Research

My research interests include energy minimization problems and related gradient flows, collective dynamics, numerical methods for kinetic and hyperbolic problems, and uncertainty quantification.

Selected publications:

[19] José A. Carrillo and Ruiwen Shu, From radial symmetry to fractal behavior of aggregation equilibria for repulsive-attractive potentials, submitted.

[18] Mingchang Ding, Jing-Mei Qiu and Ruiwen Shu, Accuracy and stability analysis of the Semi-Lagrangian method for stiff hyperbolic relaxation systems and kinetic BGK model, submitted.

[17] Mingchang Ding, Jing-Mei Qiu and Ruiwen Shu, Semi-Lagrangian nodal discontinuous Galerkin method for the BGK Model, submitted.

[16] Sigal Gottlieb, Zachary Grant, Jingwei Hu and Ruiwen Shu, High order unconditionally strong stability preserving multi-derivative implicit and IMEX Runge-Kutta methods with asymptotic preserving properties, SIAM Numer. Anal., accepted.

[15] Douglas Hardin, Edward Saff, Ruiwen Shu and Eitan Tadmor, Dynamics of particles on a curve with pairwise hyper-singular repulsion, Discrete Contin. Dyn. Syst., accepted.

[14] Ruiwen Shu and Eitan Tadmor, Newtonian repulsion and radial confinement: convergence towards steady state, Mathematical Models and Methods in Applied Sciences, 1-25, 2021.

[13] Ruiwen Shu, Tightness of radially-symmetric solutions to 2D aggregation-diffusion equations with weak interaction forces, submitted.

[12] Ruiwen Shu, Equilibration of aggregation-diffusion equations with weak interaction forces, SIAM J. Math. Anal., accepted.

[11] Jingwei Hu and Ruiwen Shu, On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations, Mathematics of Computation, 90: 641-670, 2021.

[10] Ruiwen Shu and Eitan Tadmor, Anticipation breeds alignment, Archive for Rational Mechanics and Analysis, 240(1): 203-241, 2021.

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

[8] Ruiwen Shu and Eitan Tadmor, Flocking hydrodynamics with external potentials, Archive for Rational Mechanics and Analysis, 2020: 1-35.

[7] Jingwei Hu and Ruiwen Shu, A second-order asymptotic-preserving and positivity-preserving exponential Runge-Kutta method for a class of stiff kinetic equations, SIAM Multiscale Model. Simul., 17(4): 1123-1146, 2019.

[6] Ruiwen Shu and Shi Jin, A study of Landau damping with random initial inputs, J. Differ. Equat., 266(4): 1922-1945, 2019.

[5] Jingwei Hu, Ruiwen Shu and Xiangxiong Zhang, Asymptotic-preserving and positivity-preserving implicit-explicit schemes for the stiff BGK equation, SIAM J. Numer. Anal., 56(2): 942-973, 2018.

[4] Qin Li, Jian-Guo Liu and Ruiwen Shu, Sensitivity analysis of Burgers’ equation with shocks, SIAM/ASA J. Uncertainty Quantification, 8(4): 1493-1521, 2020.

[3] Qin Li, Ruiwen Shu and Li Wang, A new numerical approach to inverse transport equation with error analysis, SIAM J. Numer. Anal., 56(6): 3358-3385, 2018.

[2] 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, ESAIM Math. Model. Numer. Anal., 52(5): 1651-1678, 2018.

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