Shi Jin（金石）
Director and Chair Professor
Brief Introduction
Shi Jin, Chair Professor. He obtained 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 has been a full professor in the mathematics department, University of WisconsinMadison, serving as the department chair from 2008 to 2011. In 2015, he was awarded Vilas Distinguished Achievement Professor. He was appointed as Sequoia Chair Professor of Shanghai Jiao Tong University in June 2009. He won the Sigma Xi Young Faculty Award of Georgia Tech in 1997. He was honored with Feng Kang Prize of Scientific Computing by Chinese Academy of Sciences in 2001. He was a Chang Jiang Visiting Chair Professor at Tsinghua University by the Ministry of Education of China from 2001 to 2006. He received an Excellent Young Scientist award by National Natural Science Foundation of China in 2002. His honor and awards include a Van Vleck Distinguished Research Prize of the University of WisconsinMadison and a Morningside Silver Medal at the fourth International Congress of Chinese Mathematicians, a Vilas Associate award from University of WisconsinMadison in 2010, an inaugural fellow of the American Mathematical Society in 2012, a fellow of the Society for Industrial and Applied Mathematics in 2013, and a 45minute Invited Lecture at the International Congress of Mathematicians to be held in Rio de Janeiro, Brazil, 2018. He founded and has been serving its EditorinChief since 2012 for the International Press journal “Communications in Mathematical Sciences”. He has also served in the editorial boards of 8 other leading journals of computational and applied mathematics.
Research Interests
Computational fluid dynamics, hyperbolic conservation laws, kinetic equations, high frequency wave simulation, computational physics and computational methods for multiscale problems, and uncertainty quantification, etc.
Research Highlights

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

Introduced the concept of “asymptoticpreserving shcemes” for timespace 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 asymptoticpreserving schemes for transport equation, Boltzmann equation, Landau equation, kineticfluid coupling multiphase problems etc. that allow efficient numerical capturing of both kinetic and hydrodynamic regimes without numerically resolving the microscopic physical scales.

