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Fourier-Spectral Method for the Phase-Field Equations

Authors
Yoon, SunghaJeong, DaraeLee, ChaeyoungKim, HyundongKim, SangkwonLee, Hyun GeunKim, Junseok
Issue Date
8월-2020
Publisher
MDPI
Keywords
Fourier-spectral method; phase-field equations; code implementations
Citation
MATHEMATICS, v.8, no.8
Indexed
SCIE
SCOPUS
Journal Title
MATHEMATICS
Volume
8
Number
8
URI
https://scholar.korea.ac.kr/handle/2021.sw.korea/54290
DOI
10.3390/math8081385
ISSN
2227-7390
Abstract
In this paper, we review the Fourier-spectral method for some phase-field models: Allen-Cahn (AC), Cahn-Hilliard (CH), Swift-Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are very important parabolic partial differential equations and are applicable to many interesting scientific problems. The AC equation is a reaction-diffusion equation modeling anti-phase domain coarsening dynamics. The CH equation models phase segregation of binary mixtures. The SH equation is a popular model for generating patterns in spatially extended dissipative systems. A classical PFC model is originally derived to investigate the dynamics of atomic-scale crystal growth. An isotropic symmetry MBE growth model is originally devised as a method for directly growing high purity epitaxial thin film of molecular beams evaporating on a heated substrate. The Fourier-spectral method is highly accurate and simple to implement. We present a detailed description of the method and explain its connection to MATLAB usage so that the interested readers can use the Fourier-spectral method for their research needs without difficulties. Several standard computational tests are done to demonstrate the performance of the method. Furthermore, we provide the MATLAB codes implementation in the Appendix A.
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