A Laplace transform certified reduced basis method; application to the heat equation and wave equation
We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filte...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Elsevier
2015
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| Online Access: | http://hdl.handle.net/1721.1/99386 https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1826211592139702272 |
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| author | Knezevic, David Patera, Anthony T. Huynh, Dinh Bao Phuong |
| author2 | Massachusetts Institute of Technology. Department of Mechanical Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Mechanical Engineering Knezevic, David Patera, Anthony T. Huynh, Dinh Bao Phuong |
| author_sort | Knezevic, David |
| collection | MIT |
| description | We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach. |
| first_indexed | 2024-09-23T15:08:25Z |
| format | Article |
| id | mit-1721.1/99386 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:08:25Z |
| publishDate | 2015 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | mit-1721.1/993862022-10-02T00:49:47Z A Laplace transform certified reduced basis method; application to the heat equation and wave equation Knezevic, David Patera, Anthony T. Huynh, Dinh Bao Phuong Massachusetts Institute of Technology. Department of Mechanical Engineering Huynh, Dinh Bao Phuong Knezevic, David Patera, Anthony T. We present a certified reduced basis (RB) method for the heat equation and wave equation. The critical ingredients are certified RB approximation of the Laplace transform; the inverse Laplace transform to develop the time-domain RB output approximation and rigorous error bound; a (Butterworth) filter in time to effect the necessary “modal” truncation; RB eigenfunction decomposition and contour integration for Offline–Online decomposition. We present numerical results to demonstrate the accuracy and efficiency of the approach. United States. Air Force Office of Scientific Research (Grant FA9550-07-1-0425) United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0613) 2015-10-21T14:52:27Z 2015-10-21T14:52:27Z 2011-03 2010-09 Article http://purl.org/eprint/type/JournalArticle 1631073X http://hdl.handle.net/1721.1/99386 Huynh, D.B. Phuong, David J. Knezevic, and Anthony T. Patera. “A Laplace Transform Certified Reduced Basis Method; Application to the Heat Equation and Wave Equation.” Comptes Rendus Mathematique 349, no. 7–8 (April 2011): 401–5. https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1016/j.crma.2011.02.003 Comptes Rendus Mathematique Creative Commons Attribution-Noncommercial-NoDerivatives http://creativecommons.org/licenses/by-nc-nd/4.0/ application/pdf Elsevier MIT Web Domain |
| spellingShingle | Knezevic, David Patera, Anthony T. Huynh, Dinh Bao Phuong A Laplace transform certified reduced basis method; application to the heat equation and wave equation |
| title | A Laplace transform certified reduced basis method; application to the heat equation and wave equation |
| title_full | A Laplace transform certified reduced basis method; application to the heat equation and wave equation |
| title_fullStr | A Laplace transform certified reduced basis method; application to the heat equation and wave equation |
| title_full_unstemmed | A Laplace transform certified reduced basis method; application to the heat equation and wave equation |
| title_short | A Laplace transform certified reduced basis method; application to the heat equation and wave equation |
| title_sort | laplace transform certified reduced basis method application to the heat equation and wave equation |
| url | http://hdl.handle.net/1721.1/99386 https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 |
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