Linearly implicit methods for Allen-Cahn equation

Date

2023-08-01

Author

Uzunca, Murat
Karasözen, Bülent

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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 developed for energy-preserving methods for conservative systems with polynomial Hamiltonians, which are based on the concept of polarization. In this paper, we construct linearly 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.

Subject Keywords

Allen-Cahn equation, Energy dissipation, Gradient systems, Linearly implicit methods

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85150901804&origin=inward
https://hdl.handle.net/11511/102994

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Department of Mathematics, Article