Reduced-basis output bound methods for parametrized partial differential equations
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2005
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| Online Access: | http://hdl.handle.net/1721.1/16956 |
| _version_ | 1826190971440726016 |
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| author | Rovas, Dimitrios V. (Dimitrios Vasileios), 1975- |
| author2 | Anthony T. Patera. |
| author_facet | Anthony T. Patera. Rovas, Dimitrios V. (Dimitrios Vasileios), 1975- |
| author_sort | Rovas, Dimitrios V. (Dimitrios Vasileios), 1975- |
| collection | MIT |
| description | Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003. |
| first_indexed | 2024-09-23T08:48:06Z |
| format | Thesis |
| id | mit-1721.1/16956 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T08:48:06Z |
| publishDate | 2005 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/169562019-04-10T13:21:51Z Reduced-basis output bound methods for parametrized partial differential equations Rovas, Dimitrios V. (Dimitrios Vasileios), 1975- Anthony T. Patera. Massachusetts Institute of Technology. Dept. of Mechanical Engineering. Massachusetts Institute of Technology. Dept. of Mechanical Engineering. Mechanical Engineering. Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003. Includes bibliographical references (p. 189-200). This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. An efficient and reliable method for the prediction of outputs of interest of partial differential equations with affine parameter dependence is presented. To achieve efficiency we employ the reduced-basis method: a weighted residual Galerkin-type method, where the solution is projected onto low-dimensional spaces with certain problem-specific approximation properties. Reliability is obtained by a posteriori error estimation methods - relaxations of the standard error-residual equation that provide inexpensive but sharp and rigorous bounds for the error in outputs of interest. Special affine parameter dependence of the differential operator is exploited to develop a two-stage off-line/on-line blackbox computational procedure. In the on-line stage, for every new parameter value, we calculate the output of interest and an associated error bound. The computational complexity of the on-line stage of the procedure scales only with the dimension of the reduced-basis space and the parametric complexity of the partial differential operator; the method is thus ideally suited for the repeated and rapid evaluations required in the context of parameter estimation, design, optimization, and real-time control. The theory and corroborating numerical results are presented for: symmetric coercive problems (e.g. problems in conduction heat transfer), parabolic problems (e.g. unsteady heat transfer), noncoercive problems (e.g. the reduced-wave, or Helmholtz, equation), the Stokes problem (e.g flow of highly viscous fluids), and certain nonlinear equations (e.g. eigenvalue problems). by Dimitrios V. Rovas. Ph.D. 2005-05-19T15:26:00Z 2005-05-19T15:26:00Z 2003 2003 Thesis http://hdl.handle.net/1721.1/16956 53370937 eng M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. http://dspace.mit.edu/handle/1721.1/7582 200 p. 4176450 bytes 4175214 bytes application/pdf application/pdf application/pdf Massachusetts Institute of Technology |
| spellingShingle | Mechanical Engineering. Rovas, Dimitrios V. (Dimitrios Vasileios), 1975- Reduced-basis output bound methods for parametrized partial differential equations |
| title | Reduced-basis output bound methods for parametrized partial differential equations |
| title_full | Reduced-basis output bound methods for parametrized partial differential equations |
| title_fullStr | Reduced-basis output bound methods for parametrized partial differential equations |
| title_full_unstemmed | Reduced-basis output bound methods for parametrized partial differential equations |
| title_short | Reduced-basis output bound methods for parametrized partial differential equations |
| title_sort | reduced basis output bound methods for parametrized partial differential equations |
| topic | Mechanical Engineering. |
| url | http://hdl.handle.net/1721.1/16956 |
| work_keys_str_mv | AT rovasdimitriosvdimitriosvasileios1975 reducedbasisoutputboundmethodsforparametrizedpartialdifferentialequations |