million all-atom particles in a single graphics processing unit, preprint.

[249] Shi Jin, Nana Liu, Analog quantum simulation of parabolic partial differential equations using Jaynes-Cummings-like models, preprint.

[248] Chunhui Chen, Jing Chen, Baojia Luo, Shi Jin, Hao Wu, A numerical algorithm with linear complexity for Multi-marginal Optimal Transport with L1 Cost, preprint.

[247] J. A. Carrillo, Shi Jin, Haoyu Zhang, Yuhua Zhu, An interacting particle consensus method for constrained global optimization, preprint.

[246] Shi Jin, Nana Liu, Yue Yu, Quantum simulation of the Fokker-Planck equation via Schrodingerization, preprint.

[245] Shi Jin, Nana Liu and Chuwen Ma, Schrödingerisation based computationally stable algorithms for ill-posed problems in partial differential equations, preprint.

[244] Junpeng Hu, Shi Jin, Nana Liu, Lei Zhang, Quantum Circuits for partial differential equations via Schrödingerisation, preprint.

[243] Shi Jin, Nana Liu and Chuwen Ma, On Schrödingerization based quantum algorithms for linear dynamical systems with inhomogeneous terms, preprint.

[242] Zhenyu Huang, Shi Jin, and Lei Li, Mean field error estimate of the random batch method for large interacting particle systems, preprint.

[241] Yu Cao, Shi Jin and Nana Liu, Quantum simulation for time-dependent Hamiltonians -- with applications to non-autonomous ordinary and partial differential equations, preprint.

[240] Shi Jin, Nana Liu and Yue Yu, Quantum simulation of partial differential equations via Schrodingerisation, preprint

[239] Francois Golse, Shi Jin and Nana Liu, Quantum algorithms for uncertainty quantification: application to partial differential equations, preprint

Accepted

[238] Shi Jin, Nana Liu, Chuwen Ma, Quantum simulation of Maxwell's equations via Schrödingersation, Math. Model Num. Anal., to appear.

[237] Shi Jin and Nana Liu, Analog quantum simulation of partial differential equations, Quantum Sci. Tech., to appear.

[236] Junpeng Hu, Shi Jin, Lei Zhang, Quantum algorithms for multiscale partial differential equations, (SIAM) Multiscale Model. Simulation, to appear.

[235] Shi Jin and Yiwen Lin, Energy estimates and hypocoercivity analysis for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with uncertainty, Comm. Comp. Phys., to appear.

[234] Shi Jin and Xiantao Li, A partially random algorithm for quantum Hamiltonian simulations, Comm. Applied Math. and Comp. (A special issue in memory of Prof. Zhong-ci Shi), to appear.

2024

[233] Shi Jin and Nana Liu, Quantum simulation of discrete linear dynamical systems and simple iterative methods in linear algebra via Schrodingerisation, Proc. Royal Soc. London A, 480, 20230370, 2024.

[232] Shi Jin, Xiantao Li， Nana Liu and Yue Yu, Quantum Simulation for Quantum Dynamics with Artificial Boundary Conditions, SIAM J. Sci. Comp., 46， B403–B421， 2024.

[231] Yiwen Lin, Shi Jin, Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs, Kinetic and Related Models 17, 807-837， 2024.

[230] Shi Jin and Nana Liu, Quantum algorithms for nonlinear partial differential equations, Bull. Math. Sci., 194，103457， 2024.

[229] Shi Jin, Zheng Ma, Tian-ai Zhang, Asymptotic-preserving neural networks for multiscale Vlasov-Poisson-Fokker-Planck system in the high-field regime, J. Sci. Comput. 99， no. 3, Paper No. 61, 2024.

[228] Chuwen Ma and Shi Jin, An implicit, asymptotic-preserving and energy-charge-conserving method for the Vlasov-Maxwell system near quasineutrality, Comm. Comp. Phys., 35 (2024), no. 3, 724–760

[227] Shi Jin, Zheng Ma and Keke Wu, Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations, Commun. Comput. Phys. 35, 693–723, 2024.

[226] Shi Jin and Yiwen Lin, Asymptotic-preserving schemes for kinetic-fluid modeling of mixture flows with distinct particle sizes, J. Diff. Eqs., 400, 110–145, 2014.

[225] Hanzhi Zhao, Suming Weng, Zhengming Sheng, Shi Jin, Jie Zhang,A Vlasov-Fokker-Planck-Landau code for the simulation of colliding supersonic dense plasma flows, J. Comp. Phys. 503, 112843, 2024.

[224] Shi Jin, Xiaotao Li, Nana Liu and Yue Yu, Quantum Simulation for Partial Differential Equations with Physical Boundary or Interface Conditions, J. Comp. Phys., 498，Paper No. 112707， 2024.

[223] Keke Wu, Xiong-bin Yan, Shi Jin, Zheng Ma, Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONet, Comput. Methods Appl. Mech. Engrg. 418, Paper No. 116531， 2024.

[222] Qichen Liao, Jing Chen, Zihao Wang, Bo Bai, Shi Jin and Hao Wu, Fast Sinkhorn II: Collinear triangular matrix and linear time accurate computation of optimal transport, J. Sci. Comput. 98, no. 1, Paper No. 1， 2024.

2023

[221] Jingrun Chen, Shi Jin and Liyao Lyu, A Deep Learning Based Discontinuous Galerkin Method for Hyperbolic Equations with Discontinuous Solutions and Random Uncertainties, J. Comput. Math. 41, no. 6, 1281–1304。 2023.

[220] Shi Jin, Nana Liu and Yue Yu, Quantum simulation of partial differential equations: Applications and detailed analysis, Phys. Rev. A 108 (2023), no. 3, Paper No. 032603.

[219] Xiaoyang He, Shi Jin and Yue Yu, Time complexity analysis of quantum difference methods for the multiscale transport equations, East Asian J. Appl. Math., 13, p717-739, 2023 (A special issue on the occasion of the 60th birthday of Prof. Tao Tang).

[218] Lijie Ji, Zhiguo Yang, Zhuoning Li, Dong Wu, Shi Jin, and Zhenli Xu, An Asymptotic-Preserving and Energy-Conserving Particle-In-Cell Method for Vlasov-Maxwell Equations, J. Math. Phys. 64, 2023,  Paper No. 063503.

[217] Shi Jin, Nana Liu and Yue Yu, Time complexity analysis of quantum algorithms via linear representations for nonlinear ordinary and partial differential equations, J. Comput. Phys. 487， 112149， 2023.

[216] Yuelin Wang, Kai Yi, Xinliang Liu, Yu Guang Wang and Shi Jin, ACMP: Allen-Cahn Message Passing for Graph Neural Networks with Particle Phase Transition, ICLR (spotlight), 2023.

[215] Shi Jin, Lei Li, Xuda Ye, Zhennan Zhou, Ergodicity and long-time behavior of the Random Batch Method for interacting particle systems, Math. Model. Math. Appl. Sci., Math. Models Methods Appl. Sci. 33, 67–102， 2023.

[214] Shi Jin, Zheng Ma and Keke Wu, Asymptotic-Preserving Neural Networks for Multiscale Time-Dependent Linear Transport Equation,  J. Sci. Comput. 94 (2023), no. 3, Paper No. 57.

[213] Junpeng Hu, Shi Jin, Jinglai Li and Lei Zhang,On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems, J. Comp. Phys., 475 (2023), Paper No. 111847.

