2013 - SIAM Fellow For contributions to relaxation schemes, numerical algorithms for kinetic equations and high frequency wave propagation.
2013 - Fellow of the American Mathematical Society
His primary areas of investigation include Mathematical analysis, Partial differential equation, Boltzmann equation, Conservation law and Nonlinear system. All of his Mathematical analysis and Schrödinger equation, Numerical analysis, Discretization, Hyperbolic partial differential equation and Initial value problem investigations are sub-components of the entire Mathematical analysis study. His research in Partial differential equation focuses on subjects like Relaxation, which are connected to Runge–Kutta methods and Statistical physics.
The Boltzmann equation study combines topics in areas such as Convection, Heat equation, HPP model, Lattice gas automaton and Relaxation. The various areas that Shi Jin examines in his Conservation law study include Relaxation, Scalar, Random projection and Dissipative system. His Nonlinear system research includes themes of Space, Total variation diminishing and Euler's formula.
Mathematical analysis, Applied mathematics, Nonlinear system, Statistical physics and Numerical analysis are his primary areas of study. His work is connected to Schrödinger equation, Discretization, Convection–diffusion equation, Conservation law and Limit, as a part of Mathematical analysis. Shi Jin works mostly in the field of Applied mathematics, limiting it down to topics relating to Boltzmann equation and, in certain cases, Stochastic galerkin and Relaxation, as a part of the same area of interest.
Shi Jin focuses mostly in the field of Nonlinear system, narrowing it down to matters related to Space and, in some cases, Polynomial chaos. As part of one scientific family, Shi Jin deals mainly with the area of Statistical physics, narrowing it down to issues related to the Kinetic energy, and often Boltzmann constant. His Numerical analysis research is multidisciplinary, incorporating perspectives in Computation and Classical mechanics.
Shi Jin focuses on Applied mathematics, Statistical physics, Nonlinear system, Limit and Numerical analysis. He has researched Applied mathematics in several fields, including Space, Global optimization and Exponential function. His studies in Statistical physics integrate themes in fields like Boltzmann constant, Knudsen number and Kinetic energy.
His studies deal with areas such as Boltzmann equation and Semiclassical physics as well as Nonlinear system. His Limit research entails a greater understanding of Mathematical analysis. His Numerical analysis study integrates concerns from other disciplines, such as Planck constant, Quantum dynamics, Quantum, Mathematical physics and Rate of convergence.
Shi Jin spends much of his time researching Statistical physics, Nonlinear system, Applied mathematics, Limit and Batch method. His work carried out in the field of Statistical physics brings together such families of science as Particle, Knudsen number, Interaction problem and Flocking. His work in Nonlinear system addresses subjects such as Boltzmann equation, which are connected to disciplines such as Kinetic energy.
His work deals with themes such as Isotropy, Global optimization and Exponential function, which intersect with Applied mathematics. Limit is a subfield of Mathematical analysis that Shi Jin tackles. The study of Mathematical analysis is intertwined with the study of Isentropic process in a number of ways.
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The relaxation schemes for systems of conservation laws in arbitrary space dimensions
Shi Jin;Zhouping Xin.
Communications on Pure and Applied Mathematics (1995)
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing (1999)
On time-splitting spectral approximations for the Schrödinger equation in the semiclassical regime
Weizhu Bao;Shi Jin;Peter A. Markowich.
Journal of Computational Physics (2002)
Physical symmetry and lattice symmetry in the lattice Boltzmann method
Nianzheng Cao;Nianzheng Cao;Shiyi Chen;Shiyi Chen;Shi Jin;Daniel Martínez;Daniel Martínez.
Physical Review E (1997)
A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources
Francis Filbet;Shi Jin.
Journal of Computational Physics (2010)
Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms
Shi Jin;C.David Levermore.
Journal of Computational Physics (1996)
Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms
Journal of Computational Physics (1995)
Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrödinger Equations in the Semiclassical Regimes
Weizhu Bao;Shi Jin;Peter A. Markowich.
SIAM Journal on Scientific Computing (2003)
A steady-state capturing method for hyperbolic systems with geometrical source terms
Mathematical Modelling and Numerical Analysis (2001)
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
Shi Jin;Lorenzo Pareschi;Giuseppe Toscani.
SIAM Journal on Numerical Analysis (2000)
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