# Shi Jin（金石）

Chair Professor

Phone:
(86-21) 54747530
Office:
527
Email:
shijin-m@sjtu.edu.cn
Homepage:
http://www.math.wisc.edu/~jin

## Brief Introduction

Shi Jin, Chair professor, got his B.S. in mathematics from Peking University, China, in 1983, and Ph.D in applied mathematics from University of Arizona in 1991. He had postdoctoral experience at the Courant Institute of Mathematical Sciences, New York University from 1991 to 1993, and was a full professor in the mathematics department, University of Wisconsin-Madison, serving as the department chair from 2008 to 2011. In June, 2011, he started his position as the chair of mathematics department, and co-director at Institute of Natural Sciences, at Shanghai Jiao Tong University. His research fields cover computational fluid dynamics, kinetic equations, hyperbolic conservation laws, high frequency waves, computational physics and computational methods for multiscale problems. He has published more than one hundred SCI papers in these fields. He founded the International Press journal “Communications in Mathematical Sciences”. He has also served in the editorial boards of many other famous journals of computational and applied mathematics, such as SIAM Journal on Scientific Computing and SIAM Journal on Applied Mathematics.

He was honored with a Feng Kang Prize of Scientific Computing by Chinese Academy of Sciences in 2001, a Morningside Silver Medal at the fourth International Congress of Chinese Mathematicians which is held every three year. He also received a Vilas Associate award from University of Wisconsin-Madison and was invited to be a Copernicus Visiting Scientist by University of Ferrara in Italy. He was appointed as a Chang Jiang Chair Professor at Tsinghua University by the Ministry of Education of China, received an Excellent Young Scientist award by National Natural Science Foundation of China, and was selected by “the Thousand Talents Program” in China in 2011. In 2012, he was invited to be an inaugural fellow of the American Mathematical Society.

## Research Interests

Kinetic theory, computational high frequency wave propagations, semiclassical and multiscale methods in quantum dynamics, numerical methods for conservation laws and front propagation, computational fluid dynamics, etc.

## Research Highlights

1. Introduced relaxation approximations and relaxation schemes for hyperbolic conservation laws and Hamilton-Jacobi equations, which provide a new and simple way to construct approximations and computational methods to nonlinear hyperbolic systems and related problems.

2. Introduced the concept of “asymptotic-preserving shcemes” for time-space numerical integrations of multiscale kinetic and hyperbolic problems. Established rigorous theory for such schemes for linear transport equation in the diffusive regime, and constructed several classes of asymptotic-preserving schemes for transport equation, Boltzmann equation, Landau equation, kinetic-fluid coupling multiphase problems etc. that allow efficient numerical capturing of both kinetic and hydrodynamic regimes without numerically resolving the microscopic physical scales.

3. Constructed several classes of efficient semiclassical or multiscale computational methods for quantum dynamics and high frequency waves that are able to capture important microscopic quantum information, such as tunneling, surface hopping, diffraction, etc. with computational cost essentially at the level of classical mechanics.

## Selected Publications

### 2016

• 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.
• 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

• 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.
• 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.
• 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
• 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.
• 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)
• 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

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

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

• 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.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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

• 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).
• A Hybrid Schrodinger/Gaussian Beam Solver for Quantum Barriers and Surface Hopping, (with Peng Qi), Kinetic and Related Models 4, 1097-1120, 2011.
• A class of asymmptotic-preserving schemes for the Fokker-Planck-Landau equation , (with Bokai Yan), J. Comp. Phys. 230, 6420-6437, 2011.
• Mathematical and computational methods for semiclassical Schrodinger equations , (with P.A. Markowich and C. Sparber), Acta Numerica 20, 211-289, 2011.[PDF]
• On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations , (with Jingwei Hu), Kinetic and Related Models 4, 517-530, 2011.[PDF]
• 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. [PDF]
• 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. [PDF] An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation, (with F. Filbet), J. Sci. Comp. 46, 204-224, 2011. [PDF]/li> 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. [PDF]

### 2010

• 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.[PDF]
• 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. [PDF]
• 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. [PDF]
• A micro-macro decomposition based asymptotic-preserving scheme for the multispecies Boltzmann equation , (with Yingzhe Shi), SIAM J. Sci. Comp. 31, 4580-4606, 2010. [PDF]
• 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. [PDF]
• A coherent semiclassical transport model for pure-state quantum scattering, (with K. Novak), Comm. Math. Sci. 8, 253-275, 2010. [PDF]

### 2009

• 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[PDF]
• 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. [PDF]
• 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.[PDF]
• 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.[PDF]
• 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. [PDF]