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Linearly implicit methods for Allen-Cahn equation
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DOI：10.1016/j.amc.2023.127984.png)
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Abstract
En 中文
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.
Keywords:
Allen -Cahn equation
Gradient systems
Energy dissipation
Linearly implicit methods
Journal
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3.4
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2.3W
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3.3W