A second-order accurate numerical method with unconditional energy stability for the Lifshitz–Petrich equation on curved surfaces

In this paper, we introduce an efficient numerical algorithm for solving the Lifshitz–Petrich equation on closed surfaces. The algorithm involves discretizing the surface with a triangular mesh, allowing for an explicit definition of the Laplace–Beltrami operator based on the neighborhood informatio...

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Bibliographic Details
Published in:	Applied mathematics letters Vol. 163; p. 109439
Main Authors:	Hu, Xiaochuan, Xia, Qing, Xia, Binhu, Li, Yibao
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 01.04.2025
Subjects:	Curved surfaces Lifshitz–Petrich crystal model Second-order algorithm Unconditional stability Curved surfaces Unconditional stability Lifshitz–Petrich crystal model Second-order algorithm
ISSN:	0893-9659
Online Access:	Get full text
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Summary:	In this paper, we introduce an efficient numerical algorithm for solving the Lifshitz–Petrich equation on closed surfaces. The algorithm involves discretizing the surface with a triangular mesh, allowing for an explicit definition of the Laplace–Beltrami operator based on the neighborhood information of the mesh elements. To achieve second-order temporal accuracy, the backward differentiation formula scheme and the scalar auxiliary variable method are employed for Lifshitz–Petrich equation. The discrete system is subsequently solved using the biconjugate gradient stabilized method, with incomplete LU decomposition of the coefficient matrix serving as a preprocessor. The proposed algorithm is characterized by its simplicity in implementation and second-order precision in both spatial and temporal domains. Numerical experiments are conducted to validate the unconditional energy stability and efficacy of the algorithm.
ISSN:	0893-9659
DOI:	10.1016/j.aml.2024.109439