2026-09-18T22:20:38Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/824512022-01-13T07:54:05Zcom_1721.1_7582com_1721.1_7581col_1721.1_131024
Benoit Forget.
Vafadari, Cyrus
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering.
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
2013-11-18T19:24:46Z
2013-11-18T19:24:46Z
2013
http://hdl.handle.net/1721.1/82451
863057698
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.
27 pages
eng
Massachusetts Institute of Technology
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
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http://dspace.mit.edu/handle/1721.1/7582
Nuclear Science and Engineering.
Monte Carlo methods for parallel processing of diffusion equations
Thesis
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<Abstract>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.</Abstract>
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