
BoundPreserving FiniteVolume Schemes for Systems of Continuity Equations with Saturation
We propose finitevolume schemes for general continuity equations which ...
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Implicit Regularization Effects of the Sobolev Norms in Image Processing
In this paper, we propose to use the general L^2based Sobolev norms (i....
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A structure preserving numerical scheme for FokkerPlanck equations of structured neural networks with learning rules
In this work, we are concerned with a FokkerPlanck equation related to ...
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Multiscale and Nonlocal Learning for PDEs using Densely Connected RNNs
Learning timedependent partial differential equations (PDEs) that gover...
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An entropic method for discrete systems with Gibbs entropy
We consider general systems of ordinary differential equations with mono...
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A fast PetrovGalerkin spectral method for the multidimensional Boltzmann equation using mapped Chebyshev functions
Numerical approximation of the Boltzmann equation presents a challenging...
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Positivitypreserving and energydissipative finite difference schemes for the FokkerPlanck and KellerSegel equations
In this work, we introduce semiimplicit or implicit finite difference s...
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High order unconditionally strong stability preserving multiderivative 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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An efficient dynamical lowrank algorithm for the BoltzmannBGK equation close to the compressible viscous flow regime
It has recently been demonstrated that dynamical lowrank algorithms can...
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A new stability and convergence proof of the FourierGalerkin spectral method for the spatially homogeneous Boltzmann equation
Numerical approximation of the Boltzmann equation is a challenging probl...
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An asymptoticpreserving dynamical lowrank method for the multiscale multidimensional linear transport equation
We introduce a dynamical lowrank method to reduce the computational com...
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A fast Fourier spectral method for the homogeneous Boltzmann equation with noncutoff collision kernels
We introduce a fast Fourier spectral method for the spatially homogeneou...
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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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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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On the uniform accuracy of implicitexplicit backward differentiation formulas (IMEXBDF) for stiff hyperbolic relaxation systems and kinetic equations
Many hyperbolic and kinetic equations contain a nonstiff convection/tra...
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A structure preserving numerical scheme for FokkerPlanck equations of neuron networks: numerical analysis and exploration
In this work, we are concerned with the FokkerPlanck equations associat...
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A particle method for the homogeneous Landau equation
We propose a novel deterministic particle method to numerically approxim...
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A Discontinuous Galerkin Fast Spectral Method for the Full Boltzmann Equation with General Collision Kernels
The Boltzmann equation, an integrodifferential equation for the molecul...
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Jingwei Hu
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