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Research article
Error Estimation and Adaptivity for PGD based on Complementary Solutions
Pedro Diez
Universitat Politecnica de Catalunya
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6464-6407
License:
This work is licensed under a CC BY 4.0 License. Read Full License
View the published version at Advanced Modeling and Simulation in Engineering Sciences.
Reduced order methods are powerful tools for the design and analysis of sophisticated systems, reducing computational costs and speeding up the development process. Among these reduced order methods, the Proper Generalized Decomposition is a well-established one, commonly used to deal with multi-dimensional problems that often suffer from the curse of dimensionality. Although the PGD method has been around for some time now, it still lacks mechanisms to assess the quality of the solutions obtained.
This paper explores the dual error analysis in the scope of the PGD, using complementary solutions to compute error bounds and drive an adaptivity process. The energy of the error obtained from the dual analysis is used to determine the quality of the PGD approximations. We define a new adaptivity indicator based on the energy of the error and use it to drive parametric h- and p- adaptivity processes. The results are positive, with the indicator accurately capturing the parameter that will lead to lowest errors.
Keywords
Error bounds, Error estimation, Proper Generalized Decomposition, Equilibrium formulation
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CURRENT STATUS: Published
Version 1
Posted 24 May, 2020
Published
On 30 Oct, 2020
No community comments so far
Editorial decision: Minor Revision
On 20 Aug, 2020
Review #2 received
Received 17 Jul, 2020
Reviewer #2 agreed
On 05 Jun, 2020
Review #1 received
Received 27 May, 2020
Reviewer #1 agreed
On 22 May, 2020
Reviewers invited
Invitations sent on 21 May, 2020
Editor assigned
On 20 May, 2020
Submission checks complete
On 19 May, 2020
Editor invited
On 19 May, 2020
First submitted
On 14 May, 2020
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Subject Areas
Software Engineering
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This preprint is under consideration at Advanced Modeling and Simulation in Engineering Sciences. A preprint is a preliminary version of a manuscript that has not completed peer review at a journal. Research Square does not conduct peer review prior to posting preprints. The posting of a preprint on this server should not be interpreted as an endorsement of its validity or suitability for dissemination as established information or for guiding clinical practice.
Learn more about In Review
Research article
Error Estimation and Adaptivity for PGD based on Complementary Solutions
Pedro Diez
Universitat Politecnica de Catalunya
Corresponding Author
ORCiD: https://orcid.org/0000-0001-6464-6407
Badges
Prescreen
This manuscript passed our Prescreen assessment
Complete author information
Appropriate declaration statements
Potential risks to human health
Prescreen
Peer Review Timeline
CURRENT STATUS: Published
Version 1
Posted 24 May, 2020
Published
On 30 Oct, 2020
No community comments so far
Editorial decision: Minor Revision
On 20 Aug, 2020
Review #2 received
Received 17 Jul, 2020
Reviewer #2 agreed
On 05 Jun, 2020
Review #1 received
Received 27 May, 2020
Reviewer #1 agreed
On 22 May, 2020
Reviewers invited
Invitations sent on 21 May, 2020
Editor assigned
On 20 May, 2020
Submission checks complete
On 19 May, 2020
Editor invited
On 19 May, 2020
First submitted
On 14 May, 2020
Metrics
Comments: 0
PDF Downloads: ...
HTML Views: ...
Subject Areas
Software Engineering
License:
This work is licensed under a CC BY 4.0 License. Read Full License
View the published version at Advanced Modeling and Simulation in Engineering Sciences.
Reduced order methods are powerful tools for the design and analysis of sophisticated systems, reducing computational costs and speeding up the development process. Among these reduced order methods, the Proper Generalized Decomposition is a well-established one, commonly used to deal with multi-dimensional problems that often suffer from the curse of dimensionality. Although the PGD method has been around for some time now, it still lacks mechanisms to assess the quality of the solutions obtained.
This paper explores the dual error analysis in the scope of the PGD, using complementary solutions to compute error bounds and drive an adaptivity process. The energy of the error obtained from the dual analysis is used to determine the quality of the PGD approximations. We define a new adaptivity indicator based on the energy of the error and use it to drive parametric h- and p- adaptivity processes. The results are positive, with the indicator accurately capturing the parameter that will lead to lowest errors.
Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10
Figure 11
Figure 12
Due to technical limitations, full-text HTML conversion of this manuscript could not be completed. However, the manuscript can be downloaded and accessed as a PDF.