Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems (Communications in Computational Physics, 2019)
This paper presents a high order time discretization method by combining the semi-implicit spectral deferred correction method with energy stable linearschemes 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 belinear unconditionally energy stable. The scheme also takes advantage of avoidingnonlinear iteration and the restriction of time step to guarantee the nonlinear systemuniquely solvable. Moreover, the scheme leads to linear algebraic system to solve ateach 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 andefficient simulation tool when solving phase field problems. Namely, we can obtainhigh order accuracy in both time and space by solving some simple linear algebraicequations.
Keywords: Phase field problems; local discontinuous Galerkin method; linear scheme; invariant energy quadratization approach; semi-implicit spectral deferred correction method.