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arXiv · 2502.14589

Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods

Mike A. Botchev
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Abstract

The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation, especially on parallel and hybrid supercomputers. In this paper, we propose an exponential time integration method for the Cahn-Hilliard equation and describe its efficient Krylov subspace based implementation. We compare the method to a Chebyshev polynomial local iteration modified (LIM) time stepping scheme. Both methods are explicit (i.e., do not involve linear system solution) and tested with both constant and adaptively chosen time steps.

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BibTeXRIS

Mike A. Botchev. 2025-02-20. Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods. https://arxiv.org/abs/2502.14589

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