37 citations · 126 across the 18 of their papers we have counts for
17 papers · 1 filter
The sharp CFL condition of the piecewise constant sparse grid discontinuous Galerkin method for high-dimensional transport equations
Juntao Huang
We establish the sharp CFL condition for the piecewise constant sparse grid discontinuous Galerkin (DG) method with forward Euler time stepping, applied to transport equations with…
On the rotational invariance and hyperbolicity of shallow water moment equations in two dimensions
Matthew Bauerle, Andrew J. Christlieb, Mingchang Ding +1
In this paper, we investigate the two-dimensional extension of a recently introduced set of shallow water models based on a regularized moment expansion of the incompressible Navie…
Bound-preserving discontinuous Galerkin methods with modified Patankar time integrations for chemical reacting flows
Fangyao Zhu, Juntao Huang, Yang Yang
In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for chemical reactive flows. There are several difficulties in constructing suitable numerical scheme…
Adaptive sparse grid discontinuous Galerkin method: review and software implementation
Juntao Huang, Wei Guo, Yingda Cheng
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-DG) method for computing high dimensional partial differential equations (PDEs) and its software implementat…
Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations
Andrés Galindo-Olarte, Juntao Huang, Jennifer K. Ryan +1
This paper considers the discontinuous Galerkin (DG) methods for solving the Vlasov-Maxwell (VM) system, a fundamental model for collisionless magnetized plasma. The DG methods pro…
Coupling conditions for linear hyperbolic relaxation systems in two-scales problems
Juntao Huang, Ruo Li, Yizhou Zhou
This work is concerned with coupling conditions for linear hyperbolic relaxation systems with multiple relaxation times. In the region with small relaxation time, an equilibrium sy…
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
Juntao Huang, Thomas Izgin, Stefan Kopecz +2
In this paper, we perform stability analysis for a class of second and third order accurate strong-stability-preserving modified Patankar Runge-Kutta (SSPMPRK) schemes, which were…
Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds
Juntao Huang, Yingda Cheng, Andrew J. Christlieb +1
This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021g…
Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures
Juntao Huang, Yingda Cheng, Andrew J. Christlieb +2
This is the second paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation (RTE). In our previous work \cite{huang2021…
Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
Juntao Huang, Yingda Cheng, Andrew J. Christlieb +1
In this paper, we take a data-driven approach and apply machine learning to the moment closure problem for radiative transfer equation in slab geometry. Instead of learning the unc…
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…
Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws
Weifeng Zhao, Juntao Huang, Steven J. Ruuth
In \cite{ZH2019}, we developed a boundary treatment method for implicit-explicit (IMEX) Runge-Kutta (RK) methods for solving hyperbolic systems with source terms. Since IMEX RK met…
Boundary treatment of implicit-explicit Runge-Kutta method for hyperbolic systems with source terms
Weifeng Zhao, Juntao Huang
In this paper, we develop a high order finite difference boundary treatment method for the implicit-explicit (IMEX) Runge-Kutta (RK) schemes solving hyperbolic systems with possibl…
An adaptive multiresolution discontinuous Galerkin method with artificial viscosity for scalar hyperbolic conservation laws in multidimensions
Juntao Huang, Yingda Cheng
In this paper, we develop an adaptive multiresolution discontinuous Galerkin (DG) scheme for scalar hyperbolic conservation laws in multidimensions. Compared with previous work for…