2022

[212] Qichen Liao, Jing Chen, Zihao Wang, Bo Bai, Shi Jin and Hao Wu,Fast Sinkhorn I: An O(N) algorithms for the Wasserstein-1 metric, Comm. Math. Sci., 20， 2053-2067， 2022.

[211] Boyang Ye, Shi Jin, Yulong Xing and Xinghui Zhong,Hamiltonian-preserving discontinuous Galerkin methods for the Liouville equation with discontinuous potential, SIAM J. Sci. Comput.,44， A3317–A3340， 2022.

[210] Shi Jin, Nana Liu and Yue Yu, Time complexity analysis of quantum difference methods for linear high dimensional and multiscale partial differential equations, J. Comp. Phys.  471,  Paper No. 111641, 2022.

[209] Shi Jin, Lei Li and Yiqun Sun, On the Random Batch Method for second order interacting particle systems, Multiscale Model. Simult. 741–768, 2022.

[208] Jiuyang Liang, Pan Tan, Liang Hong, Shi Jin, Zhenli Xu, Lei Li, A random batch Ewald method for charged particles in the isothermal-isobaric ensemble, J. Chem. Phys.,  156, 014114, 2022

[207] Dongnam Ko, Seung-Yeal Ha, Shi Jin and Doheon Kim, Convergence analysis of the discrete consensus-based optimization algorithms with random batch interactions and heterogeneous noises, Math. Model Methods Appl Sci.,  32， 1071–1107， 2022.

[206] Jingrun Chen, Shi Jin, and Liyao Lyu, A consensus-based global optimization method with adaptive momentum estimate, Comm. Comp. Phys., 31， 1296–1316， 2022.

[205] J. Carrillo, Shi Jin and Yijia Tang, Random batch particle methods for the homogeneous Landau equation, Comm. Comp. Phys.,   31， 997–1019， 2022.

[204] Shi Jin, Xiantao Li and Nana Liu, On quantum algorithms for the Schrödinger equation in the semi-classical regime, Quantum 6, 739 (2022).

[203] Shi Jin, Asymptotic-Preserving schemes for multiscale physical problems, Acta Numerica   31, 415 – 489, 2022.

[202] Shi Jin and Lei Li, Random Batch Methods for classical and quantum interacting particle systems and statistical sampling, Active Particles, III, Birkhäuser, Cham, 153-200, 2022 (ed. N. Bellomo, J. Carrillo, and E. Tadmor).

[201] Shi Jin, E. Zuazua and Yuhua Zhu, The Vlasov-Fokker-Planck Equation with High Dimensional Parametric Forcing Term, Num. Math., 150, 479–519， 2022.

[200] Shi Jin, Min Tang and Xiaojiang Zhang, A spatial-temporal asymptotic-preserving schemes for radiation magnetohydrodynamics, J. Computational Physics 452 (2022), Paper No. 110895

[199] Jiuyang Liang, Pan Tan, Yue Zhao, Lei Li, Shi Jin, Liang Hong, Zhenli Xu, Super-Scalable Molecular Dynamics Algorithm, J. Chem. Phys. 156， 014114， 2022.

[198] Shi Jin and Lei Li, On the mean field limit of Random Batch Method for interacting particle systems, Science China Mathematics 65， 169–202， 2022. featured by Science China Mathematics

[197] Molei Tao and Shi Jin, Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials, J. Comp. Phys., 450 , Paper No. 110846， (2022)。

2021

[196] F. Golse, Shi Jin and T. Paul, The Random Batch Method for N-body quantum dynamics, J. Comp. Math. 39 ， 2021. (A special issue on "Numerical Methods for High Dimensional PDEs, ed. Shi Jin and Lexing Ying).

[195] P. Degond, Shi Jin and Yuhua Zhu,An Uncertainty Quantification Approach to the Study of Gene Expression Robustness, Methods Appl. Anal., 28, 195–220, 2021 (A special issue in honor of the 80th birthday of Prof. Ling Hsiao)

[194] Sueng-Yeal Ha, Shi Jin, Doheon Kim and Dongnam Ko, Uniform error estimates for the Random Batch Method to the first-order consensus models with anti-symmetric interacting kernels, Studies Appl. Math., 146， 983-1022， 2021.

[193] Seung-Yeal Ha, Shi Jin, Doheon Kim and Dongnam Ko, Convergence toward equilibrium of the first-order consensus model with random batch interactions, J. Diff. Eqn. 302, 585–616, 2021.

[192] I. Gamba, Shi Jin, and Liu Liu, Error estimate of a bi-fidelity method for kinetic equations with random parameters and multiple scales, Int'l J. Uncertainty Quantification 11, 57–75, 2021.

[191] Shi Jin and Ruiwen Shu, Collective dynamics of opposing groups with stochastic communication, Vietnamese J. Math. 49, 619–636， 2021 (a special issue on the occasion of the 60th birthday of Enrique Zuazua).

[190] Shi Jin, Lei Li, Zhenli Xu, and Yue Zhao, A random batch Ewald method for particle systems with Coulomb interactions, SIAM J. Sci. Comp., 43, B937–B960, 2021.

[189] Dongnam Ko， Seung-Yeal Ha and Shi Jin, Uniform-in-time Error Estimate of the Random Batch Method for the Cucker-Smale Model, Math. Models Methods Appl. Sci. 31, 1099-1135, 2021.

[188] Esther Daus, Shi Jin and Liu Liu, On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation, ESAIM Math. Model. Num. Anal. 55, 1323-1345, 2021.

[187] F. Golse, Shi Jin and T. Paul, On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime, Foundation Comp. Math. 21, 613-647, 2021.

[186] Zhiyan Ding, Seung-Yeal Ha and Shi Jin, A local sensitivity analysis in Landau Damping for the kinetic Kuramoto equation with random inputs, , Quarterly Appl. Math. 79, 229-264,2021.

[185] Shi Jin, Lei Li and Jian-Guo Liu, Convergence of Random Batch Method for interacting particles with disparate species and weights, SIAM J. Numer. Anal. 59, 746–768， 2021

[184] J. Carrillo, Shi Jin, Lei Li and Yuhua Zhu, A consensus-based global optimization method for high dimensional machine learning problems, ， ESAIM: Control, Optimisation and Calculus of Variations，27, suppl., Paper No. S5, 2021.

[183] Seung-Yeal Ha, Shi Jin and Doheon Kim, Convergence and error estimates for time-discrete consensus-based optimization algorithms , Numer. Math. 147， 255–282， 2021.

2020

[182] Shi Jin and Xiantao Li, Random Batch Algorithms for Quantum Monte Carlo simulations, Comm. Comp. Phys. 28, 1907–1936, 2020. (A special issue on "Machine Learning for Scientific Computing"，edited by W. Cai and Weinan E).

[181] Seung-Yeal Ha, Shi Jin and Doheon Kim, Convergence of a first-order consensus-based global optimization algorithm , Math. Model Method Appl. Sci., 30， 2417–2444， 2020.

[180] Jinwook Jung and Shi Jin, Emergence of the consensus and separtions in an agent-based model with attractive and singular repulsive forces, SIAM Appl. Dyn. System, 19， 2203-2134， 2020.

[179] N. Crouseilles, Shi Jin, M. Lemou and Liu Liu, Nonlinear Geometric Optics Based Multiscale Stochastic Galerkin Methods for Highly Oscillatory Transport Equations with Random Inputs, Math. Model Num. Anal.  54， 1849-1882， 2020.

[178] Xin Liu, Xi Chen, Shi Jin, Alexander Kurganov, and Hui Yu, Moving-Water Equilibria Preserving Partial Relaxation Scheme for the Saint-Venant System, , SIAM J Sci. Comp., 42, A2206–A2229， 2020.

