24 citations · 42 across the 12 of their papers we have counts for
12 papers
A Neural-network-based multiscale Hybridizable Discontinuous Galerkin method for solving PDEs in porous media
Tony Haines, Ke Shi
We develop a neural-network-accelerated multiscale hybridizable discontinuous Galerkin method for elliptic problems with heterogeneous coefficients. The method preserves the standa…
A Non-gradient DG method for second-order Elliptic Equations in the Non-divergence Form
Weifeng Qiu, Jin Ren, Ke Shi +1
based optimization is widely used in image denoising, machine learning and related applications. One of the main features of such approach is that it naturally provide a spar…
Analysis of a semi-implicit structure-preserving finite element method for the nonstationary incompressible Magnetohydrodynamics equations
Weifeng Qiu, Ke Shi
We revise the structure-preserving finite element method in [K. Hu, Y. MA and J. Xu. (2017) Stable finite element methods preserving exactly for MHD mod…
Improved Finite Difference Results for the Caputo Time-Fractional Diffusion Equation
Wesley Davis, Richard Noren, Ke Shi
We begin with a treatment of the Caputo time-fractional diffusion equation, by using the Laplace transform, to obtain a Volterra intego-differential equation where we may examine t…
Convergence of a - based finite element method for MHD models on Lipschitz domains
Kaibo Hu, Weifeng Qiu, Ke Shi
We discuss a class of magnetic-electric fields based finite element schemes for stationary magnetohydrodynamics (MHD) systems with two types of boundary conditions. We establish a…
A Mixed DG method and an HDG method for incompressible magnetohydrodynamics
Weifeng Qiu, Ke Shi
In this paper we propose and analyze a mixed DG method and an HDG method for the stationary Magnetohydrodynamics (MHD) equations with two types of boundary (or constraint) conditio…
Exploratory investigation of the HIPPO gas-jet target fluid dynamic properties
Zach Meisel, Ke Shi, Aleksandar Jemcov +1
In order to optimize the performance of gas-jet targets for future nuclear reaction measurements, a detailed understanding of the dependence of the gas-jet properties on experiment…
A superconvergent HDG method for the Maxwell equations
Huangxin Chen, Weifeng Qiu, Ke Shi
We present and analyze a new hybridizable discontinuous Galerkin (HDG) method for the steady state Maxwell equations. In order to make the problem well-posed, a condition of diverg…
A superconvergent HDG method for the Incompressible Navier-Stokes Equations on general polyhedral meshes
Weifeng Qiu, Ke Shi
We present a superconvergent hybridizable discontinuous Galerkin (HDG) method for the steady-state incompressible Navier-Stokes equations on general polyhedral meshes. For arbitrar…
A Generalized Multiscale Finite Element Method for the Brinkman Equation
Guanglian Li, Juan Galvis, Ke Shi
In this paper we consider the numerical upscaling of the Brinkman equation in the presence of high-contrast permeability fields. We develop and analyze a robust and efficient Gener…
An HDG method for linear elasticity with strong symmetric stresses
Weifeng Qiu, Jiguang Shen, Ke Shi
This paper presents a new hybridizable discontinuous Galerkin (HDG) method for linear elasticity on general polyhedral meshes, based on a strong symmetric stress formulation. The k…
A multiscale HDG method for second order elliptic equations. Part I. Polynomial and homogenization-based multiscale spaces
Yalchin Efendiev, Raytcho Lazarov, Ke Shi
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation o…