A Parareal exponential integrator finite element method for linear parabolic equations Article Swipe
Jianguo Huang
,
Yuejin Xu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.01138
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2412.01138
In this paper, for solving a class of linear parabolic equations in rectangular domains, we have proposed an efficient Parareal exponential integrator finite element method. The proposed method first uses the finite element approximation with continuous multilinear rectangular basis function for spatial discretization, and then takes the Runge-Kutta approach accompanied with Parareal framework for time integration of the resulting semi-discrete system to produce parallel-in-time numerical solution. Under certain regularity assumptions, fully-discrete error estimates in $L^2$-norm are derived for the proposed schemes with random interpolation nodes. Moreover, a fast solver can be provided based on tensor product spectral decomposition and fast Fourier transform (FFT), since the mass and coefficient matrices of the proposed method can be simultaneously diagonalized with an orthogonal matrix. A series of numerical experiments in various dimensions are also presented to validate the theoretical results and demonstrate the excellent performance of the proposed method.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2412.01138
- https://arxiv.org/pdf/2412.01138
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4405033946
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- OpenAlex ID
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https://openalex.org/W4405033946Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2412.01138Digital Object Identifier
- Title
-
A Parareal exponential integrator finite element method for linear parabolic equationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2024Year of publication
- Publication date
-
2024-12-02Full publication date if available
- Authors
-
Jianguo Huang, Yuejin XuList of authors in order
- Landing page
-
https://arxiv.org/abs/2412.01138Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2412.01138Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2412.01138Direct OA link when available
- Concepts
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Integrator, Finite element method, Exponential function, Mathematics, Mathematical analysis, Applied mathematics, Physics, Voltage, Quantum mechanics, ThermodynamicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
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1Total citation count in OpenAlex
- Citations by year (recent)
-
2025: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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