Monte Carlo methods for parallel processing of diffusion equations
Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2013.
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| Format: | Thesis |
| Language: | eng |
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Massachusetts Institute of Technology
2013
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| Online Access: | http://hdl.handle.net/1721.1/82451 |
| _version_ | 1811088368173318144 |
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| author | Vafadari, Cyrus |
| author2 | Benoit Forget. |
| author_facet | Benoit Forget. Vafadari, Cyrus |
| author_sort | Vafadari, Cyrus |
| collection | MIT |
| description | Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2013. |
| first_indexed | 2024-09-23T14:01:05Z |
| format | Thesis |
| id | mit-1721.1/82451 |
| institution | Massachusetts Institute of Technology |
| language | eng |
| last_indexed | 2024-09-23T14:01:05Z |
| publishDate | 2013 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/824512019-04-11T11:35:33Z Monte Carlo methods for parallel processing of diffusion equations Vafadari, Cyrus Benoit Forget. Massachusetts Institute of Technology. Department of Nuclear Science and Engineering. Massachusetts Institute of Technology. Department of Nuclear Science and Engineering. Nuclear Science and Engineering. Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Nuclear Science and Engineering, 2013. "June 2013." Cataloged from PDF version of thesis. Includes bibliographical references (page 14). A Monte Carlo algorithm for solving simple linear systems using a random walk is demonstrated and analyzed. The described algorithm solves for each element in the solution vector independently. Furthermore, it is demonstrated that this algorithm is easily parallelized. To reduce error, each processor can compute data for an independent element of the solution, or part of the data for a given element for the solution, allowing for larger samples to decrease stochastic error. In addition to parallelization, it is also shown that a probabilistic chain termination can decrease the runtime of the algorithm while maintaining accuracy. Thirdly, a tighter lower bound for the required number of chains given a desired error is determined. by Cyrus Vafadari. S.B. 2013-11-18T19:24:46Z 2013-11-18T19:24:46Z 2013 Thesis http://hdl.handle.net/1721.1/82451 863057698 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 27 pages application/pdf Massachusetts Institute of Technology |
| spellingShingle | Nuclear Science and Engineering. Vafadari, Cyrus Monte Carlo methods for parallel processing of diffusion equations |
| title | Monte Carlo methods for parallel processing of diffusion equations |
| title_full | Monte Carlo methods for parallel processing of diffusion equations |
| title_fullStr | Monte Carlo methods for parallel processing of diffusion equations |
| title_full_unstemmed | Monte Carlo methods for parallel processing of diffusion equations |
| title_short | Monte Carlo methods for parallel processing of diffusion equations |
| title_sort | monte carlo methods for parallel processing of diffusion equations |
| topic | Nuclear Science and Engineering. |
| url | http://hdl.handle.net/1721.1/82451 |
| work_keys_str_mv | AT vafadaricyrus montecarlomethodsforparallelprocessingofdiffusionequations |