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Title: On the convergence of the fixed point method for solving neutron transport alpha eigenvalue problems

Journal Article · · Annals of Nuclear Energy
 [1]
  1. Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
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It was shown that the Fixed Point Method (also known as the Rayleigh Quotient Method) is several times faster than the Critical Search Method for solving neutron transport alpha eigenvalue problems. It was also shown that the Fixed Point Method is able to determine the alpha eigenvalues of sub-critical systems that are beyond the reach of the Critical Search Method. Despite these significant advances, the Fixed Point Method remains an unproven algorithm. Here, this report provides a proof.

Research Organization:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC52-07NA27344
OSTI ID:
2532512
Report Number(s):
LLNL--JRNL-853084; 1077709
Journal Information:
Annals of Nuclear Energy, Journal Name: Annals of Nuclear Energy Vol. 211; ISSN 0306-4549
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (10)

Spectral properties and asymptotic behavior of the linear transport equation journal June 1984
positivity in time dependent linear transport theory journal September 1984
Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator journal April 1968
On the numerical radius and its applications journal February 1982
Analytical benchmark test set for criticality code verification journal January 2003
A Rayleigh quotient method for criticality eigenvalue problems in neutron transport journal April 2020
The spectrum of the multigroup neutron transport operator for bounded spatial domains journal August 1979
On the approximation of the leading eigenelements for a class of transport operators journal February 1994
A Linear Algebraic Development of Diffusion Synthetic Acceleration for Three-Dimensional Transport Equations journal February 1995
Development of a Generalized Perturbation Theory Method for Sensitivity Analysis Using Continuous-Energy Monte Carlo Methods journal March 2016

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