9 papers
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…
Toward a Physical Interpretation of Phase Field Models with Dynamic Boundary Conditions
Xiaobo Jing, Qi Wang
In recent decades, considerable research has been devoted to partial differential equations (PDEs) with dynamic boundary conditions. However, the physical interpretation of the par…
Thermodynamically consistent dynamic boundary conditions of phase field models
Xiaobo Jing, Qi Wang
We present a general, constructive method to derive thermodynamically consistent models and consistent dynamic boundary conditions hierarchically following the generalized Onsager…
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…
Modeling Oral Multispecies Biofilm Recovery After Antibacterial Treatment
Xiaobo Jing, Xiangya Huang, Markus Haapasalo +2
Recovery of multispecies oral biofilms is investigated following treatment by chlorhexidine gluconate (CHX), iodine-potassium iodide (IPI) and Sodium hypochlorite (NaOCl) both expe…
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…