78 citations · 426 across the 35 of their papers we have counts for
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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…
Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property
Zhichao Peng, Yingda Cheng, Jing-Mei Qiu +1
In our recent work [22], a family of high order asymptotic preserving (AP) methods, termed as IMEX-LDG methods, are designed to solve some linear kinetic transport equations, inclu…
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…