12 citations · 39 across the 15 of their papers we have counts for
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A fully discrete LBRFD-IPDG method for linear fourth-order parabolic equations
Hongying Huang, Hong Zhang, Yanming Zhang
We propose a fully discrete method for linear fourth-order parabolic equations with Dirichlet boundary conditions, combining an implicit LBRFD multistep scheme in time with a mixed…
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…
Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions
Ziyuan Liu, Haifeng Wang, Hong Zhang +3
By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency th…
Mass and energy conservative high order diagonally implicit Runge--Kutta schemes for nonlinear Schrödinger equation in one and two dimensions
Ziyuan Liu, Hong Zhang, Xu Qian +1
We present and analyze a series of conservative diagonally implicit Runge--Kutta schemes for the nonlinear Schrödiner equation. With the application of the newly developed invarian…
Runge-Kutta symmetric interior penalty discontinuous Galerkin methods for modified Buckley-Leverett equations
Hong Zhang, Yunrui Guo, Weibin Li +1
We present a robust and accurate numerical method to solve the modified Buckley-Leverett equation in two-phase porous media flow with dynamic capillary pressure effect. A symmetric…
Simulation of thin film flows with a moving mesh mixed finite element method
Hong Zhang, Paul A Zegeling
We present an efficient mixed finite element method to solve the fourth-order thin film flow equations using moving mesh refinement. The moving mesh strategy is based on harmonic m…