The main goal of machine learning is the creation of self-learning algorithms in many areas
of human activity. It allows a replacement of a person with artificial intelligence in seeking to …

Phase field models, in particular, the Allen-Cahn type and Cahn-Hilliard type equations,
have been widely used to investigate interfacial dynamic problems. Designing accurate …

We propose a new numerical technique to deal with nonlinear terms in gradient flows. By
introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable …

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 …

Abstract The Molecular Beam Epitaxial model is derived from the variation of a free energy,
that consists of either a fourth order Ginzburg–Landau double well potential or a nonlinear …

We construct and analyze a class of extrapolated and linearized Runge--Kutta (RK)
methods, which can be of arbitrarily high order, for the time discretization of the Allen--Cahn …

How to develop efficient numerical schemes while preserving energy stability at the discrete
level is challenging for the three-component Cahn–Hilliard phase-field model. In this paper …

In this paper we present and analyze finite difference numerical schemes for the Cahn-
Hilliard equation with a logarithmic Flory Huggins energy potential. Both first and second …

In this paper, we consider an exponential scalar auxiliary variable (E-SAV) approach to
obtain energy stable schemes for a class of phase field models. This novel auxiliary variable …

The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …