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Numerical approximation of the conservative Allen–Cahn equation by operator splitting method
Author(s) -
Weng Zhifeng,
Zhuang Qingqu
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4317
Subject(s) - operator splitting , mathematics , lagrange multiplier , operator (biology) , numerical analysis , rate of convergence , convergence (economics) , multiplier (economics) , space (punctuation) , allen–cahn equation , mathematical analysis , mathematical optimization , computer science , biochemistry , chemistry , channel (broadcasting) , computer network , macroeconomics , economics , gene , economic growth , operating system , repressor , transcription factor
In this paper, a second‐order fast explicit operator splitting method is proposed to solve the mass‐conserving Allen–Cahn equation with a space–time‐dependent Lagrange multiplier. The space–time‐dependent Lagrange multiplier can preserve the volume of the system and keep small features. Moreover, we analyze the discrete maximum principle and the convergence rate of the fast explicit operator splitting method. The proposed numerical scheme is of spectral accuracy in space and of second‐order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, efficiency, mass conservation, and stability of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.