27 citations · 45 across the 6 of their papers we have counts for
6 papers · 1 filter
A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations
Juntao Huang, Yong Liu, Yuan Liu +2
In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) ultra-weak discontinuous Galerkin (UWDG) methods for solving some nonlinear dispers…
An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations
Zhanjing Tao, Juntao Huang, Yuan Liu +2
This paper develops a high order adaptive scheme for solving nonlinear Schrodinger equations. The solutions to such equations often exhibit solitary wave and local structures, whic…
An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form
Juntao Huang, Yuan Liu, Wei Guo +2
In this paper, we propose a class of adaptive multiresolution (also called adaptive sparse grid) discontinuous Galerkin (DG) methods for simulating scalar wave equations in second…
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…
High order operator splitting methods based on an integral deferred correction framework
Andrew J. Christlieb, Yuan Liu, Zhengfu Xu
Integral deferred correction (IDC) methods have been shown to be an efficient way to achieve arbitrary high order accuracy and possess good stability properties. In this paper, we…
Positivity-Preserving Finite Difference WENO Schemes with Constrained Transport for Ideal Magnetohydrodynamic Equations
Andrew J. Christlieb, Yuan Liu, Qi Tang +1
In this paper, we utilize the maximum-principle-preserving flux limiting technique, originally designed for high order weighted essentially non-oscillatory (WENO) methods for scala…