Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations Article Swipe
Xiaoying Dai
,
Pan Yan
,
Bin Yang
,
Aihui Zhou
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2106.01008
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2106.01008
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity.
Related Topics
Concepts
Estimator
Mathematics
Eigenvalues and eigenvectors
A priori and a posteriori
Rate of convergence
Discretization
Convergence (economics)
Computation
Applied mathematics
Partial differential equation
Mathematical optimization
Mathematical analysis
Algorithm
Computer science
Key (lock)
Physics
Economic growth
Computer security
Epistemology
Statistics
Economics
Philosophy
Quantum mechanics
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2106.01008
- https://arxiv.org/pdf/2106.01008
- OA Status
- green
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4307533988
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W4307533988Canonical identifier for this work in OpenAlex
- DOI
-
https://doi.org/10.48550/arxiv.2106.01008Digital Object Identifier
- Title
-
Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue ComputationsWork title
- Type
-
preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
-
2021Year of publication
- Publication date
-
2021-06-02Full publication date if available
- Authors
-
Xiaoying Dai, Pan Yan, Bin Yang, Aihui ZhouList of authors in order
- Landing page
-
https://arxiv.org/abs/2106.01008Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2106.01008Direct 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/2106.01008Direct OA link when available
- Concepts
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Estimator, Mathematics, Eigenvalues and eigenvectors, A priori and a posteriori, Rate of convergence, Discretization, Convergence (economics), Computation, Applied mathematics, Partial differential equation, Mathematical optimization, Mathematical analysis, Algorithm, Computer science, Key (lock), Physics, Economic growth, Computer security, Epistemology, Statistics, Economics, Philosophy, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
0Total citation count in OpenAlex
- Related works (count)
-
10Other works algorithmically related by OpenAlex
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