[177] Seung-Yeal Ha, Shi Jin, and Jinwook Jung, Local sensitivity analysis for the Kuramoto-Daido model with random inputs in a large coupling regime, SIAM J. Math. Anal. 52， 2000-2040， 2020.

[176] N. Crouseilles, S. Jin, M. Lemou and F. Mehats, _ A micro-macro method for a kinetic graphene model in one-space dimension_,(SIAM) Multiscale Modeling & Simulation 18， 444–474， 2020.

[175] Shi Jin, Lei Li and Jian-Guo Liu, Random Batch Methods (RBM) for interacting particle systems , J. Comp. Phys. 400， 108877， 2020. (selected by JCP editorial board for a JCP Seminar Series lecture based on articles that are being particularly innovative and/or have had significant recent impact)

[174] Seung-Yeal Ha, Shi Jin, Jinwook Jung and Woojoo Shim, A local sensitivity analysis for the hydrodynamic Cucker-Smale model with random inputs, , J. Diff. Eqn. 268， 636-679， 2020.

[173] Shi Jin, Liu Liu, Giovanni Russo and Zhennan Zhou, Gaussian wave packet transform based numerical scheme for the semi-classical Schrodinger equation with random inputs, ， J Comp. Phys. 401, 109015, 2020.

[172] Anton Arnold, Shi Jin and Tobias Wohrer, Sharp Decay Estimates in Local Sensitivity Analysis for Evolution Equations with Uncertainties: from ODEs to Linear Kinetic Equations, , J. Diff. Eqn. 268， 1156-1204， 2020.

2019

[171] Di Fang, Shi Jin, P.A. Markowich and B. Perthame, Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks, SMAI J. Comp. Math. 5， 229-249， 2019

[170] Jingwei Hu, Shi Jin, and Ruiwen Shu, On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime, J. Comp. Phys.397， 108838， 2019.

[169] I. Gamba, Shi Jin and Liu Liu, Asymptotic-preserving schemes for two-species binary collisional kinetic system with disparate masses I: time discretization and asymptotic analysis, Comm. Math. Sci. 17， 1257-1289， 2019. (a special issue in memory of David Cai).

[168] Di Fang, Seung-yeal Ha and Shi Jin, Emergent behaviors of the Cucker-Smale emsemble under attractive-repulsive couplings and Rayleigh frictions, Math Model Methods Appl. Sci., 29, 1349-1385, 2019. ( One of the Best Papers of 2019 published by M3AS )

[167] Shi Jin and Ruiwen Shu, A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty, Chinese Annals of Mathematics, Ser B, 40, 765-780, 2019. (a special issue in honor of Prof. Andrew Majda's 70th birthday).

[166] Zhiyan Ding and Shi Jin, Random regularity of a nonlinear Landau Damping solution for the Vlasov-Poisson equations with random inputs, Int'l J. Uncertainty Quantification, 9, 123-142, 2019.

[165] Yingda Li and Shi Jin, _ Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs,_ Kinetic and Related Models 12, 969-993, 2019.

[164] E.S. Daus, Shi Jin and Liu Liu, Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel, Kinetic and Related Models 12, 909-922, 2019.

[163] Seung-Yeal Ha, Shi Jin, and Jinwook Jung, A local sensitivity analysis for the kinetic Kuramoto model with random inputs, Networks and Heterogeneous Media 14, 317-340, 2019.

[162] Ruiwen Shu and Shi Jin, A study of Landau damping with random initial inputs, J. Diff. Eqn., 266, 1922-1945, 2019.

[161] I. Gamba, Shi Jin and Liu Liu, Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations, J. Comp. Phys. 382, 264-290, 2019.

2018

[160] Shi Jin, Hanqing Lu and Lorenzo Pareschi, A High Order Stochastic Asymptotic Preserving Scheme for Chemotaxis Kinetic Models with Random Inputs, Multiscale Model. Simult., 16, 1884-1915, 2018.

[159] Ruiwen Shu and Shi Jin, Uniform regularity in the random space and spectral accuracy of the stochastic Galerkin method for a kinetic-fluid two-phase flow model with random initial inputs in the light particle regime, Math. Model Num. Anal. 52, 1651-1678, 2018.

[158] Jingwei Hu, Shi Jin and Ruiwen Shu, A stochastic Galerkin method for the Fokker-Planck-Landau equation with random uncertainties, Proc. 16th Int'l Conf. on Hyperbolic Problems (eds. C. Klingenberg and M. Westdickenberg), Vol. 2, 1-19, Springer, 2018.

[157] Seung-Yeal Ha, Shi Jin, and Jinwook Jung, A local sensitivity analysis for the kinetic Cucker-Smale model with random inputs, J. Diff. Eqn. 265, 3618-3649, 2018.

[156] Shi Jin and Minh-Binh Tran, Quantum hydrodynamic approximations to the finite temperature trapped Bose gases, Physica D 380/381, 45-57, 2018.

[155] Shi Jin, Mathematical Analysis and Numerical Methods for Multiscale Kinetic Equations with Uncertainties, Proceedings of The International Congress of Mathematicians, Rio de Janeiro, Vol. 3, 3595-3624, 2018.

[154] Liu Liu and Shi Jin, Hypocoercivity based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs, (SIAM) Multiscale Modeling and Simulation 16, 1085-1114, 2018

[153] Di Fang, Shi Jin and Christof Sparber, An efficient time-splitting method for the Ehrenfest dynamics, (SIAM) Multiscale Modeling and Simulation 16, 900-921, 2018.

[152] Lihui Chai, Shi Jin and P.A. Markowich, A hybrid method for computing the Schrodinger equations with periodic potential with band-crossings in the momentum space, Comm. Comp. Phys. 24, 989-1020, 2018. (a special issue in honor of the 80th birthday of Prof. Houde Han).

[151] Shi Jin and Yuhua Zhu, Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales, SIAM J. Math. Anal. 50, 1790-1816, 2018.

[150] Seung-Yeal Ha and Shi Jin, Local sensitivity analysis for the Cucker-Smale model with random inputs, Kinetic and Related Models 11, 859-889, 2018. (special ten-year anniversary issue of KRM).

[149] Shi Jin, Hanqing Lu and Lorenzo Pareschi, Efficient stochastic Asymptotic-preserving IMEX methods for transport equations with diffusive scalings and random inputs, SIAM J. Sci. Comput., 40, A671-A696, 2018.

[148] Frederic Coquel, Shi Jin, Jian-Guo Liu and Li Wang, Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar hyperbolic conservation laws , Math. Comp. 87, 1083-1126, 2018

[147] Shi Jin and Zheng Ma, The discrete stochastic Galerkin method for hyperbolic equations with non-smooth and random coefficeints, J. Sci. Comp. 74, 97-121, 2018.

2017

[146] Jingwei Hu and Shi Jin, Uncertainty Quantification for Kinetic Equations, in "Uncertainty Quantification for Kinetic and Hyperbolic Equations," pp. 193-229, SEMA-SIMAI Springer Series, ed. S. Jin and L. Pareschi, Springer, 2017.

[145] Shi Jin, Jian-Guo Liu and Zheng Ma, Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition based asymptotic preserving method , Research in Math. Sci.,(a special issue in honor of the 70th birthday of Bjorn Engquist), 4:15, 2017. (inaugural) Best Article Award for the journal's first 5 years, Research in the Mathematical Sciences

[144] Yuhua Zhu and Shi Jin, The Vlasov-Poisson-Fokker-Planck system with uncertainty and a one-dimensional asymptotic-preserving method , SIAM Multiscale Model. Simul., 15, 1502-1529, 2017.

