102 citations · 185 across the 13 of their papers we have counts for
13 papers
Bound preserving and mass conservative methods for the nonlocal Cahn-Hilliard equation with the logarithmic Flory-Huggins potential
Yingying Wang, Xiao Li, Zhengru Zhang
It is well known that the exponential time differencing (ETD) method has been successfully applied to the classic Cahn-Hilliard equation with double well potential. However, this n…
Global-in-time energy stability analysis for the exponential time differencing Runge-Kutta scheme for the phase field crystal equation
Xiao Li, Zhonghua Qiao, Cheng Wang +1
The global-in-time energy estimate is derived for the second-order accurate exponential time differencing Runge-Kutta (ETDRK2) numerical scheme to the phase field crystal (PFC) equ…
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…
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…
Unconditionally stable exponential time differencing schemes for the mass-conserving Allen-Cahn equation with nonlocal and local effects
Kun Jiang, Lili Ju, Jingwei Li +1
It is well known that the classic Allen-Cahn equation satisfies the maximum bound principle (MBP), that is, the absolute value of its solution is uniformly bounded for all time by…
Stabilized integrating factor Runge-Kutta method and unconditional preservation of maximum bound principle
Jingwei Li, Xiao Li, Lili Ju +1
Maximum bound principle (MBP) is an important property for a large class of semilinear parabolic equations, in the sense that the time-dependent solution of the equation with appro…
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…
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…
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…