@Article{CiCP-24-1,
author = {},
title = {A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation},
journal = {Communications in Computational Physics},
year = {2018},
volume = {24},
number = {1},
pages = {123--151},
abstract = {<p style="text-align: justify;">In this paper, we will develop a first order and a second order convex splitting,
and a first order linear energy stable fully discrete local discontinuous Galerkin
(LDG) methods for the modified phase field crystal (MPFC) equation. In which, the
first order linear scheme is based on the invariant energy quadratization approach.
The MPFC equation is a damped wave equation, and to preserve an energy stability,
it is necessary to introduce a pseudo energy, which all increase the difficulty of constructing
numerical methods comparing with the phase field crystal (PFC) equation.
Due to the severe time step restriction of explicit time marching methods, we introduce
the first order and second order semi-implicit schemes, which are proved to be unconditionally
energy stable. In order to improve the temporal accuracy, the semi-implicit
spectral deferred correction (SDC) method combining with the first order convex splitting
scheme is employed. Numerical simulations of the MPFC equation always need
long time to reach steady state, and then adaptive time-stepping method is necessary
and of paramount importance. The schemes at the implicit time level are linear or nonlinear
and we solve them by multigrid solver. Numerical experiments of the accuracy
and long time simulations are presented demonstrating the capability and efficiency
of the proposed methods, and the effectiveness of the adaptive time-stepping strategy.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0074},
url = {https://global-sci.com/article/79941/a-high-order-adaptive-time-stepping-strategy-and-local-discontinuous-galerkin-method-for-the-modified-phase-field-crystal-equation}
}