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math.NA2026
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…
math.NA2026
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…
math.NA2026
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…