The high-order exponential semi-implicit scalar auxiliary variable approach for nonlocal Cahn-Hilliard equation

TL;DR

This paper introduces a high-order, energy-stable semi-implicit numerical scheme for the nonlocal Cahn-Hilliard equation, utilizing exponential scalar auxiliary variables and fast solvers to improve efficiency and accuracy.

Contribution

It develops a novel high-order semi-implicit scheme with unconditional energy stability for the nonlocal Cahn-Hilliard equation, incorporating efficient FFT-based solvers.

Findings

The scheme is unconditionally energy stable.

Numerical results confirm high accuracy and efficiency.

The method effectively simulates microstructure phase transitions.

Abstract

The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH) equation. In this paper, based on the exponential semi-implicit scalar auxiliary variable (ESI-SAV) method, the highly effcient and accurate schemes in time with unconditional energy stability for solving the NCH equation are proposed. On the one hand, we have demostrated the unconditional energy stability for the NCH equation with its high-order semi-discrete schemes carefully and rigorously. On the other hand, in order to reduce the calculation and storage cost in numerical simulation, we use the fast solver based on FFT and FCG for spatial discretization. Some numerical simulations involving the Gaussian kernel are presented and show the stability, accuracy, efficiency and unconditional energy stability of the proposed schemes.