{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/82451"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/82451","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Monte Carlo methods for parallel processing of diffusion equations","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. 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Thirdly, a tighter lower bound for the required number of chains given a desired error is determined.","abstract_has_math":false,"creators":["Vafadari, Cyrus"],"institution":"Massachusetts Institute of Technology","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. Department of Nuclear Science and Engineering.","school":null,"contributors":[],"advisors":["Benoit Forget."],"committee_chairs":[],"committee_members":[],"year":2013,"date_issued":"2013","date_published":"2013","updated_at":"2026-07-22T22:21:56Z","subjects":["Nuclear Science and Engineering."],"languages":["eng"],"rights":["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."],"rights_urls":["http://dspace.mit.edu/handle/1721.1/7582"],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1721.1/82451","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Benoit Forget."]},{"key":"dc:contributor.department","label":"Department","values":["Massachusetts Institute of Technology. Department of Nuclear Science and Engineering."]},{"key":"dc:contributor.other","label":"Dc Contributor Other","values":["Massachusetts Institute of Technology. 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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."],"dc:description.degree":["S.B."],"dc:identifier.uri":["http://hdl.handle.net/1721.1/82451"],"dc:language.iso":["eng"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["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. 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