First- and second-order energy stable methods for the modified phase field crystal equation
- 주제(키워드) Energy stability , Fourier spectral method , Modified phase field crystal equation , Phase field crystal equation
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Elsevier B.V.
- 발행년도 2017
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000145512
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.cma.2017.03.033
초록/요약
The phase field crystal (PFC) model was extended to the modified phase field crystal (MPFC) model, which is a sixth-order nonlinear damped wave equation, to include not only diffusive dynamics but also elastic interactions. In this paper, we present temporally first- and second-order accurate methods for the MPFC equation, which are based on an appropriate splitting of the energy for the PFC equation. And we use the Fourier spectral method for the spatial discretization. The first- and second-order methods are shown analytically to be unconditionally stable with respect to the energy and pseudoenergy of the MPFC equation, respectively. Numerical experiments are presented demonstrating the accuracy and energy stability of the proposed methods. © 2017 Elsevier B.V.
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