209 citations · 1.4k across the 114 of their papers we have counts for
18 papers · 1 filter
High-order Moment Closure Models with Random Batch Method for Efficient Computation of Multiscale Turbulent Systems
Di Qi, Jian-Guo Liu
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in mult…
Diffusion approximations of Oja's online principal component analysis
Jian-Guo Liu, Zibu Liu
Oja's algorithm of principal component analysis (PCA) has been one of the methods utilized in practice to reduce dimension. In this paper, we focus on the convergence property of t…
On the Random Batch Method for second order interacting particle systems
Shi Jin, Lei Li, Yiqun Sun
We investigate several important issues regarding the Random Batch Method (RBM) for second order interacting particle systems. We first show the uniform-in-time strong convergence…
Projection method for droplet dynamics on groove-textured surface with merging and splitting
Yuan Gao, Jian-Guo Liu
The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases…
Some random batch particle methods for the Poisson-Nernst-Planck and Poisson-Boltzmann equations
Lei Li, Jian-Guo Liu, Yijia Tang
We consider in this paper random batch interacting particle methods for solving the Poisson-Nernst-Planck (PNP) equations, and thus the Poisson-Boltzmann (PB) equation as the equil…
Convergence of Random Batch Method for interacting particles with disparate species and weights
Shi Jin, Lei Li, Jian-Guo Liu
We consider in this work the convergence of Random Batch Method proposed in our previous work [Jin et al., J. Comput. Phys., 400(1), 2020] for interacting particles to the case of…
Gradient flow formulation and second order numerical method for motion by mean curvature and contact line dynamics on rough surface
Yuan Gao, Jian-Guo Liu
We study the dynamics of a droplet moving on an inclined rough surface in the absence of inertial and viscous stress effects. In this case, the dynamics of the droplet is a purely…
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
Jingwei Hu, Jian-Guo Liu, Yantong Xie +1
In this work, we are concerned with the Fokker-Planck equations associated with the Nonlinear Noisy Leaky Integrate-and-Fire model for neuron networks. Due to the jump mechanism at…
A discretization of Caputo derivatives with application to time fractional SDEs and gradient flows
Lei Li, Jian-Guo Liu
We consider a discretization of Caputo derivatives resulted from deconvolving a scheme for the corresponding Volterra integral. Properties of this discretization, including signs o…
Random batch methods (RBM) for interacting particle systems
Shi Jin, Lei Li, Jian-Guo Liu
We develop Random Batch Methods for interacting particle systems with large number of particles. These methods use small but random batches for particle interactions, thus the comp…
Large time behaviors of upwind schemes by jump processes
Lei Li, Jian-Guo Liu
We revisit the traditional upwind schemes for linear conservation laws in the viewpoint of jump processes, allowing studying upwind schemes using probabilistic tools. In particular…
On Runge-Kutta methods for the water wave equation and its simplified nonlocal hyperbolic model
Lei Li, Jian-Guo Liu, Zibu Liu +2
There is a growing interest in investigating numerical approximations of the water wave equation in recent years, whereas the lack of rigorous analysis of its time discretization i…
An accurate front capturing scheme for tumor growth models with a free boundary limit
Jian-Guo Liu, Min Tang, Li Wang +1
We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when t…
Sensitivity analysis of Burgers' equation with shocks
Qin Li, Jian-Guo Liu, Ruiwen Shu
Generalized polynomial chaos (gPC) method has been extensively used in uncertainty quantification problems where equations contain random variables. For gPC to achieve high accurac…
Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations
Jian-Guo Liu, Li Wang, Zhennan Zhou
We propose a semi-discrete scheme for 2D Keller-Segel equations based on a symmetrization reformation, which is equivalent to the convex splitting method and is free of any nonline…
Explicit and implicit TVD schemes for conservation laws with Caputo derivatives
Jian-Guo Liu, Zheng Ma, Zhennan Zhou
In this paper, we investigate numerical approximations of the scalar conservation law with the Caputo derivative, which introduces the memory effect. We construct the first order a…
Analysis of an asymptotic preserving scheme for linear kinetic equations in the diffusion limit
Jian-Guo Liu, Luc Mieussens
We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31, pp. 334-368, 2008] for linear transport equ…
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
Philippe G. LeFloch, Jian-Guo Liu
Solutions to conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increa…