6 papers · 1 filter
High-Order Variable-Scaled Energetic Variational Neural Networks for Phase-Field Gradient Flows
Xiaobo Jing, Leiyi Dong, Jia Zhao
In this paper, we develop a high-order variable-scaled energetic variational neural network (VS-EVNN) method for phase-field gradient flows. Each discretization stage uses an updat…
Relaxed Lagrange Multiplier (RLM) Schemes for Phase Field Models Preserving the Relaxed Original Energy Dissipation Law
Xiaobo Jing, Jia Zhao
Phase-field models are typically derived from variational principles for a free-energy functional and are widely used to simulate complex multiphase phenomena in science and engine…
Strong Stability Preserving Integrating Factor Runge-Kutta Methods for Differential Lyapunov Equations with Positivity Preservation
Wenhui Zhang, Rihui Lan, Xiaobo Jing
This paper introduces second- and third-order integrating factor strong stability preserving Runge-Kutta methods for solving differential Lyapunov equations. The proposed schemes b…
Linear Second Order Energy Stable Schemes of Phase Field Model with Nonlocal Constraints for Crystal Growth
Xiaobo Jing, Qi Wang
We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn model with a nonlocal constraint for crystal growth that conserves the mass of ea…
Error Estimates of Energy Stable Numerical Schemes for Allen-Cahn Equations with Nonlocal Constraints
Shouwen Sun, Xiaobo Jing, Qi Wang
We present error estimates for four unconditionally energy stable numerical schemes developed for solving Allen-Cahn equations with nonlocal constraints. The schemes are linear and…
Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints
Xiaobo Jing, Jun Li, Xueping Zhao +1
We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase…