A parareal exponential integrator finite element method for semilinear parabolic equations
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Wiley Open Access
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| Format: | Artículo Open Access |
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Wiley
2024
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| _version_ | 1867003295112888320 |
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| author | Jianguo Huang Lili Ju Yuejin Xu |
| author_facet | Jianguo Huang Lili Ju Yuejin Xu Jianguo Huang Lili Ju Yuejin Xu |
| collection | Wiley Open Access |
| contents | A parareal exponential integrator finite element method for semilinear parabolic equations Jianguo Huang Lili Ju Yuejin Xu Numerical Methods for Partial Differential Equations AbstractIn this article, we present a parareal exponential finite element method, with the help of variational formulation and parareal framework, for solving semilinear parabolic equations in rectangular domains. The model equation is first discretized in space using the finite element method with continuous piecewise multilinear rectangular basis functions, producing the semi‐discrete system. We then discretize the temporal direction using the explicit exponential Runge–Kutta approach accompanied by the parareal framework, resulting in the fully‐discrete numerical scheme. To further improve computational speed, we design a fast solver for our method based on tensor product spectral decomposition and fast Fourier transform. Under certain regularity assumption, we successfully derive optimal error estimates for the proposed parallel‐based method with respect to ‐norm. Extensive numerical experiments in two and three dimensions are also carried out to validate the theoretical results and demonstrate the performance of our method. 10.1002/num.23116 http://onlinelibrary.wiley.com/termsAndConditions#vor |
| doi_str_mv | 10.1002/num.23116 |
| format | Artículo Open Access |
| id | wiley_oa_10_1002_num_23116 |
| institution | Wiley Open Access |
| license_str_mv | http://onlinelibrary.wiley.com/termsAndConditions#vor |
| publishDate | 2024 |
| publisher | Wiley |
| record_format | wiley_oa |
| spellingShingle | A parareal exponential integrator finite element method for semilinear parabolic equations Jianguo Huang Lili Ju Yuejin Xu Numerical Methods for Partial Differential Equations A parareal exponential integrator finite element method for semilinear parabolic equations Jianguo Huang Lili Ju Yuejin Xu Numerical Methods for Partial Differential Equations AbstractIn this article, we present a parareal exponential finite element method, with the help of variational formulation and parareal framework, for solving semilinear parabolic equations in rectangular domains. The model equation is first discretized in space using the finite element method with continuous piecewise multilinear rectangular basis functions, producing the semi‐discrete system. We then discretize the temporal direction using the explicit exponential Runge–Kutta approach accompanied by the parareal framework, resulting in the fully‐discrete numerical scheme. To further improve computational speed, we design a fast solver for our method based on tensor product spectral decomposition and fast Fourier transform. Under certain regularity assumption, we successfully derive optimal error estimates for the proposed parallel‐based method with respect to ‐norm. Extensive numerical experiments in two and three dimensions are also carried out to validate the theoretical results and demonstrate the performance of our method. 10.1002/num.23116 http://onlinelibrary.wiley.com/termsAndConditions#vor |
| title | A parareal exponential integrator finite element method for semilinear parabolic equations |
| topic | Numerical Methods for Partial Differential Equations |
| url | https://onlinelibrary.wiley.com/doi/10.1002/num.23116 |