On round-off error for adaptive finite element methods
Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a sy...
| Main Authors: | , , , , , |
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| Format: | Conference Paper |
| Published: |
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/51392 |
| _version_ | 1848758686815617024 |
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| author | Alvarez-Aramberri, J. Pardo, D. Paszynski, M. Collier, N. Dalcin, L. Calo, Victor |
| author_facet | Alvarez-Aramberri, J. Pardo, D. Paszynski, M. Collier, N. Dalcin, L. Calo, Victor |
| author_sort | Alvarez-Aramberri, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix. © 2012 Published by Elsevier Ltd. |
| first_indexed | 2025-11-14T09:47:56Z |
| format | Conference Paper |
| id | curtin-20.500.11937-51392 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:47:56Z |
| publishDate | 2012 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-513922018-03-05T09:12:14Z On round-off error for adaptive finite element methods Alvarez-Aramberri, J. Pardo, D. Paszynski, M. Collier, N. Dalcin, L. Calo, Victor Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called 'radical meshes'. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix. © 2012 Published by Elsevier Ltd. 2012 Conference Paper http://hdl.handle.net/20.500.11937/51392 10.1016/j.procs.2012.04.162 http://creativecommons.org/licenses/by-nc-nd/3.0/ fulltext |
| spellingShingle | Alvarez-Aramberri, J. Pardo, D. Paszynski, M. Collier, N. Dalcin, L. Calo, Victor On round-off error for adaptive finite element methods |
| title | On round-off error for adaptive finite element methods |
| title_full | On round-off error for adaptive finite element methods |
| title_fullStr | On round-off error for adaptive finite element methods |
| title_full_unstemmed | On round-off error for adaptive finite element methods |
| title_short | On round-off error for adaptive finite element methods |
| title_sort | on round-off error for adaptive finite element methods |
| url | http://hdl.handle.net/20.500.11937/51392 |