Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method
This paper presents a parallel implementation of the implicitly restarted Lanczos method for the solution of large and sparse eigenproblems that occur in modal analysis of complex structures using the finite element method. The implicitly restarted technique improves convergence of the desired eigen...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Universidade Federal do Rio Grande
2010-12-01
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| Series: | Vetor |
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| Online Access: | https://www.seer.furg.br/vetor/article/view/1682 |
| _version_ | 1811259705110036480 |
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| author | George O. Ainsworth Jr. Fernando L. B. Ribeiro Carlos Magluta |
| author_facet | George O. Ainsworth Jr. Fernando L. B. Ribeiro Carlos Magluta |
| author_sort | George O. Ainsworth Jr. |
| collection | DOAJ |
| description | This paper presents a parallel implementation of the implicitly restarted Lanczos method for the solution of large and sparse eigenproblems that occur in modal analysis of complex structures using the finite element method. The implicitly restarted technique improves convergence of the desired eigenvalues without the penalty of lost of orthogonality keeping the number of factorization steps in a modest size. In the parallel solution, a subdomain by subdomain approach was implemented and overlapping and non-overlapping mesh partitions were used. Compressed data structures in the formats CSRC and CSRC/CSR were employed to store the global matrices coefficients. The parallelization of numerical linear algebra operations presented in both Krylov and implicitly restarted methods are discussed. |
| first_indexed | 2024-04-12T18:35:37Z |
| format | Article |
| id | doaj.art-286a18c96dc841ac8102f97896c6aa7f |
| institution | Directory Open Access Journal |
| issn | 0102-7352 2358-3452 |
| language | English |
| last_indexed | 2024-04-12T18:35:37Z |
| publishDate | 2010-12-01 |
| publisher | Universidade Federal do Rio Grande |
| record_format | Article |
| series | Vetor |
| spelling | doaj.art-286a18c96dc841ac8102f97896c6aa7f2022-12-22T03:20:56ZengUniversidade Federal do Rio GrandeVetor0102-73522358-34522010-12-01181Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos methodGeorge O. Ainsworth Jr.Fernando L. B. RibeiroCarlos MaglutaThis paper presents a parallel implementation of the implicitly restarted Lanczos method for the solution of large and sparse eigenproblems that occur in modal analysis of complex structures using the finite element method. The implicitly restarted technique improves convergence of the desired eigenvalues without the penalty of lost of orthogonality keeping the number of factorization steps in a modest size. In the parallel solution, a subdomain by subdomain approach was implemented and overlapping and non-overlapping mesh partitions were used. Compressed data structures in the formats CSRC and CSRC/CSR were employed to store the global matrices coefficients. The parallelization of numerical linear algebra operations presented in both Krylov and implicitly restarted methods are discussed.https://www.seer.furg.br/vetor/article/view/1682Generalized eigenvalue problemLanczos methodFinite elements |
| spellingShingle | George O. Ainsworth Jr. Fernando L. B. Ribeiro Carlos Magluta Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method Vetor Generalized eigenvalue problem Lanczos method Finite elements |
| title | Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method |
| title_full | Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method |
| title_fullStr | Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method |
| title_full_unstemmed | Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method |
| title_short | Parallel solution of eigenproblems in structural dynamics using the implicitly restarted Lanczos method |
| title_sort | parallel solution of eigenproblems in structural dynamics using the implicitly restarted lanczos method |
| topic | Generalized eigenvalue problem Lanczos method Finite elements |
| url | https://www.seer.furg.br/vetor/article/view/1682 |
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