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06/14/2023
Uniform accuracy of implicit-explicit Runge-Kutta (IMEX-RK) schemes for hyperbolic systems with relaxation
Implicit-explicit Runge-Kutta (IMEX-RK) schemes are popular methods to t...
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12/22/2022
Asymptotic–preserving and energy stable dynamical low-rank approximation
Radiation transport problems are posed in a high-dimensional phase space...
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04/22/2022
Efficient dynamical low-rank approximation for the Vlasov-Ampère-Fokker-Planck system
Kinetic equations are difficult to solve numerically due to their high d...
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12/05/2021
An adaptive dynamical low rank method for the nonlinear Boltzmann equation
Efficient and accurate numerical approximation of the full Boltzmann equ...
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10/15/2021
Bound-Preserving Finite-Volume Schemes for Systems of Continuity Equations with Saturation
We propose finite-volume schemes for general continuity equations which ...
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09/13/2021
Implicit Regularization Effects of the Sobolev Norms in Image Processing
In this paper, we propose to use the general L^2-based Sobolev norms (i....
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09/10/2021
A structure preserving numerical scheme for Fokker-Planck equations of structured neural networks with learning rules
In this work, we are concerned with a Fokker-Planck equation related to ...
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09/04/2021
Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
Learning time-dependent partial differential equations (PDEs) that gover...
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06/23/2021
An entropic method for discrete systems with Gibbs entropy
We consider general systems of ordinary differential equations with mono...
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05/18/2021
A fast Petrov-Galerkin spectral method for the multi-dimensional Boltzmann equation using mapped Chebyshev functions
Numerical approximation of the Boltzmann equation presents a challenging...
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03/31/2021
Positivity-preserving and energy-dissipative finite difference schemes for the Fokker-Planck and Keller-Segel equations
In this work, we introduce semi-implicit or implicit finite difference s...
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02/23/2021
High order unconditionally strong stability preserving multi-derivative implicit and IMEX Runge–Kutta methods with asymptotic preserving properties
In this work we present a class of high order unconditionally strong sta...
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01/18/2021
An efficient dynamical low-rank algorithm for the Boltzmann-BGK equation close to the compressible viscous flow regime
It has recently been demonstrated that dynamical low-rank algorithms can...
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07/10/2020
A new stability and convergence proof of the Fourier-Galerkin spectral method for the spatially homogeneous Boltzmann equation
Numerical approximation of the Boltzmann equation is a challenging probl...
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05/13/2020
An asymptotic-preserving dynamical low-rank method for the multi-scale multi-dimensional linear transport equation
We introduce a dynamical low-rank method to reduce the computational com...
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04/23/2020
A fast Fourier spectral method for the homogeneous Boltzmann equation with non-cutoff collision kernels
We introduce a fast Fourier spectral method for the spatially homogeneou...
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04/16/2020
Uncertainty quantification for the BGK model of the Boltzmann equation using multilevel variance reduced Monte Carlo methods
We propose a control variate multilevel Monte Carlo method for the kinet...
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01/30/2020
Recent development in kinetic theory of granular materials: analysis and numerical methods
Over the past decades, kinetic description of granular materials has rec...
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12/02/2019
On the uniform accuracy of implicit-explicit backward differentiation formulas (IMEX-BDF) for stiff hyperbolic relaxation systems and kinetic equations
Many hyperbolic and kinetic equations contain a non-stiff convection/tra...
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11/18/2019
A structure preserving numerical scheme for Fokker-Planck equations of neuron networks: numerical analysis and exploration
In this work, we are concerned with the Fokker-Planck equations associat...
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10/07/2019
A particle method for the homogeneous Landau equation
We propose a novel deterministic particle method to numerically approxim...
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09/26/2018