Fourier-spectral method for the phase-field equations

Sungha Yoon, Darae Jeong, Chaeyoung Lee, Hyundong Kim, Sangkwon Kim, Hyun Geun Lee, Junseok Kim

Research output: Contribution to journalReview articlepeer-review

29 Citations (Scopus)

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.

Original languageEnglish
Article number1385
Pages (from-to)1-36
Number of pages36
JournalMathematics
Volume8
Issue number8
DOIs
Publication statusPublished - 2020 Aug

Bibliographical note

Funding Information:
Funding: The first author (S.Y.) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education. The author (D.J.) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). The author (C.L.) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A6A3A13094308). The author (H.K.) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2020R1A6A3A13077105). The author (H.L.) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2019R1C1C1011112). The corresponding author (J.K.) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2019R1A2C1003053).

Publisher Copyright:
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. T.

Keywords

  • Code implementations
  • Fourier-spectral method
  • Phase-field equations

ASJC Scopus subject areas

  • General Mathematics

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