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 asymptoticpreserving 2D staggered grid method for multiscale transport equations, , SIAM J. Num. Anal., 54, 440461, 2016.
 Bin Zhang, Hong Liu and Shi Jin, An Asymptotic Preserving Monte Carlo Method for the Multispecies Boltzmann Equation , J. Comp. Phys. 305, 575588, 2016.
2015
 Jingwei Hu, Shi Jin, and Dongbin Xiu, A stochastic Galerkin method for HamiltonJacobi equations with uncertainty, , SIAM J. Sci. Comput. 37, A2246A2269, 2015.
 Jingwei Hu, Shi Jin, and Li Wang, An asymptoticpreserving scheme for the semiconductor Boltzmann equation with twoscale collisions: a splitting approach, , Kinetic and Related Models 8, 707723, 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, 733765, 2015
 Shi Jin, Dongbin Xiu and Xueyu Zhu, Asymptoticpreserving methods for hyperbolic and transport equations with random inputs and diffusive scalings, , J. Comp. Phys. 289, 3552, 2015.
 L. Jefferis and Shi Jin, Computing high frequency solutions of symmetric hyperbolic systems with polarized waves, Comm. Math. Sci. 13, 10011024, 2015. (special issue in honor of George Papanicolaou’s 70th birthday)
 Lihui Chai, Shi Jin, Qin Li and Omar Morandi, A multiband semiclassical model for surface hopping quantum dynamics, , SIAM Multiscale Modeling and Simulation, 13, 205230, 2015.
2014
 F. Coquel, S. Jin, J.G. Liu and Li Wang, Wellposedness and singular limit of a semilinear hyperbolic relaxation system with a twoscale discontinuous relaxation rate, Arch. Rat. Mech. Anal. 214, 10511084, 2014.
 W. Ren, H. Liu and S. Jin, An AsymptoticPreserving Monte Carlo Method for the Boltzmann Equation, , J. Comp. Phys. 276, 380404, 2014.
 T. Goudon, S. Jin, JianGuo Liu, and Bokai Yan, AsymptoticPreserving schemes for kineticfluid modeling of disperse twophase flows with variable fluid density,, International Journal for Numerical Methods in Fluids 75, 81102, 2014.
 S. Jin, D. Wei and D. Yin, Gaussian beam methods for the Schrodinger equation with discontinuous potentials, J. Comp. Appl. Math. 265, 199219, 2014 (a special issue in honor of Prof. Benyu Guo’s 70th birthday).
2013
 S. Jin and Z. Zhou, A semiLagrangian time splitting method for the Schrodinger equation with vector potentials, Communications in Information and Systems, 13, 247289, 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, 27732782, 2013. (a special issue in honor of the 80th birthday of Prof. Zhongci Shi).
 Jingwei Hu and Shi Jin, On the quasirandom choice method for the Liouville equation of geometrical optics with discontinuous local wave speeds , J. Comp. Math. 31, 573591, 2013.
 Dongsheng Yin, Min Tang and Shi Jin, The Gaussian beam method for the Wigner equation with discontinuous potentials, Inverse Problems and Imaging 7, 10511074, 2013 (a special issue in honor of the 60th birthday of Tony Chan).
 Shi Jin and Li Wang, Asymptoticpreserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime, SIAM J. Sci. Comput., 35, B799B819, 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, 505532, 2013.
 T. Goudon, S. Jin, J.G. Liu and B. Yan AsymptoticPreserving schemes for kineticfluid modeling of disperse twophase flows , J. Comp. Phys. 246, 145164, 2013.
 Bokai Yan and Shi Jin, A successive penaltybased asymptoticpreserving scheme for kinetic equations , SIAM J. Sci. Comput. 35, A150A172, 2013.
 Shi Jin and Qin Li, A BGKpenalization asymptoticpreserving scheme for the multispecies Boltzmann equation, (with Qin Li), Numerical Methods for Partial Differential Equations, 29, 10561080, 2013.
 Shi Jin, JianGuo Liu and Li Wang A Domain Decomposition Method for Semilinear Hyperbolic Systems with Twoscale Relaxations , Math. Comp. 82, 749779, 2013.
2012
 S. Jin and D. Wei, A particle method for the semiclassical limit of the Schrodinger equation and the VlasovPoisson equations, , SIAM J. Num. Anal. 50, 32593279, 2012.
 Gaussian beam methods for the Dirac equation in the semiclassical regime, , (with Hao Wu, Zhongyi Huang, and Dongsheng Yin), Comm. Math. Sci. 10, 13011315, 2012.
 A numerical scheme for the quantum FokkerPlanckLandau equation efficient in the fluid regime (with Jingwei Hu and Bokai Yan), Commn. Comp. Phys. 12, 15411561, 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, 177216, 2012.
 An allspeed asymptoticpreserving method for the isentropic Euler and NavierStokes equation , (with Jeffrey Haack and JianGuo Liu), Commun. Comp. Phys. 12 (2012), pp. 955980.
 A numerical scheme for the quantum Boltzmann equation with stiff collision terms , (with Francis Filbet and Jingwei Hu), Math. Model Num. Anal. 46, 443463, 2012.
 Simulation of fluidparticles flows: heavy particles, flowing regime and asymptoticpreserving schemes, (with T. Goudon and Bokai Yan), Comm. Math. Sci. 10, 355385, 2012.
2011
 An asymptotic preserving scheme for the VlasovPoissonFokkerPlanck system in the high field regime, (with Li Wang), Acta Mathematica Scientia 31, 22192232, 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, 10971120, 2011.
 A class of asymmptoticpreserving schemes for the FokkerPlanckLandau equation , (with Bokai Yan), J. Comp. Phys. 230, 64206437, 2011.
 Mathematical and computational methods for semiclassical Schrodinger equations , (with P.A. Markowich and C. Sparber), Acta Numerica 20, 211289, 2011.[PDF]
 On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations , (with Jingwei Hu), Kinetic and Related Models 4, 517530, 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, 258281, 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, 295316, 2011. [PDF]
An asymptotic preserving scheme for the ESBGK model of the Boltzmann equation, (with F. Filbet), J. Sci. Comp. 46, 204224, 2011. [PDF]/li>
SemiEulerian and High Order Gaussian Beam Methods for the Schrodinger Equation in the Semiclassical Regime, (with Hao Wu and Xu Yang), Comm. Comp. Phys. 9, 668687, 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, 76257648, 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, 74407455, 2010. [PDF]
 Bloch DecompositionBased Gaussian Beam Method for the Schr"odinger equation with Periodic Potentials , (with Hao Wu, Xu Yang and Zhongyi Huang), J. Comp. Phys. 229, 48694883, 2010. [PDF]
 A micromacro decomposition based asymptoticpreserving scheme for the multispecies Boltzmann equation , (with Yingzhe Shi), SIAM J. Sci. Comp. 31, 45804606, 2010. [PDF]
 A numerical study of the Gaussian beam methods for onedimensional Schr"odingerPoisson equations , (with Hao Wu and Xu Yang), J. Comp. Math. 28, 261272, 2010. [PDF]
 A coherent semiclassical transport model for purestate quantum scattering, (with K. Novak), Comm. Math. Sci. 8, 253275, 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: wellbalanced 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 671, 93104, 2009, American Mathematical Society. [PDF]
 On a uniformly second order numerical method for the onedimensional discreteordinate transport equation and its diffusion limit with interface (with Min Tang and Houde Han), Networks and Heterogeneous Media 4, 3565, 2009.[PDF]
 The l^1stability of a Hamiltonianpreserving scheme for the Liouville equation with discontinuous potentials (with X. Wen), J. Comp. Math., 27 (2009), pp. 4567.[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, 1528, 2009. [PDF]