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Block-partitioned Rayleigh-Ritz method for efficient eigenpair reanalysis of large-scale finite element models.

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Τίτλος: Block-partitioned Rayleigh-Ritz method for efficient eigenpair reanalysis of large-scale finite element models.
Συγγραφείς: Yeon-Ho Jeong, Seung-Hwan Boo, Yim, Solomon C.
Πηγή: Journal of Computational Design & Engineering; Jun2023, Vol. 10 Issue 3, p959-978, 20p
Θεματικοί όροι: Rayleigh-Ritz method, Eigenvalues
Περίληψη: In this manuscript, we propose a new effective method for eigenpair reanalysis of large-scale finite element (FE) models. Our method utilizes the matrix block-partitioning algorithm in the Rayleigh-Ritz approach and expresses the Ritz basis matrix using thousands of block matrices of very small size. To avoid significant computational costs from the projection procedure, we derive a new formulation that uses tiny block computations instead of global matrix computations. Additionally, we present an algorithm that recognizes which blocks are changed in the modified FE model to achieve computational cost savings when computing new eigenpairs. Through selective updating for the recognized blocks, we can effectively construct the new Ritz basis matrix and the new reduced mass and stiffness matrices corresponding to the modified FE model. To demonstrate the performance of our proposed method, we solve several practical engineering problems and compare the results with those of the combined approximation method, the most well-known eigenpair reanalysis method, and ARPACK, an eigenvalue solver embedded in many numerical programs. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Design & Engineering is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Label: Title
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  Data: Block-partitioned Rayleigh-Ritz method for efficient eigenpair reanalysis of large-scale finite element models.
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  Data: <searchLink fieldCode="AR" term="%22Yeon-Ho+Jeong%22">Yeon-Ho Jeong</searchLink><br /><searchLink fieldCode="AR" term="%22Seung-Hwan+Boo%22">Seung-Hwan Boo</searchLink><br /><searchLink fieldCode="AR" term="%22Yim%2C+Solomon+C%2E%22">Yim, Solomon C.</searchLink>
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  Data: Journal of Computational Design & Engineering; Jun2023, Vol. 10 Issue 3, p959-978, 20p
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  Data: <searchLink fieldCode="DE" term="%22Rayleigh-Ritz+method%22">Rayleigh-Ritz method</searchLink><br /><searchLink fieldCode="DE" term="%22Eigenvalues%22">Eigenvalues</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this manuscript, we propose a new effective method for eigenpair reanalysis of large-scale finite element (FE) models. Our method utilizes the matrix block-partitioning algorithm in the Rayleigh-Ritz approach and expresses the Ritz basis matrix using thousands of block matrices of very small size. To avoid significant computational costs from the projection procedure, we derive a new formulation that uses tiny block computations instead of global matrix computations. Additionally, we present an algorithm that recognizes which blocks are changed in the modified FE model to achieve computational cost savings when computing new eigenpairs. Through selective updating for the recognized blocks, we can effectively construct the new Ritz basis matrix and the new reduced mass and stiffness matrices corresponding to the modified FE model. To demonstrate the performance of our proposed method, we solve several practical engineering problems and compare the results with those of the combined approximation method, the most well-known eigenpair reanalysis method, and ARPACK, an eigenvalue solver embedded in many numerical programs. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Computational Design & Engineering is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1093/jcde/qwad030
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      – Code: eng
        Text: English
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        PageCount: 20
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      – SubjectFull: Rayleigh-Ritz method
        Type: general
      – SubjectFull: Eigenvalues
        Type: general
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      – TitleFull: Block-partitioned Rayleigh-Ritz method for efficient eigenpair reanalysis of large-scale finite element models.
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            NameFull: Yeon-Ho Jeong
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            NameFull: Seung-Hwan Boo
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            – D: 01
              M: 06
              Text: Jun2023
              Type: published
              Y: 2023
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