4 papers · 1 filter
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…