78 citations · 98 across the 6 of their papers we have counts for
6 papers
A generalized framework for direct discontinuous Galerkin methods for nonlinear diffusion equations
Mustafa Engin Danis, Jue Yan
In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is…
Cell-average based neural network method for high dimensional parabolic differential equations
Hong Zhang, Hongying Huang, Jue Yan
In this paper, we introduce cell-average based neural network (CANN) method to solve high-dimensional parabolic partial differential equations. The method is based on the integral…
Cell-average based neural network method for hyperbolic and parabolic partial differential equations
Changxin Qiu, Jue Yan
Motivated by finite volume scheme, a cell-average based neural network method is proposed. The method is based on the integral or weak formulation of partial differential equations…
A new direct discontinuous Galerkin method with interface correction for two-dimensional compressible Navier-Stokes equations
Mustafa E. Danis, Jue Yan
We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan (H. Liu, J. Y…
Accuracy and Architecture Studies of Residual Neural Network solving Ordinary Differential Equations
Changxin Qiu, Aaron Bendickson, Joshua Kalyanapu +1
In this paper we consider utilizing a residual neural network (ResNet) to solve ordinary differential equations. Stochastic gradient descent method is applied to obtain the optimal…
Third order Maximum-Principle-Satisfying Direct discontinuous Galerkin methods for time dependent convection diffusion equations on unstructured triangle mesh
Zheng Chen, Hongying Huang, Jue Yan
We develop 3rd order maximum-principle-satisfying direct discontinuous Galerkin methods [8, 9, 19, 21] for convection diffusion equations on unstructured triangular mesh. We carefu…