62 citations · 226 across the 32 of their papers we have counts for
10 papers · 1 filter
An adaptive dynamical low rank method for the nonlinear Boltzmann equation
Jingwei Hu, Yubo Wang
Efficient and accurate numerical approximation of the full Boltzmann equation has been a longstanding challenging problem in kinetic theory. This is mainly due to the high dimensio…
Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation
Rafael Bailo, José A. Carrillo, Jingwei Hu
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the ca…
Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
Ricardo A. Delgadillo, Jingwei Hu, Haizhao Yang
Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this…
Implicit Regularization Effects of the Sobolev Norms in Image Processing
Bowen Zhu, Jingwei Hu, Yifei Lou +1
In this paper, we propose to use the general -based Sobolev norms, i.e., norms where , to measure the data discrepancy due to noise in image processing…
A structure preserving numerical scheme for Fokker-Planck equations of structured neural networks with learning rules
Qing He, Jingwei Hu, Zhennan Zhou
In this work, we are concerned with a Fokker-Planck equation related to the nonlinear noisy leaky integrate-and-fire model for biological neural networks which are structured by th…
An entropic method for discrete systems with Gibbs entropy
Zhenning Cai, Jingwei Hu, Yang Kuang +1
We consider general systems of ordinary differential equations with monotonic Gibbs entropy, and introduce an entropic scheme that simply imposes an entropy fix after every time st…
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Jingwei Hu, Xiaodong Huang, Jie Shen +1
Numerical approximation of the Boltzmann equation presents a challenging problem due to its high-dimensional, nonlinear, and nonlocal collision operator. Among the deterministic me…
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker-Planck and Keller-Segel equations
Jingwei Hu, Xiangxiong Zhang
In this work, we introduce semi-implicit or implicit finite difference schemes for the continuity equation with a gradient flow structure. Examples of such equations include the li…
High order strong stability preserving multi-derivative implicit and IMEX Runge--Kutta methods with asymptotic preserving properties
Sigal Gottlieb, Zachary J. Grant, Jingwei Hu +1
In this work we present a class of high order unconditionally strong stability preserving (SSP) implicit multi-derivative Runge--Kutta schemes, and SSP implicit-explicit (IMEX) mul…
An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime
Lukas Einkemmer, Jingwei Hu, Lexing Ying
It has recently been demonstrated that dynamical low-rank algorithms can provide robust and efficient approximation to a range of kinetic equations. This is true especially if the…