2 citations · 2 across the 6 of their papers we have counts for
6 papers
Capturing the Diffusive Behavior of the Multiscale Linear Transport Equations by Asymptotic-Preserving Convolutional DeepONets
Keke Wu, Xiong-bin Yan, Shi Jin +1
In this paper, we introduce two types of novel Asymptotic-Preserving Convolutional Deep Operator Networks (APCONs) designed to address the multiscale time-dependent linear transpor…
Asymptotic-Preserving Neural Networks for Multiscale Kinetic Equations
Shi Jin, Zheng Ma, Keke Wu
In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equatio…
Numerical Stability for Differential Equations with Memory
Guihong Wang, Yuqing Li, Tao Luo +3
In this work, we systematically investigate linear multi-step methods for differential equations with memory. In particular, we focus on the numerical stability for multi-step meth…
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…
The Discrete Stochastic Galerkin Method for Hyperbolic Equations with Non-smooth and Random Coefficients
Shi Jin, Zheng Ma
We develop a general polynomial chaos (gPC) based stochastic Galerkin (SG) for hyperbolic equations with random and singular coefficients. Due to the singu- lar nature of the solut…
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…