[143] Nicolas Crouseilles, Shi Jin and Mohammed Lemou, Nonlinear geometric optics method based multi-scale numerical schemes for a class of highly-oscillatory transport equations, Math. Model Methods Applied Sci., 27, 2031-2070, 2017.

[142] Ruiwen Shu, Jingwei Hu and Shi Jin, A Stochastic Galerkin Method for the Boltzmann Equation with multi-dimensional random inputs using sparse wavelet bases, Num. Math.: Theory, Methods and Applications (NMTMA) 10, 465-488, 2017. (A special issue in honor of the 80th birthday of Prof. Zhenhuan Teng)

[141] Shi Jin and Ruiwen Shu, A stochastic Asymptotic-Preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty, J. Comp. Phys., 335, 905-924, 2017.

[140] Shi Jin and Hanqing Lu, An Asymptotic-Preserving Stochastic Galerkin Method for the Radiative Heat Transfer Equations with Random Inputs and Diffusive Scalings, J. Comp. Phys., 334, 182-206, 2017.

[139] Shi Jin and Liu Liu, An Asymptotic-Preserving Stochastic Galerkin Method for the Semiconductor Boltzmann Equation with Random Inputs and Diffusive Scalings SIAM Multiscale Modeling and Simulation 15, 157-183, 2017. Erratum

[138] Jingwwei Hu, Shi Jin and Qin Li, Asymptotic-Preserving schemes for multiscale hyperbolic and kinetic equations , Handbook of Numerical Methods for Hyperbolic Problems, (ed. by R. Abgrall and C.-W. Shu), North Holland/Elsevier, Vol 18, 103-129, 2017.

[137] Ali Faraj and Shi Jin, The Landau-Zener transition and the surface hopping method for the 2D Dirac equation for graphene , Comm. Comp. Phys., 21, 313-357, 2017.

[136] Shi Jin, C. Sparber and Zhennan Zhou, On the classical limit of a time-dependent self-consistent field system: analysis and computation, Kinetic and Related Models 10, 263-298, 2017. (A special issue in honor of the 60th birthday of Peter Markowich).

2016

[135] Jingwei Hu and Shi Jin, A stochastic Galerkin method for the Boltzmann equation with uncertainty , J. Comp. Phys. 315, 150-168, 2016.

[134] Shi Jin, Dongbin Xiu and Xueyu Zhu, A well-balanced stochastic Galerkin method for scalar hyperbolic balance laws with random inputs , J. Sci. Comp., 67, 1198-1218, 2016.

[133] Kerstin Kupper, Martin Frank and Shi Jin, An asymptotic-preserving 2-D staggered grid method for multiscale transport equations, , SIAM J. Num. Anal., 54, 440-461, 2016.

[132] Bin Zhang, Hong Liu and Shi Jin, An Asymptotic Preserving Monte Carlo Method for the Multispecies Boltzmann Equation , J. Comp. Phys. 305, 575-588, 2016.

2015

[131] Shi Jin, Schrodinger equation: Computation, Invited contribution to Springer "Encyclopedia of Applied and Computational Mathematics", ed. by B. Engquist, pp. 1299-1301, 2015.

[130] Jingwei Hu, Shi Jin, and Dongbin Xiu, A stochastic Galerkin method for Hamilton-Jacobi equations with uncertainty, , SIAM J. Sci. Comput. 37, A2246-A2269, 2015.

[129] Jingwei Hu, Shi Jin, and Li Wang, An asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: a splitting approach, , Kinetic and Related Models 8, 707-723, 2015.

[128] L. Jefferis and S. Jin, A Gaussian Beam Method for High Frequency Solution of Symmetric Hyperbolic Systems with Polarized Waves, SIAM Multiscale Model. Simulation 13, 733-765, 2015

[127] Shi Jin, Dongbin Xiu and Xueyu Zhu, Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings, , J. Comp. Phys. 289, 35-52, 2015.

[126] L. Jefferis and Shi Jin, Computing high frequency solutions of symmetric hyperbolic systems with polarized waves, Comm. Math. Sci. 13, 1001-1024, 2015. (special issue in honor of George Papanicolaou's 70th birthday)

[125] Lihui Chai, Shi Jin, Qin Li and Omar Morandi, A multi-band semi-classical model for surface hopping quantum dynamics, , SIAM Multiscale Modeling and Simulation, 13, 205-230, 2015.

2014

[124] F. Coquel, S. Jin, J.-G. Liu and Li Wang, Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate, Arch. Rat. Mech. Anal. 214, 1051-1084, 2014.

[123] W. Ren, H. Liu and S. Jin, An Asymptotic-Preserving Monte Carlo Method for the Boltzmann Equation, , J. Comp. Phys. 276, 380-404, 2014.

[122] T. Goudon, S. Jin, Jian-Guo Liu, and Bokai Yan, Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density,, International Journal for Numerical Methods in Fluids 75, 81-102, 2014.

[121] S. Jin, D. Wei and D. Yin, Gaussian beam methods for the Schrodinger equation with discontinuous potentials, J. Comp. Appl. Math. 265, 199-219, 2014 (a special issue in honor of Prof. Benyu Guo's 70th birthday).

2013

[120] S. Jin and Z. Zhou, A semi-Lagrangian time splitting method for the Schrodinger equation with vector potentials, Communications in Information and Systems, 13, 247-289, 2013. (a special issue in honor of Marshall Slemrod's 70th birthday)

[119] S. Jin and P. Qi, $l^{1}$-error estimates on the immersed interface upwind scheme for linear convection equations with piecewise constant coefficients: a simple proof , Science China Mathematics 56, 2773-2782, 2013. (a special issue in honor of the 80th birthday of Prof. Zhong-ci Shi).

[118] Jingwei Hu and Shi Jin, On the quasi-random choice method for the Liouville equation of geometrical optics with discontinuous local wave speeds , J. Comp. Math. 31, 573-591, 2013.

[117] Dongsheng Yin, Min Tang and Shi Jin, The Gaussian beam method for the Wigner equation with discontinuous potentials, Inverse Problems and Imaging 7, 1051-1074, 2013 (a special issue in honor of the 60th birthday of Tony Chan).

[116] Shi Jin and Li Wang, Asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime, SIAM J. Sci. Comput., 35, B799-B819, 2013

[115] Lihui Chai, Shi Jin, and Qin Li, Semiclassical Models for the Schrodinger Equation with Periodic Potentials and Band Crossings, Kinetic and Related Models 6, 505-532, 2013.

[114] T. Goudon, S. Jin, J.G. Liu and B. Yan Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows , J. Comp. Phys. 246, 145-164, 2013.

[113] Bokai Yan and Shi Jin, A successive penalty-based asymptotic-preserving scheme for kinetic equations , SIAM J. Sci. Comput. 35, A150-A172, 2013.

[112] Shi Jin and Qin Li, A BGK-penalization asymptotic-preserving scheme for the multispecies Boltzmann equation, (with Qin Li), Numerical Methods for Partial Differential Equations, 29, 1056-1080, 2013.

[111] Shi Jin, Jian-Guo Liu and Li Wang A Domain Decomposition Method for Semilinear Hyperbolic Systems with Two-scale Relaxations , Math. Comp. 82, 749-779, 2013.

2012

[110] S. Jin and D. Wei, A particle method for the semiclassical limit of the Schrodinger equation and the Vlasov-Poisson equations, , SIAM J. Num. Anal. 50, 3259-3279, 2012.

