Monte Carlo methods for parallel processing of diffusion equations

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.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Nuclear Science and Engineering.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2013

Author dc:creator

• Vafadari, Cyrus

Advisor dc:contributor.advisor

• Benoit Forget.

• Nuclear Science and Engineering.

Statement 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. See provided URL for inquiries about permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/82451

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/82451