7 papers
Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using General Multipliers
Chaoyu Quan, Huaijin Wang, Xuping Wang +1
A unified framework is proposed to establish the energy dissipation of implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, based on general multipliers that…
Energy Dissipation Analysis of Implicit-Explicit Linear Multistep Methods for Gradient Flows Using a Simple Multiplier
Chaoyu Quan, Huaijin Wang, Xuping Wang +1
This paper proposes a theoretical framework for establishing the energy dissipation of general implicit-explicit linear multistep methods (IMEX-LMMs) for gradient flows, by constru…
A generalized matrix-valued Allen--Cahn model and its numerical solution
Yaru Liu, Chaoyu Quan, Dong Wang
This paper introduces a generalized matrix-valued Allen--Cahn model, where the unknown matrix-valued field belongs to with dimension . By…
Unconditional energy dissipation of Strang splitting for the matrix-valued Allen-Cahn equation
Chaoyu Quan, Tao Tang, Dong Wang
The energy dissipation property of the Strang splitting method was first demonstrated for the matrix-valued Allen-Cahn (MAC) equation under restrictive time-step constraints [J. Co…
Maximum bound preservation of exponential integrators for Allen-Cahn equations
Chaoyu Quan, Pingzhong Zheng, Zhi Zhou
We develop and analyze a class of arbitrarily high-order, maximum bound preserving time-stepping schemes for solving Allen-Cahn equations. These schemes are constructed within the…
Stability and Convergence of Strang Splitting Method for the Allen-Cahn Equation with Homogeneous Neumann Boundary Condition
Chaoyu Quan, Zhijun Tan, Yanyao Wu
The Strang splitting method has been widely used to solve nonlinear reaction-diffusion equations, with most theoretical convergence analysis assuming periodic boundary conditions.…