Lipid membranes can spontaneously organize their components into domains of different
sizes and properties. The organization of membrane lipids into nanodomains might …

Along with finite differences and finite elements, spectral methods are one of the three main
methodologies for solving partial differential equations on computers. This book provides a …

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 …

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 unconditionally stable, unconditionally uniquely solvable, and second-order
accurate (in time) schemes for gradient flows with energy of the form \int_Ω(F(∇ϕ(\bfx))+ϵ …

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 …

We present two accurate and efficient numerical schemes for a phase field dendritic crystal
growth model, which is derived from the variation of a free‐energy functional, consisting of a …

In this paper we propose and analyze an energy stable numerical scheme for the Cahn–
Hilliard equation, with second order accuracy in time and the fourth order finite difference …

We present an unconditionally energy stable finite difference scheme for the Modified Phase
Field Crystal equation, a generalized damped wave equation for which the usual Phase …