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02/14/2023
Stability analysis of the Eulerian-Lagrangian finite volume methods for nonlinear hyperbolic equations in one space dimension
In this paper, we construct a novel Eulerian-Lagrangian finite volume (E...
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10/13/2022
A Local Macroscopic Conservative (LoMaC) low rank tensor method with the discontinuous Galerkin method for the Vlasov dynamics
In this paper, we propose a novel Local Macroscopic Conservative (LoMaC)...
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08/08/2022
Fourth-order conservative non-splitting semi-Lagrangian Hermite WENO schemes for kinetic and fluid simulations
We present fourth-order conservative non-splitting semi-Lagrangian (SL) ...
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07/27/2022
A mass conservative Eulerian-Lagrangian Runge-Kutta discontinuous Galerkin method for wave equations with large time stepping
We propose an Eulerian-Lagrangian (EL) Runge-Kutta (RK) discontinuous Ga...
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07/01/2022
A Local Macroscopic Conservative (LoMaC) low rank tensor method for the Vlasov dynamics
In this paper, we propose a novel Local Macroscopic Conservative (LoMaC)...
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01/25/2022
A conservative low rank tensor method for the Vlasov dynamics
In this paper, we propose a conservative low rank tensor method to appro...
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06/16/2021
A Low Rank Tensor Representation of Linear Transport and Nonlinear Vlasov Solutions and Their Associated Flow Maps
We propose a low-rank tensor approach to approximate linear transport an...
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06/04/2021
High Order Semi-implicit WENO Schemes for All Mach Full Euler System of Gas Dynamics
In this paper, we propose high order semi-implicit schemes for the all M...
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05/06/2021
Accuracy and stability analysis of the Semi-Lagrangian method for stiff hyperbolic relaxation systems and kinetic BGK model
In this paper, we develop a family of third order asymptotic-preserving ...
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05/06/2021
Semi-Lagrangian nodal discontinuous Galerkin method for the BGK Model
In this paper, we propose an efficient, high order accurate and asymptot...
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02/22/2021
A Generalized Eulerian-Lagrangian Discontinuous Galerkin Method for Transport Problems
We propose a generalized Eulerian-Lagrangian (GEL) discontinuous Galerki...
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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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02/07/2020
An Eulerian-Lagrangian discontinuous Galerkin method for transport problems and its application to nonlinear dynamics
We propose a new Eulerian-Lagrangian (EL) discontinuous Galerkin (DG) me...
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11/27/2019
High Order Semi-Lagrangian Discontinuous Galerkin Method Coupled with Runge-Kutta Exponential Integrators for Nonlinear Vlasov Dynamics
In this paper, we propose a semi-Lagrangian discontinuous Galerkin metho...
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07/13/2019