Classical dynamical density functional theory (DDFT) is one of the cornerstones of modern
statistical mechanics. It is an extension of the highly successful method of classical density …

This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …

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 …

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 …

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 …

Here, we review the basic concepts and applications of the phase-field-crystal (PFC)
method, which is one of the latest simulation methodologies in materials science for …

In this paper we construct two classes, based on stabilization and convex splitting, of
decoupled, unconditionally energy stable schemes for Cahn--Hilliard phase-field models of …

We present an unconditionally energy stable finite-difference scheme for the phase field
crystal equation. The method is based on a convex splitting of a discrete energy and is semi …

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 …

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 …