A semi-analytical Fourier spectral method for the Allen-Cahn equation
- 주제(키워드) Phase-field method , Stabilized semi-implicit Fourier spectral method , Unconditional stability , First and second order convergence
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 PERGAMON-ELSEVIER SCIENCE LTD
- 발행년도 2014
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000098759
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.camwa.2014.05.015
초록/요약
In recent years, Fourier spectral methods have been widely used as a powerful tool for solving phase-field equations. To improve its effectiveness, many researchers have employed stabilized semi-implicit Fourier spectral (SIFS) methods which allow a much larger time step than a usual explicit scheme. Our mathematical analysis and numerical experiments, however, suggest that an effective time step is smaller than a time step specified in the SIFS schemes. In consequence, the SIFS scheme is inaccurate for a considerably large time step and may lead to incorrect morphologies in phase separation processes. In order to remove the time step constraint and guarantee the accuracy in time for a sufficiently large time step, we present a first and a second order semi-analytical Fourier spectral (SAFS) methods for solving the Allen-Cahn equation. The core idea of the methods is to decompose the original equation into linear and nonlinear subequations, which have closed-form solutions in the Fourier and physical spaces, respectively. Both the first and the second order methods are unconditionally stable and numerical experiments demonstrate that our proposed methods are more accurate than the stabilized semiimplicit Fourier spectral method. (C) 2014 Elsevier Ltd. All rights reserved.
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