[109] Gaussian beam methods for the Dirac equation in the semi-classical regime, , (with Hao Wu, Zhongyi Huang, and Dongsheng Yin), Comm. Math. Sci. 10, 1301-1315, 2012.

[108] A numerical scheme for the quantum Fokker-Planck-Landau equation efficient in the fluid regime (with Jingwei Hu and Bokai Yan), Commn. Comp. Phys. 12, 1541-1561, 2012.

[107] Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review._Lecture Notes for Summer School on ''Methods and Models of Kinetic Theory" (M&MKT), Porto Ercole (Grosseto, Italy), June 2010. Rivista di Matematica della Universita di Parma 3, 177-216, 2012.
_

_[106] An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equation , (with Jeffrey Haack and Jian-Guo Liu), Commun. Comp. Phys. 12 (2012), pp. 955-980.
_

_[105] A numerical scheme for the quantum Boltzmann equation with stiff collision terms , (with Francis Filbet and Jingwei Hu), Math. Model Num. Anal. 46, 443-463, 2012.
_

_[104] Simulation of fluid-particles flows: heavy particles, flowing regime and asymptotic-preserving schemes, _(with T. Goudon and Bokai Yan), Comm. Math. Sci. 10, 355-385, 2012.

2011

[103] An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime, (with Li Wang), Acta Mathematica Scientia 31, 2219-2232, 2011 ( special issue in honor of Peter Lax's 85th birthday).

[102] A Hybrid Schrodinger/Gaussian Beam Solver for Quantum Barriers and Surface Hopping, (with Peng Qi), Kinetic and Related Models 4, 1097-1120, 2011.

[101] A class of asymmptotic-preserving schemes for the Fokker-Planck-Landau equation , (with Bokai Yan), J. Comp. Phys. 230, 6420-6437, 2011.

[100] Mathematical and computational methods for semiclassical Schrodinger equations , (with P.A. Markowich and C. Sparber), Acta Numerica 20, 211-289, 2011.

[99] On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations , (with Jingwei Hu), Kinetic and Related Models 4, 517-530, 2011.

[98] An Eulerian surface hopping method for the Schr\"{o}dinger equation with conical crossings , (with Peng Qi and Zhiwen Zhang), SIAM Multiscale Modeling & Simulation 9, 258-281, 2011.

[97] Computational High Frequency Wave Diffraction by a Corner via the Liouville equation and Geometric Theory of Diffraction , (with Dongsheng Yin), Kinetic and Related Models 4, 295-316, 2011.

[96] An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation , (with F. Filbet), J. Sci. Comp. 46, 204-224, 2011.

[95] Semi-Eulerian and High Order Gaussian Beam Methods for the Schrodinger Equation in the Semiclassical Regime , (with Hao Wu and Xu Yang), Comm. Comp. Phys. 9, 668-687, 2011.

2010

[94] A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources , (with Francis Filbet), J. Comp. Phys. 229, 7625-7648, 2010. ( On the list of the most cited papers of J. Comp. Phys. published since 2010) (No. 8 by Sept 2015) .

[93] A level set method for the semiclassical limit of the Schrodinger equation with discontinuous potentials , (with Dongming Wei, Richard Tsai and Xu Yang), J. Comp. Phys. 229, 7440-7455, 2010.

[92] Bloch Decomposition-Based Gaussian Beam Method for the Schr\"odinger equation with Periodic Potentials , (with Hao Wu, Xu Yang and Zhongyi Huang), J. Comp. Phys. 229, 4869-4883, 2010.

[91] A micro-macro decomposition based asymptotic-preserving scheme for the multispecies Boltzmann equation , (with Yingzhe Shi), SIAM J. Sci. Comp. 31, 4580-4606, 2010.

[90] A numerical study of the Gaussian beam methods for one-dimensional Schr\"odinger-Poisson equations , (with Hao Wu and Xu Yang), J. Comp. Math. 28, 261-272, 2010.

[89] A coherent semiclassical transport model for pure-state quantum scattering , (with K. Novak), Comm. Math. Sci. 8, 253-275, 2010.

2009

[88] Recent computational methods for high frequency waves in heterogeneous media, , Industrial and Applied Mathematics in China, 49--64, Ser. Contemp. Appl. Math. CAM, 10, Higher Ed. Press, Beijing, 2009

[87] Numerical methods for hyperbolic systems with singular coefficients: well-balanced scheme, Hamiltonian preservation, and beyond, , Proc. of the 12th International Conference on Hyperbolic Problems: Theory, Numerics, Applications, Univeristy of Maryland, College Park. Proceedings of Symposia in Applied Mathematics Vol 67-1, 93-104, 2009, American Mathematical Society.

[86] On a uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface (with Min Tang and Houde Han), Networks and Heterogeneous Media 4, 35-65, 2009.

[85] The l^1-stability of a Hamiltonian-preserving scheme for the Liouville equation with discontinuous potentials (with X. Wen), J. Comp. Math., 27 (2009), pp. 45-67.

[84] On the Bloch decomposition based spectral method for wave propagation in periodic media , (with Z.Y. Huang, P.A. Markowich and C. Sparber ), Wave Motion 46, 15-28, 2009.

2008

[83] A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians , (with H. Wu and Z.Y. Huang), SIAM J. Sci. Comput. 31, 1303-1321, 2008.

[82] Gaussian beam methods for the Schrodinger equation in the semi-classical regime: Lagrangian and Eulerian formulations , (with H. Wu and X. Yang), Comm. Math. Sci. 6, 995-1020, 2008.

[81] On the time-splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit (with P. Degond and Min Tang), SIAM J. Sci. Comp. 30, 2466-2487, 2008.

[80] The Vlasov-Poisson equations as the semiclassical Limit of the Schrodinger-Poisson Equations: a numerical study (with Xiaomei Liao and Xu Yang), J. Hyperbolic Diff. Eqn., 5(3), 569-587, 2008.

[79] The l^1-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials (with Xin Wen), SIAM J. Num. Anal. 46, 2688-2714, 2008.

[78] Computation of the semiclassical limit of the Schrodinger equation with phase shift by a level set method (with Xu Yang), J. Sci. Comp. 35, Nos. 2-3, 144-169, 2008.

[77] Computation of high frequency wave diffraction by a half plane via the Loiuville equation and Geometric Theory of Diffraction, (with Dongsheng Yin), Comm Comput Phys. 4, No. 5, 1106-1128, 2008.

[76] Numerical simulation of the nonlinear Schrodinger equation with multi-dimensional periodic potentials (with Z.Y. Huang, P.A. Markowich and C. Sparber), SIAM Multiscale Modeling and Simulation 7, 539-564, 2008.

[75] Computational high frequency waves through curved interfaces via the Loiuville equation and Geometric Theory of Diffraction, (with Dongsheng Yin), J. Comp. Phys. 227, 6106-6139, 2008.

[74] Computation of interface reflection and regular or diffuse transmission of the planar symmetric radiative transfer equation with isotropic scattering and its diffusion limit (with Xiaomei Liao and Xu Yang), SIAM J. Sci. Comp. 30, 1992-2017, 2008.

[73] A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface, (with X. Yang and G.W. Yuan) , Kinetic and Related Models, 1, 65-84, 2008.

[72] Convergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients I: L^1-error estimates (with Xin Wen), J. Comp. Math. 26, 1-22, 2008.

2007

[71] Mach-number uniform asymptotic-preserving gauge schemes for compressible flows (with Pierre Degond and Jian-Guo Liu), Bulletin of the Institute of Mathematics, Academia Sinica, New Series, 2, No. 4, 851-892, 2007.

