Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers
In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N...
| Main Authors: | , , , , |
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| Format: | Journal Article |
| Published: |
Pergamon Press
2014
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| Online Access: | http://hdl.handle.net/20.500.11937/51576 |
| _version_ | 1848758732166529024 |
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| author | Wozniak, M. Kuznik, K. Paszynski, M. Calo, Victor Pardo, D. |
| author_facet | Wozniak, M. Kuznik, K. Paszynski, M. Calo, Victor Pardo, D. |
| author_sort | Wozniak, M. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved. |
| first_indexed | 2025-11-14T09:48:40Z |
| format | Journal Article |
| id | curtin-20.500.11937-51576 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:48:40Z |
| publishDate | 2014 |
| publisher | Pergamon Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-515762018-03-29T09:08:37Z Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers Wozniak, M. Kuznik, K. Paszynski, M. Calo, Victor Pardo, D. In this paper we present computational cost estimates for parallel shared memory isogeometric multi-frontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as O( p2log(N/p)) for one dimensional problems, O(Np2) for two dimensional problems, and O(N4/3p2) for three dimensional problems, where N is the number of degrees of freedom, and p is the polynomial order of approximation. The computational costs of the shared memory parallel isogeometric direct solver are compared with those corresponding to the sequential isogeometric direct solver, being the latest equal to O(N p2) for the one dimensional case, O(N1.5p3) for the two dimensional case, and O(N2p3) for the three dimensional case. The shared memory version significantly reduces both the scalability in terms of N and p. Theoretical estimates are compared with numerical experiments performed with linear, quadratic, cubic, quartic, and quintic B-splines, in one and two spatial dimensions. © 2014 Elsevier Ltd. All rights reserved. 2014 Journal Article http://hdl.handle.net/20.500.11937/51576 10.1016/j.camwa.2014.03.017 Pergamon Press restricted |
| spellingShingle | Wozniak, M. Kuznik, K. Paszynski, M. Calo, Victor Pardo, D. Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| title | Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| title_full | Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| title_fullStr | Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| title_full_unstemmed | Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| title_short | Computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| title_sort | computational cost estimates for parallel shared memory isogeometric multi-frontal solvers |
| url | http://hdl.handle.net/20.500.11937/51576 |