Linearly implicit methods for Allen-Cahn equation

Uzunca M., KARASÖZEN B.

Applied Mathematics and Computation, cilt.450, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 450
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.amc.2023.127984
  • Dergi Adı: Applied Mathematics and Computation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Allen -Cahn equation, Gradient systems, Energy dissipation, Linearly implicit methods, SCHEMES, INTEGRATION
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

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 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.