[70] A Semiclassical Transport Model for Two-Dimensional Thin Quantum Barriers (with K. Novak), J. Comp. Phys. 226, 1623-1644, 2007.

[69] A Bloch decomposition based time-splitting pseudospectral method for quantum dynamics with periodic potentials (with Z.Y. Huang, P.A. Markowich and C. Sparber), SIAM J. Sci. Comp. 29, 515-538, 2007.

2006

[68] A Hamiltonian-preserving scheme for high frequency elastic waves in heterogeneous media (with Xiaomei Liao), J. Hyperbolic Diff Eqn. 3, No. 4, 741-777, 2006.

[67] Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with partial transmissions and reflections (with X. Wen), SIAM J. Num. Anal. 44, 1801-1828, 2006.

[66] A Semiclassical Transport Model for Thin Quantum Barriers (with K. Novak), Multiscale Modeling and Simulation, 5(4), 1063-1086, 2006.

[65] Computation of Transmissions and Reflections in Geometrical Optics via the Reduced Liouville Equation (with X. Wen), Wave Motion, 43(8), 667-688, 2006.

[64] Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, (with X. Wen), J. Comp. Phys. 214, 672-697, 2006.

[63] A time-splitting spectral method for the generlized Zakharov system in multi-dimensions (with C.X. Zheng), J. Sci. Comp. 26, 127-149, 2006.

[62] Numerical study of a domain decomposition method for a two-scale linear transport equation (with X. Yang, F. Golse, Z.Y. Huang), Networks and Heterogeneous Media 1(1), 143-166, 2006.

2005

[61] Computing multi-valued physical observables for high frequency limit of symmetric hyperbolic systems (with H. Liu, S. Osher and R. Tsai), J. Comp. Phys. 210, 497-518, 2005.

[60] Two interface type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations (with X. Wen), SIAM J. Sci. Comp. 26, 2079-2101, 2005 (electronic).

[59] Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials (with X. Wen), Comm. Math. Sci. 3, 285-315, 2005.

[58] A Smooth Transition Model Between Kinetic and Hydrodynamic Equations (with P. Degond and L. Mieussens), J. Comp. Phys. 209, 665-694, 2005.

[57] A time-splitting spectral scheme for the Maxwell-Dirac system (with Z.Y. Huang, Peter A. Markowich, Christof Sparber and C.X. Zheng), J. Comp. Phys. 208, 761-789, 2005.

[56] A smooth transition model between kinetic and diffusion equations, (with P. Degond), SIAM J. Num. Anal. 42, 2671 - 2687, 2005 (electronic)

[55] Computing multivalued physical observables for the semiclassical limit of the Schrodinger equations, (with H.L. Liu, S. Osher and R. Tsai), J. Comp. Phys. 205, 222-241, 2005.

[54] Eulerian calculations of electron overtaking and multi-valued solutions in a traveling wave tube, (with J.G. Wohlbier and S. Sengele), Physics of Plasmas 12, 023106, 2005.

2004

[53] Numerical simulation of a generalized Zakharov system (with P.A. Markowich and C.X. Zheng), J. Comp. Phys. 201, 376-395, 2004.

[52] An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons, (with X.T. Li, J.G. Wohlbier and J.H. Booske), Phys Rev E. 70, 016502, 2004.

[51] An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, (with X. Wen), J. Comp. Math. 22, 230-249, 2004.

2003

[50] On Two Moment Systems for Computing Multiphase Semiclassical Limits of the Schrodinger Equation, (with L. Gosse and X.T. Li), Math. Model Methods Appl. Sci. 13, No. 12, 1689-1723, 2003.

[49] Front Motion in Multi-Dimensional Viscous Conservation Laws with Stiff Source Terms Driven by Mean Curvature and Variation of Front Thickness (with H.T. Fan), Quarterly Appl. Math. LXI (4), 701-721, 2003.

[48] A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem, (with F. Golse and C.D. Levermore), Math. Model Num. Anal. 37, 869-892, 2003.

[47] A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations, (with S. Osher), Comm. Math. Sci. 1(3), 575-591, 2003.

[46] Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrodinger Equations in the Semi-clasical Regimes (with W.Z. Bao and P. Markowich), SIAM J. Sci. Comp. 25, 27-64, 2003 (elctronic).

[45] Multi-phase Computations of the Semiclassical Limit of the Schrodinger Equation and Related Problems: Whitham vs. Wigner, (with X.T. Li), Physica D 182, 46-85, 2003.

[44] High Frequency Behavior of the Focusing Nonlinear Schroedinger Equation with Random Inhomogeneities , (with A. Fannjiang and G. Papanicolaou), SIAM J. Appl. Math. 63, 1328 - 1358, 2003 (electronic).

[43] Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration III: Three Space Dimension, (with X.L. Wang), J. Comp. Phys. 186, 582-595, 2003.

[42] Numerical Approximations of Pressureless and Isothermal Gas Dynamics, (with F. Bouchut and X.T. Li), SIAM J. Num. Anal. 41, 135-158, 2003.

[41] Wave Patterns, Stability and Slow Motions in Inviscid and Viscous Hyperbolic Equations with Stiff Reaction Terms, (with H.T. Fan and J. Miller), J. Diff. Eqn. 189, 267-291, 2003.

[40] High-Order I-Stable Central Difference Schemes for Viscous Compressible Flows , (with W.Z. Bao), J. Comp. Math. 21, 101-112, 2003

2002

[39] Error Estimates on the Random Projection Methods for Hyperbolic Systems with Stiff Reaction Terms , (with W.Z. Bao), Appl. Num. Math. 43, 315-333, 2002

[38] Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration II: Two Dimensional Anisotropic Fronts (with X.L. Wang), J. Comp. Phys. 179, 557-577, 2002

[37] The Random Projection Method for Stiff Multi-Species Detonation Capturing , (with W.Z. Bao), J. Comp. Phys. 178, 37-57, 2002.

[36] A Relaxation Scheme for Solving the Boltzmann Equation Based on the Chapman-Enskog Expansion (with L. Pareschi and M. Slemrod) , Acta Mathematicas Applicatae Sinica (English Series) 18, 37-62, 2002.

[35] On Time-Splitting Spectral Approximations for the Schrodinger Equation in the Semiclassical Regime, (with W.Z. Bao and P. Markowich), J. Comp. Phys., 175, 487-524, 2002.

2001

[34] The Random Projection Method for Stiff Detonation Waves , (with W.Z. Bao), SIAM J. Sci. Comp. 23, 1000-1026, 2001.

[33] A steady-state capturing method for hyperbolic systems with geometrical source terms , , Math. Model. Num. Anal. 35, 631-646, 2001.

[32] Weakly Compressible High-Order I-Stable Central Difference Schemes for Incompressible Viscous Flows , (with W.Z. Bao), Comput. Methods Appl. Mech. Eng., 190, 5009-5026, 2001.

[31] Regularization of the Burnett Equations via Relaxation , (with M. Slemrod), J. Stat. Phys. 103, 1009-1033, 2001.

[30] On the Computation of Roll Waves , (with Y.J. Kim), Math. Model. Num. Anal. 35, 463-480, 2001.

[29] Regularization of the Burnett Equations for Fast Granular Flows via Relaxation, (with M. Slemrod), Physica D 150, 207-218, 2001.

2000

[28] Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms, (with H. Fan and Z.-H. Teng), J. Differential Equations 168, 270-294, 2000.

