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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 8, Pages 1366–1387
DOI: https://doi.org/10.31857/S0044466924080034 (Mi zvmmf11806) 		 
General numerical methods

Efficient and stable time integration of Cahn–Hilliard equations: explicit, implicit, and explicit iterative schemes

M. A. Botcheva, I. A. Fakhrutdinovab, E. B. Savenkova

a Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 125047, Moscow, Russia
b National Research Nuclear University Moscow Engineering Physics Institute, 115409, Moscow, Russia
DOI: https://doi.org/10.31857/S0044466924080034
Abstract: To solve the Cahn–Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the implicit system arising each time integration step. The proposed method is gradient-stable and allows one to use large time steps, whereas, regarding its computational structure, it is an explicit time integration scheme. Numerical tests are presented to demonstrate abilities of the new method and compare it with other time integration methods for Cahn–Hilliard equation.
Key words: Cahn–Hilliard equation, gradient-stable schemes, Eyre splitting, local iteration modified scheme.
Funding agency Grant number
Russian Science Foundation 22-11-00203
This work was supported by ongoing institutional funding. E.B. Savenkov’s research was supported by the Russian Science Foundation, grant no. 22-11-00203.
Received: 02.04.2024
Revised: 02.04.2024
Accepted: 02.05.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 8, Pages 1726–1746
DOI: https://doi.org/10.1134/S0965542524700945
Bibliographic databases:
Document Type: Article
UDC: 519.635
Language: Russian
Citation: M. A. Botchev, I. A. Fakhrutdinov, E. B. Savenkov, “Efficient and stable time integration of Cahn–Hilliard equations: explicit, implicit, and explicit iterative schemes”, Zh. Vychisl. Mat. Mat. Fiz., 64:8 (2024), 1366–1387; Comput. Math. Math. Phys., 64:8 (2024), 1726–1746
Citation in format AMSBIB
\Bibitem{BotFakSav24}
\by M.~A.~Botchev, I.~A.~Fakhrutdinov, E.~B.~Savenkov
\paper Efficient and stable time integration of Cahn--Hilliard equations: explicit, implicit, and explicit iterative schemes
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 8
\pages 1366--1387
\mathnet{http://mi.mathnet.ru/zvmmf11806}
\crossref{https://doi.org/10.31857/S0044466924080034}
\elib{https://elibrary.ru/item.asp?id=75224101}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 8
\pages 1726--1746
\crossref{https://doi.org/10.1134/S0965542524700945}
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