An inherently parallel Monte Carlo linear systems solver applied to neutron diffusion equations Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/cj82kb580

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  • Linear solvers are often used to solve neutron diffusion problems. These tools have two significant shortcomings. First, parallel implementations provide only a modest speedup. The operations cannot be divided cleanly between processors. Second, for large matrices they can be very slow. Our primary goal is to find a new method for solving linear systems which reduces the impact of these two problems. In this study, we consider a different kind of approach. We employ a Monte Carlo algorithm in two dimensions to solve our linear systems probabilistic ally. We develop our probabilistic model and describe the formulation of our linear system. We also discuss our random sampling technique in some detail. We tally our solutions for both the forward and adjoint problems using path length and last event estimators. Computational results are compared to analytic and numerical benchmark solutions for three metrics: accuracy, convergence, and efficiency. The results detailed herein indicate that the method we have developed can be competitive with common linear solvers. We develop an on-the-fly algorithm as well, which is intended to make more efficient use of our computing resources. While this algorithm exhibits longer run-times, it is far less taxing on the system memory.
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