A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systems

Xufeng Xiao and Xinlong Feng

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 202, issue C, 36-58

Abstract: In this paper, a highly efficient space–time operator splitting finite element method is presented to solve the two- and three-dimensional Allen–Cahn equations. The main advantage of the proposed method is that it reduces the high storage requirements and complexity of the high-dimensional computation by splitting the high-dimensional problem into a series of one-dimensional subproblems. The proposed method is space–time second-order and can be performed in parallel. Moreover, a bound preserving least-distance modification technique is developed to force the discrete maximum bound principle in solving each one-dimensional subproblem. Finally, numerical simulations including the two- and multi-phase separations, mean curvature flows and dendritic crystal growth in two and three dimensions are provided to demonstrate the validity and accuracy of the proposed method.

Keywords: Operator splitting method; Allen–Cahn equation; Maximum bound principle preservation; Parallel algorithm (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:202:y:2022:i:c:p:36-58

DOI: 10.1016/j.matcom.2022.05.024

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