62 citations · 226 across the 32 of their papers we have counts for
32 papers
Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation
Jingwei Hu, Ruiwen Shu
Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to treat multiscale equations that contain a stiff part and a non-stiff part, where the stiff part is characteri…
Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system
Jingwei Hu, Ansgar Jüngel, Nicola Zamponi
The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker-Planck-Landau system for plasmas in the three-dimensional whole space is shown. The Fo…
Asymptotic--preserving and energy stable dynamical low-rank approximation
Lukas Einkemmer, Jingwei Hu, Jonas Kusch
Radiation transport problems are posed in a high-dimensional phase space, limiting the use of finely resolved numerical simulations. An emerging tool to efficiently reduce computat…
Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system
Jack Coughlin, Jingwei Hu
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, whi…
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…
A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation
Jingwei Hu, Kunlun Qi, Tong Yang
Numerical approximation of the Boltzmann equation is a challenging problem due to its high-dimensional, nonlocal, and nonlinear collision integral. Over the past decade, the Fourie…
An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
Lukas Einkemmer, Jingwei Hu, Yubo Wang
We introduce a dynamical low-rank method to reduce the computational complexity for solving the multi-scale multi-dimensional linear transport equation. The method is based on a ma…
Uncertainty quantification for the BGK model of the Boltzmann equation using multilevel variance reduced Monte Carlo methods
Jingwei Hu, Lorenzo Pareschi, Yubo Wang
We propose a control variate multilevel Monte Carlo method for the kinetic BGK model of the Boltzmann equation subject to random inputs. The method combines a multilevel Monte Carl…
A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
Jingwei Hu, Kunlun Qi
We introduce a fast Fourier spectral method for the spatially homogeneous Boltzmann equation with non-cutoff collision kernels. Such kernels contain non-integrable singularity in t…
Recent development in kinetic theory of granular materials: analysis and numerical methods
Jose Antonio Carrillo, Jingwei Hu, Zheng Ma +1
Over the past decades, kinetic description of granular materials has received a lot of attention in mathematical community and applied fields such as physics and engineering. This…
On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations
Jingwei Hu, Ruiwen Shu
Many hyperbolic and kinetic equations contain a non-stiff convection/transport part and a stiff relaxation/collision part (characterized by the relaxation or mean free time $\varep…
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 particle method for the homogeneous Landau equation
Jose A. Carrillo, Jingwei Hu, Li Wang +1
We propose a novel deterministic particle method to numerically approximate the Landau equation for plasmas. Based on a new variational formulation in terms of gradient flows of th…
Quantification of thermally-driven flows in microsystems using Boltzmann equation in deterministic and stochastic contexts
Shashank Jaiswal, Aaron Pikus, Andrew Strongrich +3
When the flow is sufficiently rarefied, a temperature gradient, for example, between two walls separated by a few mean free paths, induces a gas flow---an observation attributed to…
A discontinuous Galerkin fast spectral method for multi-species full Boltzmann on streaming multi-processors
Shashank Jaiswal, Jingwei Hu, Julien K. Brillon +1
When the molecules of a gaseous system are far apart, say in microscale gas flows where the surface to volume ratio is high and hence the surface forces dominant, the molecule-surf…