Port reduction in parametrized component static condensation: approximation and a posteriori error estimation
We introduce a port (interface) approximation and a posteriori error bound framework for a general component-based static condensation method in the context of parameter-dependent linear elliptic partial differential equations. The key ingredients are as follows: (i) efficient empirical port approxi...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Wiley Blackwell
2015
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| Online Access: | http://hdl.handle.net/1721.1/97696 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826201653790900224 |
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| author | Eftang, Jens L. Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Eftang, Jens L. Patera, Anthony T. |
| author_sort | Eftang, Jens L. |
| collection | MIT |
| description | We introduce a port (interface) approximation and a posteriori error bound framework for a general component-based static condensation method in the context of parameter-dependent linear elliptic partial differential equations. The key ingredients are as follows: (i) efficient empirical port approximation spaces—the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system; and (ii) a computationally tractable a posteriori error bound realized through a non-conforming approximation and associated conditioner—the error in the global system approximation, or in a scalar output quantity, may be bounded relatively sharply with respect to the underlying finite element discretization.
Our approximation and a posteriori error bound framework is of particular computational relevance for the static condensation reduced basis element (SCRBE) method. We provide several numerical examples within the SCRBE context, which serve to demonstrate the convergence rate of our port approximation procedure as well as the efficacy of our port reduction error bounds. |
| first_indexed | 2024-09-23T11:55:01Z |
| format | Article |
| id | mit-1721.1/97696 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:55:01Z |
| publishDate | 2015 |
| publisher | Wiley Blackwell |
| record_format | dspace |
| spelling | mit-1721.1/976962022-10-01T06:55:21Z Port reduction in parametrized component static condensation: approximation and a posteriori error estimation Eftang, Jens L. Patera, Anthony T. Massachusetts Institute of Technology. Department of Mechanical Engineering Eftang, Jens L. Patera, Anthony T. We introduce a port (interface) approximation and a posteriori error bound framework for a general component-based static condensation method in the context of parameter-dependent linear elliptic partial differential equations. The key ingredients are as follows: (i) efficient empirical port approximation spaces—the dimensions of these spaces may be chosen small to reduce the computational cost associated with formation and solution of the static condensation system; and (ii) a computationally tractable a posteriori error bound realized through a non-conforming approximation and associated conditioner—the error in the global system approximation, or in a scalar output quantity, may be bounded relatively sharply with respect to the underlying finite element discretization. Our approximation and a posteriori error bound framework is of particular computational relevance for the static condensation reduced basis element (SCRBE) method. We provide several numerical examples within the SCRBE context, which serve to demonstrate the convergence rate of our port approximation procedure as well as the efficacy of our port reduction error bounds. Research Council of Norway United States. Office of Naval Research (Grant N00014-11-0713) 2015-07-07T15:55:41Z 2015-07-07T15:55:41Z 2013-07 Article http://purl.org/eprint/type/JournalArticle 00295981 1097-0207 http://hdl.handle.net/1721.1/97696 Eftang, Jens L., and Anthony T. Patera. “Port Reduction in Parametrized Component Static Condensation: Approximation and a Posteriori Error Estimation.” Int. J. Numer. Meth. Engng (July 2013): n/a–n/a. https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1002/nme.4543 International Journal for Numerical Methods in Engineering Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Wiley Blackwell MIT web domain |
| spellingShingle | Eftang, Jens L. Patera, Anthony T. Port reduction in parametrized component static condensation: approximation and a posteriori error estimation |
| title | Port reduction in parametrized component static condensation: approximation and a posteriori error estimation |
| title_full | Port reduction in parametrized component static condensation: approximation and a posteriori error estimation |
| title_fullStr | Port reduction in parametrized component static condensation: approximation and a posteriori error estimation |
| title_full_unstemmed | Port reduction in parametrized component static condensation: approximation and a posteriori error estimation |
| title_short | Port reduction in parametrized component static condensation: approximation and a posteriori error estimation |
| title_sort | port reduction in parametrized component static condensation approximation and a posteriori error estimation |
| url | http://hdl.handle.net/1721.1/97696 https://orcid.org/0000-0002-2631-6463 |
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