Explicitly Restarted Arnoldi's Method for Monte Carlo Nuclear CriticalityCalculations.
[摘要] A Monte Carlo implementation of explicitly restarted Arnoldi’s method is developedfor estimating eigenvalues and eigenvectors of the transport-fission operator inthe Boltzmann transport equation. Arnoldi’s method is an improvement over thepower method which has been used for decades. Arnoldi’s method can estimate multipleeigenvalues by orthogonalising the resulting fission sources from the applicationof the transport-fission operator. As part of implementing Arnoldi’s method, a solutionto the physically impossible—but mathematically real—negative fission sourcesis developed. The fission source is discretized using a first order accurate spatialapproximation to allow for orthogonalization and normalization of the fission sourcerequired for Arnoldi’s method. The eigenvalue estimates from Arnoldi’s method arecompared with published results for homogeneous, one-dimensional geometries, and itis found that the eigenvalue and eigenvector estimates are accurate within statisticaluncertainty.The discretization of the fission sources creates an error in the eigenvalue estimates.A second order accurate spatial approximation is created to reduce the errorin eigenvalue estimates. An inexact application of the transport-fission operator isalso investigated to reduce the computational expense of estimating the eigenvaluesand eigenvectors.The convergence of the fission source and eigenvalue in Arnoldi’s method is analysedand compared with the power method. Arnoldi’s method is superior to the powermethod for convergence of the fission source and eigenvalue because both convergenearly instantly for Arnoldi’s method while the power method may require hundredsof iterations to converge. This is shown using both homogeneous and heterogeneousone-dimensional geometries with dominance ratios close to 1.
[发布日期] [发布机构] University of Michigan
[效力级别] Arnoldi" [学科分类]
[关键词] Monte Carlo;Arnoldi"s Method;Power Method;Nuclear Criticality;Nuclear Engineering and Radiological Sciences;Engineering;Nuclear Engineering & Radiological Sciences [时效性]
