TY - JOUR
T1 - Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems
AU - Ruihan Guo & Yan Xu
JO - Communications in Computational Physics
VL - 1
SP - 87
EP - 113
PY - 2019
DA - 2019/02
SN - 26
DO - http://doi.org/10.4208/cicp.OA-2018-0034
UR - https://global-sci.org/intro/article_detail/cicp/13027.html
KW - Phase field problems, local discontinuous Galerkin method, linear scheme, invariant
energy quadratization approach, semi-implicit spectral deferred correction method.
AB - <p style="text-align: justify;">This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linear
schemes to simulate a series of phase field problems. We start with the linear scheme,
which is based on the invariant energy quadratization approach and is proved to be
linear unconditionally energy stable. The scheme also takes advantage of avoiding
nonlinear iteration and the restriction of time step to guarantee the nonlinear system
uniquely solvable. Moreover, the scheme leads to linear algebraic system to solve at
each iteration, and we employ the multigrid solver to solve it efficiently. Numerical results are given to illustrate that the combination of local discontinuous Galerkin (LDG)
spatial discretization and the high order temporal scheme is a practical, accurate and
efficient simulation tool when solving phase field problems. Namely, we can obtain
high order accuracy in both time and space by solving some simple linear algebraic
equations.</p>