23 citations · 44 across the 10 of their papers we have counts for
11 papers
A fifth-order absolutely convergent fixed-point fast sweeping hybrid alternative WENO scheme for steady state of hyperbolic conservation laws
Liang Li, Jun Zhu, Shanqin Chen +1
In this paper, we extend the previous work on absolutely convergent fixed-point fast sweeping WENO methods by Li et al. (J. Comput. Phys. 443: 110516, 2021) and design a fifth-orde…
A Conservative and Positivity-Preserving Discontinuous Galerkin Method for the Population Balance Equation
Ziyao Xu, Guanyang Liu, Yong-Tao Zhang
We develop a conservative, positivity-preserving discontinuous Galerkin (DG) method for the population balance equation (PBE), which models the distribution of particle numbers acr…
Exponential Time Differencing Runge-Kutta Discontinuous Galerkin (ETD-RKDG) Methods for Nonlinear Degenerate Parabolic Equations
Ziyao Xu, Yong-Tao Zhang
In this paper, we study high-order exponential time differencing Runge-Kutta (ETD-RK) discontinuous Galerkin (DG) methods for nonlinear degenerate parabolic equations. This class o…
Stability and Time-Step Constraints of Exponential Time Differencing Runge--Kutta Discontinuous Galerkin Methods for Advection-Diffusion Equations
Ziyao Xu, Zheng Sun, Yong-Tao Zhang
In this paper, we investigate the stability and time-step constraints for solving advection-diffusion equations using exponential time differencing (ETD) Runge-Kutta (RK) methods i…
High-order exponential time differencing multi-resolution alternative finite difference WENO methods for nonlinear degenerate parabolic equations
Ziyao Xu, Yong-Tao Zhang
In this paper, we focus on the finite difference approximation of nonlinear degenerate parabolic equations, a special class of parabolic equations where the viscous term vanishes i…
An absolutely convergent fixed-point fast sweeping WENO method on triangular meshes for steady state of hyperbolic conservation laws
Liang Li, Jun Zhu, Yong-Tao Zhang
High order fast sweeping methods for efficiently solving steady state solutions of hyperbolic PDEs were not available yet on unstructured meshes. In this paper, we extend high orde…
Sparse grid implementation of a fixed-point fast sweeping WENO scheme for Eikonal equations
Zachary M. Miksis, Yong-Tao Zhang
Fixed-point fast sweeping methods are a class of explicit iterative methods developed in the literature to efficiently solve steady state solutions of hyperbolic partial differenti…
Fast sparse grid simulations of fifth order WENO scheme for high dimensional hyperbolic PDEs
Xiaozhi Zhu, Yong-Tao Zhang
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). H…
Absolutely convergent fixed-point fast sweeping WENO methods for steady state of hyperbolic conservation laws
Liang Li, Jun Zhu, Yong-Tao Zhang
Fixed-point iterative sweeping methods were developed in the literature to efficiently solve steady state solutions of Hamilton-Jacobi equations and hyperbolic conservation laws. S…
Krylov implicit integration factor discontinuous Galerkin methods on sparse grids for high dimensional reaction-diffusion equations
Yuan Liu, Yingda Cheng, Shanqin Chen +1
Computational costs of numerically solving multidimensional partial differential equations (PDEs) increase significantly when the spatial dimensions of the PDEs are high, due to la…
Third order WENO scheme on sparse grids for hyperbolic equations
Dong Lu, Shanqin Chen, Yong-Tao Zhang
The weighted essentially non-oscillatory (WENO) schemes are a popular class of high order accurate numerical methods for solving hyperbolic partial differential equations (PDEs). T…