A Two-Step Certified Reduced Basis Method
In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (D...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Springer-Verlag
2013
|
| Online Access: | http://hdl.handle.net/1721.1/79382 https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 |
| _version_ | 1811091973114691584 |
|---|---|
| author | Eftang, Jens L. Huynh, Dinh Bao Phuong Knezevic, Jovana Patera, Anthony T. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Eftang, Jens L. Huynh, Dinh Bao Phuong Knezevic, Jovana Patera, Anthony T. |
| author_sort | Eftang, Jens L. |
| collection | MIT |
| description | In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (DRB) model of dimension M≤N. The construction of the DRB model is effected at cost O(N) and in particular at cost independent of N ; subsequent evaluation of the DRB model may then be effected at cost O(M) . The DRB model comprises both the DRB output and a rigorous a posteriori error bound for the error in the DRB output with respect to the truth discretization.
The new approach is of particular interest in two contexts: focus calculations and hp-RB approximations. In the former the new approach serves to reduce online cost, M≪N: the DRB model is restricted to a slice or subregion of a larger parameter domain associated with the intermediate RB model. In the latter the new approach enlarges the class of problems amenable to hp-RB treatment by a significant reduction in offline (precomputation) cost: in the development of the hp parameter domain partition and associated “local” (now derived) RB models the finite element truth is replaced by the intermediate RB model. We present numerical results to illustrate the new approach. |
| first_indexed | 2024-09-23T15:10:53Z |
| format | Article |
| id | mit-1721.1/79382 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:10:53Z |
| publishDate | 2013 |
| publisher | Springer-Verlag |
| record_format | dspace |
| spelling | mit-1721.1/793822022-09-29T13:13:10Z A Two-Step Certified Reduced Basis Method Eftang, Jens L. Huynh, Dinh Bao Phuong Knezevic, Jovana Patera, Anthony T. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Department of Mechanical Engineering Eftang, Jens L. Huynh, Dinh Bao Phuong Knezevic, Jovana Patera, Anthony T. In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (DRB) model of dimension M≤N. The construction of the DRB model is effected at cost O(N) and in particular at cost independent of N ; subsequent evaluation of the DRB model may then be effected at cost O(M) . The DRB model comprises both the DRB output and a rigorous a posteriori error bound for the error in the DRB output with respect to the truth discretization. The new approach is of particular interest in two contexts: focus calculations and hp-RB approximations. In the former the new approach serves to reduce online cost, M≪N: the DRB model is restricted to a slice or subregion of a larger parameter domain associated with the intermediate RB model. In the latter the new approach enlarges the class of problems amenable to hp-RB treatment by a significant reduction in offline (precomputation) cost: in the development of the hp parameter domain partition and associated “local” (now derived) RB models the finite element truth is replaced by the intermediate RB model. We present numerical results to illustrate the new approach. United States. Air Force Office of Scientific Research (AFOSR Grant number FA9550-07-1-0425) United States. Department of Defense. Office of the Secretary of Defense (OSD/AFOSR Grant number FA9550-09-1-0613) Norwegian University of Science and Technology 2013-06-27T20:08:25Z 2013-06-27T20:08:25Z 2011-05 Article http://purl.org/eprint/type/JournalArticle 0885-7474 1573-7691 http://hdl.handle.net/1721.1/79382 Eftang, J. L., D. B. P. Huynh, D. J. Knezevic, and A. T. Patera. A Two-Step Certified Reduced Basis Method. Journal of Scientific Computing 51, no. 1 (April 12, 2012): 28-58. https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 en_US http://dx.doi.org/10.1007/s10915-011-9494-2 Journal of Scientific Computing Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf Springer-Verlag MIT web domain |
| spellingShingle | Eftang, Jens L. Huynh, Dinh Bao Phuong Knezevic, Jovana Patera, Anthony T. A Two-Step Certified Reduced Basis Method |
| title | A Two-Step Certified Reduced Basis Method |
| title_full | A Two-Step Certified Reduced Basis Method |
| title_fullStr | A Two-Step Certified Reduced Basis Method |
| title_full_unstemmed | A Two-Step Certified Reduced Basis Method |
| title_short | A Two-Step Certified Reduced Basis Method |
| title_sort | two step certified reduced basis method |
| url | http://hdl.handle.net/1721.1/79382 https://orcid.org/0000-0002-2794-1308 https://orcid.org/0000-0002-2631-6463 |
| work_keys_str_mv | AT eftangjensl atwostepcertifiedreducedbasismethod AT huynhdinhbaophuong atwostepcertifiedreducedbasismethod AT knezevicjovana atwostepcertifiedreducedbasismethod AT pateraanthonyt atwostepcertifiedreducedbasismethod AT eftangjensl twostepcertifiedreducedbasismethod AT huynhdinhbaophuong twostepcertifiedreducedbasismethod AT knezevicjovana twostepcertifiedreducedbasismethod AT pateraanthonyt twostepcertifiedreducedbasismethod |