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A Second-Order Maximum-Bound-Preserving and Energy-Stable Exponential Time-Differencing Method for Allen--Cahn-Type Gradient Flows
Wenshuai Hu, Guanghua Ji, Xiao Li
The energy dissipation law and the maximum bound principle (MBP) are two important physical features of the well-known Allen--Cahn equation. In this paper, we develop and analyze n…
Energy stability and error estimates for a second-order structure-preserving exponential integrator method for smectic-A liquid crystals
Wenshuai Hu, Guanghua Ji, Xiao Li
In this work, we develop a second-order, linear, decoupled, and structure-preserving numerical scheme for the modified Landau--de Gennes model of smectic-A (SmA) liquid crystals. T…
Efficient Numerical Schemes for a Two-Phase Hydrodynamical Model of Active Liquid Crystals and Solids
Xuelong Gu, Guanghua Ji, Qi Wang
We propose several linear, fully decoupled numerical schemes with first- and second-order temporal accuracy for a novel Q-tensor-based two-phase hydrodynamic model describing the c…
A Structure-Preserving GSAV Exponential Integrator for Smectic-A Liquid Crystals
Wenshuai Hu, Guanghua Ji, Xiao Li
The modified Landau--de Gennes (mLdG) theory provides a powerful continuum framework for modeling smectic-A (SmA) liquid crystals by coupling the tensorial orientational order para…
Efficient numerical methods for computing stationary states of spherical Landau-Brazovskii model
Qun Qiu, Wei Si, Guanghua Ji +1
In this paper, we develop a set of efficient methods to compute stationary states of the spherical Landau-Brazovskii (LB) model in a discretization-then-optimization way. First, we…