Monte Carlo methods for parallel processing of diffusion equations
Name
863057698-MIT.pdf
Description
Full printable version
Size
909.49 KB
Format
Adobe PDF
Checksum (MD5)
248634d3b4a8c05911552e25ba42153f
Author(s)
Vafadari, Cyrus
Advisor(s)
Benoit Forget.
Date Issued
2013
Publisher
Massachusetts Institute of Technology
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.
Description
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).
Subjects
Nuclear Science and Engineering.
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
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