102 citations · 347 across the 29 of their papers we have counts for
30 papers
Inverse Evolution Layers: Physics-informed Regularizers for Deep Neural Networks
Chaoyu Liu, Zhonghua Qiao, Chao Li +1
Traditional image processing methods employing partial differential equations (PDEs) offer a multitude of meaningful regularizers, along with valuable theoretical foundations for a…
Energy regularized models for logarithmic SPDEs and their numerical approximations
Jianbo Cui, Dianming Hou, Zhonghua Qiao
Understanding the properties of the stochastic phase field models is crucial to model processes in several practical applications, such as soft matters and phase separation in rand…
A linear second-order maximum bound principle-preserving BDF scheme for the Allen-Cahn equation with a general mobility
Dianming Hou, Lili Ju, Zhonghua Qiao
In this paper, we propose and analyze a linear second-order numerical method for solving the Allen-Cahn equation with a general mobility. The proposed fully-discrete scheme is care…
An energy-stable Smoothed Particle Hydrodynamics discretization of the Navier-Stokes-Cahn-Hilliard model for incompressible two-phase flows
Xiaoyu Feng, Zhonghua Qiao, Shuyu Sun +1
Varieties of energy-stable numerical methods have been developed for incompressible two-phase flows based on the Navier-Stokes-Cahn-Hilliard (NSCH) model in the Eulerian framework,…
An energy stable and maximum bound principle preserving scheme for the dynamic Ginzburg-Landau equations under the temporal gauge
Limin Ma, Zhonghua Qiao
This paper proposes a decoupled numerical scheme of the time-dependent Ginzburg--Landau equations under the temporal gauge. For the magnetic potential and the order parameter, the…
Double stabilizations and convergence analysis of a second-order linear numerical scheme for the nonlocal Cahn-Hilliard equation
Xiao Li, Zhonghua Qiao, Cheng Wang
In this paper, we study a second-order accurate and linear numerical scheme for the nonlocal Cahn-Hilliard equation. The scheme is established by combining a modified Crank-Nicolso…
Structure-preserving numerical method for Maxwell-Ampère Nernst-Planck model
Zhonghua Qiao, Zhenli Xu, Qian Yin +1
Charge dynamics play essential role in many practical applications such as semiconductors, electrochemical devices and transmembrane ion channels. A Maxwell-Ampère Nernst-Planck (M…
An implicit--explicit second order BDF numerical scheme with variable steps for gradient flows
Dianming Hou, Zhonghua Qiao
In this paper, we propose and analyze an efficient implicit--explicit (IMEX) second order in time backward differentiation formulation (BDF2) scheme with variable time steps for gr…
Multi-phase image segmentation by the Allen--Cahn Chan--Vese model
Chaoyu Liu, Zhonghua Qiao, Qian Zhang
This paper proposes an Allen-Cahn Chan-Vese model to settle the multi-phase image segmentation. We first integrate the Allen--Cahn term and the Chan--Vese fitting energy term to es…
An Active Contour Model with Local Variance Force Term and Its Efficient Minimization Solver for Multi-phase Image Segmentation
Chaoyu Liu, Zhonghua Qiao, Qian Zhang
In this paper, we propose an active contour model with a local variance force (LVF) term that can be applied to multi-phase image segmentation problems. With the LVF, the proposed…
Stabilized exponential-SAV schemes preserving energy dissipation law and maximum bound principle for the Allen-Cahn type equations
Lili Ju, Xiao Li, Zhonghua Qiao
It is well-known that the Allen-Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in the sense that the absolute valu…
Generalized SAV-exponential integrator schemes for Allen-Cahn type gradient flows
Lili Ju, Xiao Li, Zhonghua Qiao
The energy dissipation law and the maximum bound principle (MBP) are two important physical features of the well-known Allen-Cahn equation. While some commonly-used first-order tim…
A Maxwell-Ampère Nernst-Planck Framework for Modeling Charge Dynamics
Zhonghua Qiao, Zhenli Xu, Qian Yin +1
Understanding the properties of charge dynamics is crucial to many practical applications, such as electrochemical energy devices and transmembrane ion channels. This work proposes…
Two-phase segmentation for intensity inhomogeneous images by the Allen-Cahn Local Binary Fitting Model
Chaoyu liu, Zhonghua Qiao, Qian Zhang
This paper proposes a new variational model by integrating the Allen-Cahn term with a local binary fitting energy term for segmenting images with intensity inhomogeneity and noise.…
Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator
Zhonghua Qiao, Qian Zhang
Based on a nonlocal Laplacian operator, a novel edge detection method of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels fo…
Maximum bound principle preserving integrating factor Runge-Kutta methods for semilinear parabolic equations
Lili Ju, Xiao Li, Zhonghua Qiao +1
A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise b…
Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
Qiang Du, Lili Ju, Xiao Li +1
The ubiquity of semilinear parabolic equations has been illustrated in their numerous applications ranging from physics, biology, to materials and social sciences. In this paper, w…
A third order exponential time differencing numerical scheme for no-slope-selection epitaxial thin film model with energy stability
Kelong Cheng, Zhonghua Qiao, Cheng Wang
In this paper we propose and analyze a (temporally) third order accurate exponential time differencing (ETD) numerical scheme for the no-slope-selection (NSS) equation of the epita…
Maximum principle preserving exponential time differencing schemes for the nonlocal Allen-Cahn equation
Qiang Du, Lili Ju, Xiao Li +1
The nonlocal Allen-Cahn (NAC) equation is a generalization of the classic Allen-Cahn equation by replacing the Laplacian with a parameterized nonlocal diffusion operator, and satis…
Convergence analysis for a stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation
Xiao Li, Zhonghua Qiao, Cheng Wang
In this paper, we provide a detailed convergence analysis for a first order stabilized linear semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, which follows…
Strong Approximation of Monotone Stochastic Partial Differential Equations Driven by Multiplicative Noise
Zhihui Liu, Zhonghua Qiao
We establish a general theory of optimal strong error estimation for numerical approximations of a second-order parabolic stochastic partial differential equation with monotone dri…
Strong Approximation of Stochastic Allen-Cahn Equation with White Noise
Zhihui Liu, Zhonghua Qiao
We establish an optimal strong convergence rate of a fully discrete numerical scheme for second order parabolic stochastic partial differential equations with monotone drifts, incl…
Wong--Zakai Approximations of Stochastic Allen-Cahn Equation
Zhihui Liu, Zhonghua Qiao
We establish a unconditional and optimal strong convergence rate of Wong--Zakai type approximations in Banach space norm for a parabolic stochastic partial differential equation wi…
Resolving Knudsen Layer by High Order Moment Expansion
Yuwei Fan, Jun Li, Ruo Li +1
We model the Knudsen layer in Kramers' problem by linearized high order hyperbolic moment system. Due to the hyperbolicity, the boundary conditions of the moment system is properly…