[27] The Random Projection Method for Hyperbolic Systems with Stiff Reaction Terms , (with W.Z. Bao), J. Comp. Phys. 163, 216-248, 2000

[26] Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations, (with L. Pareschi and G. Toscani), SIAM J. Num. Anal. 38, 913-936, 2000 (electronic).

[25] Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration I: Two Space Dimension , (with X.L. Wang, T.L. Starr and X.F. Chen), J. Comp. Phys. 162, 467-482, 2000.

[24] Hyperbolic Systems with Supercharacteristic Relaxations and Roll Waves , (with M.A. Katsoulakis), SIAM J. Appl. Math. 61, 273-292, 2000 (electronic).

[23] A Diffusive Subcharacteristic Condition for Hyperbolic Systems with Diffusive Relaxation, (with H.L. Liu), Transport Theory and Statistical Physics 29, 583-593, 2000.

[22] Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation Schemes, , (with L. Pareschi), J. Comp. Phys. 161, 312-330, 2000.

1999

[21] Relaxation Schemes for Curvature-Dependent Front Propagation , (with M. Katsoulakis and Z.P. Xin), Comm. Pure Appl. Math. 52, 1587-1615, 1999.

[20] Efficient Asymptotic-Preserving (AP) Schemes for Some Multiscale Kinetic Equations , SIAM J. Sci. Comp. 21, 441-454, 1999 (electronic).

[19] A Model for Front Evolution with a Non-Local Growth Rate , (with X.L. Wang and T.L. Starr), J. Material Research 14, No.10, 3829-3832, 1999.

[18] The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: The Discrete-Ordinate Method (with F. Golse and C.D. Levermore), SIAM J. Numerical Analysis, 36, 1333-1369, 1999.

1998

[17] Diffusive Relaxation Schemes for Discrete-Velocity Kinetic Equations (with L. Pareschi and G. Toscani), SIAM J. Numerical Analysis, 35, 2405-2439, 1998.

[16] Numerical Passage from Systems of Conservation Laws to Hamilton-Jacobi Equation, and a Relaxation Scheme (with Z.P. Xin), SIAM J. Numerical Analysis 35, 2385-2404, 1998.

[15] Diffusion Limit of a Hyperbolic System with Relaxation (with H.L. Liu), Methods and Applications of Analysis, 5, 317-334, 1998.

[14] Application of Relaxation Scheme to Wave Propagation Simulation in Open-Channel Networks (with M.M. Aral and Y. Zhang), J. Hydraulic Engineering 124, 1125-1133, 1998.

1997

[13] Relaxation Approximations to Front Propagation (with M. Katsoulakis), Journal of Differential Equations 138, 380-387 (1997).

[12] Uniformly Accurate Schemes for Hyperbolic Systems with Relaxations (with R.E. Caflisch and G. Russo), SIAM J. Numerical Analysis 34, 246-281 (1997).

[11] Physical Symmetry and Lattice Symmetry in Lattice Boltzmann Method (with N. Cao, S.Y. Chen and D. Martinez), Physical Review E 55, 21 (1997).

1996

[10] The Effects of Numerical Viscosities I: Slowly Moving Shocks (with J.G. Liu), J. Computational Physics 126 (1996), 373-389.

[9] A Convex Entropy for a Hyperbolic System with Relaxation , J. Differential Equations, 127, 95-107 (1996).

[8] Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms (with C.D. Levermore), J. Computational Physics 126 (1996), 449-467.

1995

[7] Numerical Integrations of Systems of Conservation Laws of Mixed Type, SIAM J. Applied Mathematics, 55 (1995), 1536-1551.

[6] Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms, J. Computational Physics, 122 (1995), 51-67.

[5] The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions (with Z.P. Xin), Communication on Pure and Applied Mathematics, 48 (1995), 235-276.

1994

[4] Relaxation and Diffusion Enhanced Dispersive Waves (with J.G. Liu), Proceedings of Royal Society London A, 446 (1994), 555-563.

1993

[3] Fully-Discrete Numerical Transfer in Diffusive Regimes (with C.D. Levermore), Transport Theory and Statistical Physics 22 (1993), 739-791.

1991

[2] The Discrete-Ordinate Method in Diffusive Regime (with C.D. Levermore), Transport Theory and Statistical Physics 20 (1991), 413-439.

1989

[1] Numerical Methods for Turbines Flow Mixed with Cold Air (with J. Shi, J.S. Li and P.Q. Wang), J. Aerodynamics, 4(4), 305-309 (1989), (in Chinese).

In refereed conference proceedings, lecture notes or book chapters

[10] Multi-phase computations of the semiclassical limit of the Schrodinger equation , (with X.T. Li), Geometry and Nonl. PDEs 29, 63-75, 2002.

[9] A steady-state capturing method for hyperbolic systems with geometrical source terms , , to appear.

[8] The random projection method for stiff multi-species detonation computation , (with W.Z. Bao), pp 139-148, in Hyperbolic Problems: Theory, Numerics, Applications, Ed. H. Freistuhler and G. Warnecke, Birkhauser-Verlag, Berlin, 2001.

[7] Asymptotic-Preserving (AP) Schemes for Multiscale Kinetic Equations: a Unified Approach , (with L. Pareschi), pp 573-582, in Hyperbolic Problems: Theory, Numerics, Applications, Ed. H. Freistuhler and G. Warnecke, Birkhauser-Verlag, Berlin, 2001.

[6] Remarks on the Relaxation Approximations of the Burnett Equations, (with M. Slemrod), Methods Appl. Anal. 8, 539-544, 2001.

[5] Relaxation and the Chapman-Enskog Expansion , (with M. Slemrod), WASCOM 99". 10th Conference on Waves and Stability in Continuous Media (Vulcano), 265--271, World Sci. Publishing, River Edge, NJ, 2001.

[4] The Random projection Method , (with W.Z. Bao), pp. 1-11, Advances in Scientific Computing, Ed. by Z.C. Shi, M. Mu, W. Xue and J. Zou, Science Press, 2001.

[3] Modern Shock Capturing Methods for Conservation Laws, invited review paper for "Some New Directions in Science on Computers", eds. G. Bhanot, S.Y. Chen and P. Seiden, World Scientific, pp. 64-90, 1997.

[2] Oscillations Induced by Numerical Viscosities (with J.G. Liu), Mathem\'atica Contempor^nea 10, 169-180 (1996).

[1] The Relaxation Schemes (with Z.P. Xin), Proceedings of the Fifth International Conference on Hyperbolic Problems, 361-367 (ed. J. Glimm etc.), World Scientific (1996).

