Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916622939193344 |
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| author | Botchev, Mike A. |
| author_facet | Botchev, Mike A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods Botchev, Mike A. Numerical Analysis Computational Engineering, Finance, and Science Computational Physics 65M20, 65L04, 65L20 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. |
| title | Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods |
| topic | Numerical Analysis Computational Engineering, Finance, and Science Computational Physics 65M20, 65L04, 65L20 |
| url | https://arxiv.org/abs/2502.14589 |