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06/12/2023
On the rotational invariance and hyperbolicity of shallow water moment equations in two dimensions
In this paper, we investigate the two-dimensional extension of a recentl...
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11/10/2022
Bound-preserving discontinuous Galerkin methods with modified Patankar time integrations for chemical reacting flows
In this paper, we develop bound-preserving discontinuous Galerkin (DG) m...
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11/03/2022
Adaptive sparse grid discontinuous Galerkin method: review and software implementation
This paper reviews the adaptive sparse grid discontinuous Galerkin (aSG-...
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10/14/2022
Superconvergence and accuracy enhancement of discontinuous Galerkin solutions for Vlasov-Maxwell equations
This paper considers the discontinuous Galerkin (DG) methods for solving...
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07/14/2022
Coupling conditions for linear hyperbolic relaxation systems in two-scales problems
This work is concerned with coupling conditions for linear hyperbolic re...
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05/03/2022
On the stability of strong-stability-preserving modified Patankar Runge-Kutta schemes
In this paper, we perform stability analysis for a class of second and t...
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09/02/2021
Machine learning moment closure models for the radiative transfer equation III: enforcing hyperbolicity and physical characteristic speeds
This is the third paper in a series in which we develop machine learning...
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05/30/2021
Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures
This is the second paper in a series in which we develop machine learnin...
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05/12/2021
Machine learning moment closure models for the radiative transfer equation I: directly learning a gradient based closure
In this paper, we take a data-driven approach and apply machine learning...
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04/12/2021
A class of adaptive multiresolution ultra-weak discontinuous Galerkin methods for some nonlinear dispersive wave equations
In this paper, we propose a class of adaptive multiresolution (also call...
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01/17/2021
Data-driven discovery of multiscale chemical reactions governed by the law of mass action
In this paper, we propose a data-driven method to discover multiscale ch...
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09/28/2020
Learning Interpretable and Thermodynamically Stable Partial Differential Equations
In this work, we develop a method for learning interpretable and thermod...
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07/03/2020
An adaptive multiresolution ultra-weak discontinuous Galerkin method for nonlinear Schrodinger equations
This paper develops a high order adaptive scheme for solving nonlinear S...
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05/29/2020
An adaptive sparse grid local discontinuous Galerkin method for Hamilton-Jacobi equations in high dimensions
We are interested in numerically solving the Hamilton-Jacobi (HJ) equati...
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04/18/2020
An adaptive multiresolution interior penalty discontinuous Galerkin method for wave equations in second order form
In this paper, we propose a class of adaptive multiresolution (also call...
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01/24/2020
Boundary treatment of high order Runge-Kutta methods for hyperbolic conservation laws
In <cit.>, we developed a boundary treatment method for implicit-explici...
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08/02/2019