Improving the accuracy and consistency of the energy quadratization method with an energy-optimized technique Article Swipe
Xiaoqing Meng
,
Aijie Cheng
,
Zhengguang Liu
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2404.01747
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2404.01747
We propose an energy-optimized invariant energy quadratization method to solve the gradient flow models in this paper, which requires only one linear energy-optimized step to correct the auxiliary variables on each time step. In addition to inheriting the benefits of the baseline and relaxed invariant energy quadratization method, our approach has several other advantages. Firstly, in the process of correcting auxiliary variables, we can directly solve linear programming problem by the energy-optimized technique, which greatly simplifies the nonlinear optimization problem in the previous relaxed invariant energy quadratization method. Secondly, we construct new linear unconditionally energy stable schemes by applying backward Euler formulas and Crank-Nicolson formula, so that the accuracy in time can reach the first- and second-order. Thirdly, comparing with relaxation technique, the modified energy obtained by energy-optimized technique is closer to the original energy, meanwhile the accuracy and consistency of the numerical solutions can be improved. Ample numerical examples have been presented to demonstrate the accuracy, efficiency and energy stability of the proposed schemes.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2404.01747
- https://arxiv.org/pdf/2404.01747
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4393929853
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- OpenAlex ID
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https://openalex.org/W4393929853Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2404.01747Digital Object Identifier
- Title
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Improving the accuracy and consistency of the energy quadratization method with an energy-optimized techniqueWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2024Year of publication
- Publication date
-
2024-04-02Full publication date if available
- Authors
-
Xiaoqing Meng, Aijie Cheng, Zhengguang LiuList of authors in order
- Landing page
-
https://arxiv.org/abs/2404.01747Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2404.01747Direct 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/2404.01747Direct OA link when available
- Concepts
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Consistency (knowledge bases), Energy (signal processing), Statistics, Computer science, Mathematics, Artificial intelligenceTop concepts (fields/topics) attached by OpenAlex
- Cited by
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0Total citation count in OpenAlex
- Related works (count)
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10Other works algorithmically related by OpenAlex
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