Professor Shi JinThe department is delighted to welcome Professor Shi Jin (University of Wisconsin-Madison/Shanghai Jiao Tong University) as a Nelder Fellow in 2018.

Uncertainty Quantification for Kinetic Equations

Lecture 1: Basics of Kinetic Equations, Asymptotic Limits, and Asymptotic-Preserving Schemes

In this lecture we will review  some basic properties of kinetic equations, their various asymptotic limits, and introduce the Asymptotic-Preserving paradigm for multiscale kinetic equations and related problems.

View Professor Jin's slides for Lecture 1 (PDF)

Lecture 2: Kinetic equations with random uncertainties, numerical methods, and stochastic Asymptotic-Preserving Schemes

In this lecture we will study polynomial chaos based stochastic Galerkin methods for multiscale kinetic equations with random uncertainties, and introduce the notation of stochastic Asymptotic-Preserving schemes to handle both multiscales and uncertainty.

View Professor Jin's slides for Lecture 2 (PDF)

Lecture 3: Hypocoercivity theory based regularity, sensitivity and numerical analysis for uncertain kinetic equations

Hypocoercivity theory plays important role in studying the long-time behavior of kinetic equations. We will show how such a theory, well-established for deterministic kinetic equations, can be extended to study the regularity, local sensitivity with respect to random inputs in initial data and collision kernels, and long-time behavior of the solution in the random space. We will also use such theory to establish spectral accuracy, error estimates and long-time behavior of polynomial chaos based stochastic Galerkin methods.

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Lecture 4: High dimensional random space

We will introduce some techniques to handle high dimensional random space for linear kinetic equations with random inputs. Examples include sparse grids, best-N approximations and greedy algorithms.

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Applied PDEs seminar

Semiclassical computational methods for quantum dynamics with band-crossing and uncertainty

Band-crossing is a quantum dynamical behavior that contributes to important physics and chemistry phenomena such as quantum tunneling, Berry connection, chemical reaction etc. In this talk, we will discuss some recent works in developing semiclassical methods for band-crossing in surface hopping. For such systems we will also introduce a nonlinear geometric method based "asymptotic-preserving" method that is accurate uniformly for all wave numbers, including the problem with random uncertain band gaps.
 
View the seminar slides: Professor Shi Jin seminar slides (PDF)

Speaker biography

Shi Jin is a Vilas Distinguished Achievement Professor of Mathematics at the University of Wisconsin-Madison. He earned his B.S. from Peking University and his Ph.D. from the University of Arizona. His research fields include computational fluid dynamics, kinetic equations, hyperbolic conservation laws, high frequency waves, quantum dynamics, and uncertainty quantification – fields in which he has published over 150 papers. He has been honored with the Feng Kang Prize in Scientific Computing and the Morningside Silver Medal of Mathematics at the Fourth International Congress of Chinese Mathematicians, and is a Fellow of both the American Mathematical Society (AMS) and the Society for Industrial and Applied Mathematics (SIAM).. He is an invited speaker at the International Congress of Mathematicians in Rio De Janeiro, 2018.

View Professor Shi Jin's website