The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has
been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar …

In this paper, we establish a novel linear relaxation method with regularized energy
reformulation for phase field models, which we name the RRER method. We employ the …

In this paper, we consider the Cahn-Hilliard equation coupled with the incompressible
Navier-Stokes equation, usually known as the Cahn-Hilliard-Navier-Stokes (CHNS) system …

In this paper, a non-uniform time-stepping convex-splitting numerical algorithm for solving
the widely used time-fractional Cahn–Hilliard equation is introduced. The proposed …

In this paper we present two fully discrete time-marching schemes including the first order
and the second order schemes for the Cahn–Hilliard equation. The proposed method is …

In this work, we develop high-order convex splitting implicit–explicit Runge–Kutta methods
for Molecular Beam Epitaxy (MBE) model with slope selection, which plays key roles in …

As a promising strategy to adjust the order in the variable-order BDF algorithm, a time
filtered backward Euler scheme is investigated for the molecular beam epitaxial equation …

An efficient modified leapfrog time-marching scheme for the diblock copolymer model is
investigated in this paper. The proposed scheme offers three main advantages. Firstly, it is …

This paper introduces a novel paradigm for constructing linearly implicit and high-order
unconditionally energy-stable schemes for general gradient flows, utilizing the scalar …

In this paper, we introduce a new deep learning framework for discovering the phase-field
models from existing image data. The new framework embraces the approximation power of …