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11/09/2022
A micro-macro decomposed reduced basis method for the time-dependent radiative transfer equation
Kinetic transport equations are notoriously difficult to simulate becaus...
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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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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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03/12/2021
A reduced basis method for radiative transfer equation
Linear kinetic transport equations play a critical role in optical tomog...
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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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05/11/2020
Stability-enhanced AP IMEX1-LDG method: energy-based stability and rigorous AP property
In our recent work [22], a family of high order asymptotic preserving (A...
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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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12/09/2019
An adaptive high-order piecewise polynomial based sparse grid collocation method with applications
This paper constructs adaptive sparse grid collocation method onto arbit...
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03/05/2019