Linearly implicit methods for Allen-Cahn equation
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Tarih
2023
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Elsevier Science Inc
Erişim Hakkı
info:eu-repo/semantics/closedAccess
Özet
It is well known that the Allen-Cahn equation satisfies a nonlinear stability property, i.e., the free-energy functional decreases in time. Linearly implicit integrators have been de-veloped for energy-preserving methods for conservative systems with polynomial Hamil-tonians, which are based on the concept of polarization. In this paper, we construct lin-early implicit methods for gradient flows preserving the energy dissipation by polarizing the free-energy functional. Two-step linearly implicit methods are derived for the Allen -Cahn equation inheriting energy dissipation law. Numerical experiments for one-, two-, and three-dimensional Allen-Cahn equations demonstrate the energy dissipation and the accuracy of the linearly implicit methods.(c) 2023 Elsevier Inc. All rights reserved.
Açıklama
Anahtar Kelimeler
Allen -Cahn equation, Gradient systems, Energy dissipation, Linearly implicit methods
Kaynak
Applied Mathematics and Computation
WoS Q Değeri
Q1
Scopus Q Değeri
Q1
Cilt
450
