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First- and second-order energy stable methods for the modified phase field crystal equation

Title
First- and second-order energy stable methods for the modified phase field crystal equation
Authors
Lee H.G.Shin J.Lee J.-Y.
Ewha Authors
이준엽신재민
SCOPUS Author ID
이준엽scopus; 신재민scopus
Issue Date
2017
Journal Title
Computer Methods in Applied Mechanics and Engineering
ISSN
0045-7825JCR Link
Citation
vol. 321, pp. 1 - 17
Keywords
Energy stabilityFourier spectral methodModified phase field crystal equationPhase field crystal equation
Publisher
Elsevier B.V.
Indexed
SCI; SCIE; SCOPUS WOS scopus
Abstract
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.
DOI
10.1016/j.cma.2017.03.033
Appears in Collections:
자연과학대학 > 수학전공 > Journal papers
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