7 citations · 17 across the 7 of their papers we have counts for
7 papers
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 sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions
Wei Guo, Juntao Huang, Zhanjing Tao +1
We are interested in numerically solving the Hamilton-Jacobi (HJ) equations, which arise in optimal control and many other applications. Oftentimes, such equations are posed in hig…
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…
An adaptive high-order piecewise polynomial based sparse grid collocation method with applications
Zhanjing Tao, Yan Jiang, Yingda Cheng
This paper constructs adaptive sparse grid collocation method onto arbitrary order piecewise polynomial space. The sparse grid method is a popular technique for high dimensional pr…
Sparse Grid Central Discontinuous Galerkin Method for Linear Hyperbolic Systems in High Dimensions
Zhanjing Tao, Anqi Chen, Mengping Zhang +1
In this paper, we develop sparse grid central discontinuous Galerkin (CDG) scheme for linear hyperbolic systems with variable coefficients in high dimensions. The scheme combines t…
Sparse Grid Discontinuous Galerkin Methods for the Vlasov-Maxwell System
Zhanjing Tao, Wei Guo, Yingda Cheng
In this paper, we develop sparse grid discontinuous Galerkin (DG) schemes for the Vlasov-Maxwell (VM) equations. The VM system is a fundamental kinetic model in plasma physics, and…