An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential Equations Article Swipe
Xiaoying Dai
,
Miao Hu
,
Jack Xin
,
Aihui Zhou
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2304.09007
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2304.09007
In this paper, we propose an augmented subspace based adaptive proper orthogonal decomposition (POD) method for solving the time dependent partial differential equations. By augmenting the POD subspace with some auxiliary modes, we obtain an augmented subspace. We use the difference between the approximation obtained in this augmented subspace and that obtained in the original POD subspace to construct an error indicator, by which we obtain a general framework for augmented subspace based adaptive POD method. We then provide two strategies to obtain some specific augmented subspaces, the random vector based augmented subspace and the coarse-grid approximations based augmented subspace. We apply our new method to two typical 3D advection-diffusion equations with the advection being the Kolmogorov flow and the ABC flow. Numerical results show that our method is more efficient than the existing adaptive POD methods, especially for the advection dominated models.
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- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2304.09007
- https://arxiv.org/pdf/2304.09007
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4366459190
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https://openalex.org/W4366459190Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2304.09007Digital Object Identifier
- Title
-
An Augmented Subspace Based Adaptive Proper Orthogonal Decomposition Method for Time Dependent Partial Differential EquationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2023Year of publication
- Publication date
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2023-04-18Full publication date if available
- Authors
-
Xiaoying Dai, Miao Hu, Jack Xin, Aihui ZhouList of authors in order
- Landing page
-
https://arxiv.org/abs/2304.09007Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2304.09007Direct 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/2304.09007Direct OA link when available
- Concepts
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Subspace topology, Linear subspace, Mathematics, Applied mathematics, Point of delivery, Random subspace method, Mathematical optimization, Partial differential equation, Algorithm, Computer science, Mathematical analysis, Pure mathematics, Agronomy, BiologyTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
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10Other works algorithmically related by OpenAlex
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