102 citations · 347 across the 29 of their papers we have counts for
23 papers · 1 filter
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 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…
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…
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…
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…
Acceleration for Microflow Simulations of High-Order Moment Models by Using Lower-Order Model Correction
Zhicheng Hu, Ruo Li, Zhonghua Qiao
We study the acceleration of steady-state computation for microflow, which is modeled by the high-order moment models derived recently from the steady-state Boltzmann equation with…
An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
Xiao Li, Zhonghua Qiao, Hui Zhang
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting techniqu…
Convergence of a Fast Explicit Operator Splitting Method for the Molecular Beam Epitaxy Model
Xiao Li, Zhonghua Qiao, Hui Zhang
A fast explicit operator splitting (FEOS) method for the molecular beam epitaxy model has been presented in [Cheng, et al., Fast and stable explicit operator splitting methods for…
Characterizing the stabilization size for semi-implicit Fourier-spectral method to phase field equations
Dong Li, Zhonghua Qiao, Tao Tang
Recent results in the literature provide computational evidence that stabilized semi-implicit time-stepping method can efficiently simulate phase field problems involving fourth-or…