Volume 26, Issue 1
Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems

Ruihan Guo & Yan Xu

Commun. Comput. Phys., 26 (2019), pp. 87-113.

Published online: 2019-02

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  • Abstract

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.

  • Keywords

Phase field problems, local discontinuous Galerkin method, linear scheme, invariant energy quadratization approach, semi-implicit spectral deferred correction method.

  • AMS Subject Headings

65M60, 35L75, 35G25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-26-87, author = {}, title = {Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {1}, pages = {87--113}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0034}, url = {http://global-sci.org/intro/article_detail/cicp/13027.html} }
TY - JOUR T1 - Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems JO - Communications in Computational Physics VL - 1 SP - 87 EP - 113 PY - 2019 DA - 2019/02 SN - 26 DO - http://dor.org/10.4208/cicp.OA-2018-0034 UR - https://global-sci.org/intro/cicp/13027.html KW - Phase field problems, local discontinuous Galerkin method, linear scheme, invariant energy quadratization approach, semi-implicit spectral deferred correction method. AB -

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.

Ruihan Guo & Yan Xu. (2019). Semi-Implicit Spectral Deferred Correction Method Based on the Invariant Energy Quadratization Approach for Phase Field Problems. Communications in Computational Physics. 26 (1). 87-113. doi:10.4208/cicp.OA-2018-0034
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