Fourier-Spectral Method for the Phase-Field Equations

Sungha Yoon, Darae Jeong, Chaeyoung Lee, Hyundong Kim, Sangkwon Kim, Hyun Geun Lee and Junseok Kim
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Sungha Yoon: Department of Mathematics, Korea University, Seoul 02841, Korea
Darae Jeong: Department of Mathematics, Kangwon National University, Gangwon-do 24341, Korea
Chaeyoung Lee: Department of Mathematics, Korea University, Seoul 02841, Korea
Hyundong Kim: Department of Mathematics, Korea University, Seoul 02841, Korea
Sangkwon Kim: Department of Mathematics, Korea University, Seoul 02841, Korea
Hyun Geun Lee: Department of Mathematics, Kwangwoon University, Seoul 01897, Korea
Junseok Kim: Department of Mathematics, Korea University, Seoul 02841, Korea

Mathematics, 2020, vol. 8, issue 8, 1-36

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.

Keywords: Fourier-spectral method; phase-field equations; code implementations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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