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11/03/2022
On the invariant region for compressible Euler equations with a general equation of state
The state space for solutions of the compressible Euler equations with a...
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08/03/2022
SGEM: stochastic gradient with energy and momentum
In this paper, we propose SGEM, Stochastic Gradient with Energy and Mome...
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03/23/2022
An Adaptive Gradient Method with Energy and Momentum
We introduce a novel algorithm for gradient-based optimization of stocha...
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10/11/2021
A global convergence theory for deep ReLU implicit networks via over-parameterization
Implicit deep learning has received increasing attention recently due to...
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01/29/2021
Positivity-preserving third order DG schemes for Poisson–Nernst–Planck equations
In this paper, we design and analyze third order positivity-preserving d...
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01/01/2021
Energy stable Runge-Kutta discontinuous Galerkin schemes for fourth order gradient flows
We present unconditionally energy stable Runge-Kutta (RK) discontinuous ...
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10/10/2020
AEGD: Adaptive Gradient Decent with Energy
In this paper, we propose AEGD, a new algorithm for first-order gradient...
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08/27/2020
On the SAV-DG method for a class of fourth order gradient flows
For a class of fourth order gradient flow problems, integration of the s...
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05/16/2020
An energy stable and positivity-preserving scheme for the Maxwell-Stefan diffusion system
We develop a new finite difference scheme for the Maxwell-Stefan diffusi...
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02/04/2020
Radially symmetric solutions of the ultra-relativistic Euler equations
The ultra-relativistic Euler equations for an ideal gas are described in...
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01/23/2020
Efficient, positive, and energy stable schemes for multi-D Poisson-Nernst-Planck systems
In this paper, we design, analyze, and numerically validate positive and...
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12/21/2019
Unconditionally energy stable discontinuous Galerkin schemes for the Cahn-Hilliard equation
In this paper, we introduce novel discontinuous Galerkin (DG) schemes fo...
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12/02/2019
A positivity-preserving energy stable scheme for a quantum diffusion equation
We propose a new fully-discretized finite difference scheme for a quantu...
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10/01/2019
Unconditionally energy stable DG schemes for the Swift-Hohenberg equation
The Swift-Hohenberg equation as a central nonlinear model in modern phys...
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09/30/2019
Positive and free energy satisfying schemes for diffusion with interaction potentials
In this paper, we design and analyze second order positive and free ener...
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09/30/2019
A mixed discontinuous Galerkin method without interior penalty for time-dependent fourth order problems
A novel discontinuous Galerkin (DG) method is developed to solve time-de...
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09/28/2019
Unconditional positivity-preserving and energy stable schemes for a reduced Poisson-Nernst-Planck system
The Poisson-Nernst-Planck (PNP) system is a widely accepted model for si...
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07/27/2019