Former Ph.D. Students

My former Ph.D. students have won many prestigious awards, including:

[1] Xiantao Li, UW-Madison, Ph.D. 2002.
Dissertation: Numerical Computation of the Semiclassical Limit of the Schrodinger Equation and Related Problems
First position after Ph.D: Postdoc at Program in Applied and Computational Mathematics, Princeton University
Current position: Professor of Mathematics at Pennsylvania State University

[2] Xuelei Wang, Georgia Tech, Ph.D. 2003.
Dissertation: Level Set Model of Microstructure Evolution in the Chemical Vapor Infiltration Process
First position after Ph.D: Software Engineer at Verizon

[3] Kyle Novak, UW-Madison, Ph.D. 2006
Dissertation: A Semiclassical Model for Thin Quantum Barriers
First position after Ph.D: Assistant Professor, Air Force Institute of Technology
Current: Deputy Chief Analyst for Analyses and Assessments at Headquarters, United States Air Force

[4] Xiaomei Liao, UW-Madison, Ph.D. 2007
Dissertation: Computational High Frequency Waves in Heterogeneous Media
First position after Ph.D: Postdoc at Department of Biostatistics, Harvard University
Current: Research Scientist, Department of Epidemiology and Department of Biostatistics, Harvard University

[5] Xu Yang, UW-Madison, Ph.D. 2008
Dissertation: Numerical Methods for Multiscale Kinetic Transport and High Frequency Waves
First position after Ph.D: Postdoc at Program in Applied and Computational Mathematics, Princeton University
Current: Associate Professor of Mathematics, University of California-Santa Barbara

[6] Min Tang, Tsinghua University, Ph.D. 2008
Dissertation: Aymptotic-Preserving Methods for Multiscale Waves and Transport
First position after Ph.D: Postdoc at Universite Paul Sabatier-Toulouse, France
Current: Professor at Department of Mathematics and Institute of Natural Science, Shanghai Jiao Tong University, China

[7] Yingzhe Shi, UW-Madison, Ph.D. 2009
Dissertation: Numerical Methods for the Coupling of Multispecies Kinetic and Hydrodynamic Equations
First position after Ph.D: Assistant Professor, Department of Financial Engineering, Central University of Finance and Economics, Beijing, China
Current: Associate Professor at Department of Financial Engineering, Central University of Finance and Economics, Beijing, China

[8] Hao Wu, Tsinghua University, Ph.D. 2009
Dissertation: Fast Computational Methods for High Frequency Waves
First position after Ph.D: Postdoc at Universite Paul Sabatier-Toulouse, France
Current: Associate Professor at Department of Mathematical Science, Tsinghua University, China

[9] Jeff Haack, UW-Madison; Ph.D. 2010
Dissertation: Asymptotic Preserving Numerical Schemes for Transport and Fluid Equations
First position after Ph.D: Postdoc, Department of Mathematics, University of Texas-Austin;
current: Research Staff, Los Alamos National Laboratory

[10] Jingwei Hu, UW-Madison, Ph.D 2011
Dissertation: Numerical Methods for Quantum Kinetic Equations and High Frequency Waves
First position after Ph.D: Postdoc at ICES, University of Texas-Austin
Current: Associate Professor, Department of Mathematics, Purdue University

[11] Zhiwen Zhang, Tsinghua University (co-advised with Houde Han), Ph.D. 2011
Dissertation: Artificial Boundary Conditions for Klein-Gordon Equation and Schrodinger Equation
First position after Ph.D: Postdoc at Division of Applied and Computational Mathematics, California Institute of Technology
Current: Assistant Professor, Department of Mathematics, University of Hong Kong

[12] Bokai Yan, UW-Madison, Ph.D. 2011
Dissertation: Asymptotic-Preserving Schemes for Kinetic and Related Systems
First position after Ph.D: Postdoc at Department of Mathematics, University of California-Los Angeles
Current: Quantitative FinanceAnalyst, Bank of America

[13] Jia Deng, Tsinghua University, Ph.D. 2012
Dissertation: Efficient Implicit Asymptotic Preserving Schemes in the Diffusive Regime of Linear Boltzmann Equation
First position after Ph.D: Assistant Research Professor at First Institute of Oceanography, State Oceanic Administration, Qingdao, China

[14] Peng Qi, UW-Madison, Ph.D. 2012
Dissertation: New Surface Hopping Methods in Quantum Dynamics
First position after Ph.D: Quantitative Associate, Wells Fargo Bank
Current: Data Scientist, Facebook

[15] Li Wang, UW-Madison, Ph.D. 2012
Dissertation: Numerical Methods for Multiscale Hyperbolic and Kinetic Equations
First position after Ph.D: (non-tenure track) Assistant Professor at Department of Mathematics, University of Michigan, Ann-Arbor and CAM Assistant Adjunct Professor, Department of Mathematics, University of California, Los Angeles
Current: Assistant Professor, Department of Mathematics, University of Minnesota

[16] Qin Li, UW-Madison, Ph.D. 2013
Dissertation: Modeling and Computational Methods for Multiscale Quantum Dynamics and Kinetic Equations
First position after Ph.D: von Karman Instructor at California Institute of Technology
Current: Associate Professor, Department of Mathematics, University of Wisconsin-Madison

[17] Lihui Chai, Tsinghua University, Ph.D. 2013
Dissertation: Semiclassical Models for Quantum Systems and Band crossings
First position after Ph.D: Postdoc at University of California , Santa Barbara Current: Assistant Professor, School of Mathematiccal Sciences, Sun Yet-Sen University , China

[18] Leland Jefferis, UW-Madison, Ph.D. 2014
Dissertation: Computation of High Frequency Wave Solutions to Symmetric Hyperbolic Systems with Polarized Waves
First position after Ph.D: NSF Postdoc at Department of Mathematics, Stanford University
Current: Software Engineer, Google

[19] Zhennan Zhou, UW-Madison, Ph.D. 2014
Dissertation: Computational Methods for Semi-classical Schrodinger Equations with Vector Potentials and Erhenfest Dynamics
First position after Ph.D: Postdoc at Department of Mathematics, Duke University
Current: Assistant Professor, Beijing International Center for Mathematics Research, Peking University, China

[20] Zheng Ma, Shanghai Jiao Tong University, Ph.D. 2017
Dissertation: Computational Methods for Transport and Waves with Multiple Scales and Uncertainty
First position after Ph.D: Golomb Visiting Assistant Professor of Mathematics, Purdue University. Now Associate Professor at Shanghai Jiao Tong University, China.

[21] Liu Liu, UW-Madison, Ph.D. 2017
Dissertation: Uncertainty Quantification for Multi-scale Kinetic Equations and Quantum Dynamics
First position after Ph.D: Peter O'Donell, Jr. Postdoctoral Fellow, ICES, University of Texas, Austin. Now Assistant Professor at Chinese University of Hong Kong.

[22] Ruiwen Shu, UW-Madison, Ph.D. 2018
Dissertation: Uncertainty Quantification and Sensitivity Analysis for Multiscale Kinetic Equations with Random Inputs
First position after Ph.D: Postdoc., Department of Mathematics, University of Maryland, College Park. Now Assistant Professor at University of Georgia.

[23] Xinchun Li, Shanghai Jiao Tong University, Ph.D. 2018
Dissertation: Hyperbolic Equations with Discontinuous Coefficients: Numerical Schemes and Numerical Error Estimates
First position after Ph.D: Assistant Quantitative Analyst, Zhongtai Securities, Shanghai, China

[24] Di Fang, UW-Madison, Ph.D. 2019.
Dissertation: Numerical Analysis and Computational Methods for Non-adiabatic Quantum Dynamics and Biological Models.
First position after Ph.D: Morrey Assistant Professor, Department of Mathematics, University of California, Berkeley

[25] Yuhua Zhu, UW-Madison, Ph.D. 2019.
Dissertation: Uncertainty Quantification for Fokker Planck Equation and Its Connection with Machine Learning.
First position after Ph.D: Postdoc, Department of Mathematics, Stanford University. Now Assistant Professor at University of California, San Diego.

[26] Yijia Tang, Shanghai Jiao Tong University , Ph.D. 2023.
Dissertation: Random batch particle methods for the Poisson-Nernst-Planck, Poisson-Boltzmann and Fokker-Planck-Landau equations. First position after Ph.D: Postdoc, Karlsruhe Institute of Technology, Germany.

Editorships

Committees Served (Selected)

Honors, Awards and Fellowships

Selected Invited Lecture