Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems  

作　　者：Ruihan Guo Yan Xu 

机构地区：[1]School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,Henan 450001,P.R.China [2]School of Mathematical Sciences,University of Science and Technology of China,Hefei,Anhui 230026,P.R.China

出　　处：《Communications in Computational Physics》2019年第6期87-113,共27页计算物理通讯（英文）

基　　金：Research of R.Guo is supported by NSFC grant No.11601490;Research of Y.Xu is supported by NSFC grant No.11722112,91630207.

摘　　要：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 re-sults 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.

关 键 词：Phase field problems local discontinuous Galerkin method linear scheme invariant energy quadratization approach semi-implicit spectral deferred correction method 

分 类 号：O17[理学—数学]