Reduced basis method for Boltzmann equation
Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2007
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| Online Access: | http://hdl.handle.net/1721.1/39218 |
| _version_ | 1826207444983873536 |
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| author | Garlapati, Revanth Reddy |
| author2 | Anthony T. Patera. |
| author_facet | Anthony T. Patera. Garlapati, Revanth Reddy |
| author_sort | Garlapati, Revanth Reddy |
| collection | MIT |
| description | Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. |
| first_indexed | 2024-09-23T13:49:46Z |
| format | Thesis |
| id | mit-1721.1/39218 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T13:49:46Z |
| publishDate | 2007 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/392182019-04-10T21:55:07Z Reduced basis method for Boltzmann equation Garlapati, Revanth Reddy Anthony T. Patera. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Massachusetts Institute of Technology. Computation for Design and Optimization Program. Computation for Design and Optimization Program. Thesis (S.M.)--Massachusetts Institute of Technology, Computation for Design and Optimization Program, 2006. Includes bibliographical references (p. 103-106). The main aim of the project is to solve the BGK model of the Knudsen parameterized Boltzmann equation which is 1-d with respect to both space and velocity. In order to solve the Boltzmann equation, we first transform the original differential equation by replacing the dependent variable with another variable, weighted with function t(y); next we obtain a Petrov Galerkin weak form of this new transformed equation. To obtain a stable and accurate solution of this weak form, we perform a transformation of the velocity variable y, such that the semi-infinite domain is mapped into a finite domain; we choose the weighting function t(y), to balance contributions at infinity. Once we obtain an accurate and well defined finite element solution of the problem. The next step is to perform the reduced basis analysis of the equation using these accurate finite element solutions. We conclude the project by verifying that the orthonormal reduced Basis method based on the greedy algorithm converges rapidly over the chosen test space. by Revanth Reddy Garlapati. S.M. 2007-10-19T20:32:33Z 2007-10-19T20:32:33Z 2006 2006 Thesis http://hdl.handle.net/1721.1/39218 85844342 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 106 p. application/pdf Massachusetts Institute of Technology |
| spellingShingle | Computation for Design and Optimization Program. Garlapati, Revanth Reddy Reduced basis method for Boltzmann equation |
| title | Reduced basis method for Boltzmann equation |
| title_full | Reduced basis method for Boltzmann equation |
| title_fullStr | Reduced basis method for Boltzmann equation |
| title_full_unstemmed | Reduced basis method for Boltzmann equation |
| title_short | Reduced basis method for Boltzmann equation |
| title_sort | reduced basis method for boltzmann equation |
| topic | Computation for Design and Optimization Program. |
| url | http://hdl.handle.net/1721.1/39218 |
| work_keys_str_mv | AT garlapatirevanthreddy reducedbasismethodforboltzmannequation |