48 citations · 101 across the 12 of their papers we have counts for
12 papers
A linear unconditionally structure-preserving L1 scheme for the time-fractional Allen-Cahn equation
Dianming Hou, Zhonghua Qiao, Tao Tang
As a variational phase-field model, the time-fractional Allen-Cahn (TFAC) equation enjoys the maximum bound principle (MBP) and a variational energy dissipation law. In this work,…
Dynamic-stabilization-based linear schemes for the Allen-Cahn equation with degenerate mobility: MBP and energy stability
Hongfei Fu, Dianming Hou, Zhonghua Qiao +1
In this paper, we investigate linear first- and second-order numerical schemes for the Allen--Cahn equation with a general (possibly degenerate) mobility. Compared with existing nu…
A linear doubly stabilized Crank-Nicolson scheme for the Allen-Cahn equation with a general mobility
Dianming Hou, Zhonghua Qiao, Lili Ju
In this paper, a linear second order numerical scheme is developed and investigated for the Allen-Cahn equation with a general positive mobility. In particular, our fully discrete…
Energy-dissipative spectral renormalization exponential integrator method for gradient flow problems
Dianming Hou, Lili Ju, Zhonghua Qiao
In this paper, we present a novel spectral renormalization exponential integrator method for solving gradient flow problems. Our method is specifically designed to simultaneously s…
Energy stable and maximum bound principle preserving schemes for the Q-tensor flow of liquid crystals
Dianming Hou, Xiaoli Li, Zhonghua Qiao +1
In this paper, we propose two efficient fully-discrete schemes for Q-tensor flow of liquid crystals by using the first- and second-order stabilized exponential scalar auxiliary var…
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…
A linear adaptive second-order backward differentiation formulation scheme for the phase field crystal equation
Dianming Hou, Zhonghua Qiao
In this paper, we present and analyze a linear fully discrete second order scheme with variable time steps for the phase field crystal equation. More precisely, we construct a line…
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…
Highly efficient and energy dissipative schemes for the time fractional Allen-Cahn equation
Dianming Hou, Chuanju Xu
In this paper, we propose and analyze a time-stepping method for the time fractional Allen-Cahn equation. The key property of the proposed method is its unconditional stability for…
Highly efficient schemes for time fractional Allen-Cahn equation using extended SAV approach
Dianming Hou, Hongyi Zhu, Chuanju Xu
In this paper, we propose and analyze high order efficient schemes for the time fractional Allen-Cahn equation. The proposed schemes are based on the L1 discretization for the time…
A Müntz-Collocation spectral method for weakly singular volterra integral equations
Dianming Hou, Yumin Lin, Mejdi Azaiez +1
In this paper we propose and analyze a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel $(x-s)^{-μ},…