TY - JOUR
T1 - First- and second-order energy stable methods for the modified phase field crystal equation
AU - Lee, Hyun Geun
AU - Shin, Jaemin
AU - Lee, June Yub
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - 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.
AB - 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.
KW - Energy stability
KW - Fourier spectral method
KW - Modified phase field crystal equation
KW - Phase field crystal equation
UR - http://www.scopus.com/inward/record.url?scp=85018244711&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2017.03.033
DO - 10.1016/j.cma.2017.03.033
M3 - Article
AN - SCOPUS:85018244711
SN - 0045-7825
VL - 321
SP - 1
EP - 17
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -