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Title: Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport

Abstract

Today's "grand challenge" neutron transport problems require 3-D meshes with billions of cells, hundreds of energy groups, and accurate quadratures and scattering expansions. Leadership-class computers provide platforms on which high-fidelity fluxes can be calculated. However, appropriate methods are needed that can use these machines effectively. Such methods must be able to use hundreds of thousands of cores and have good convergence properties. Rayleigh quotient iteration (RQI) is an eigenvalue solver that has been added to the Sn code Denovo to address convergence. Rayleigh quotient iteration is an optimal shifted inverse iteration method that should converge in fewer iterations than the more common power method and other shifted inverse iteration methods for many problems of interest. Denovo's RQI uses a new multigroup Krylov solver for the fixed source solutions inside every iteration that allows parallelization in energy in addition to space and angle. This Krylov solver has been shown to scale successfully to 200,000 cores: for example one test problem scaled from 69,120 cores to 190,080 cores with 98% efficiency. This paper shows that RQI works for some small problems. However, the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems. This result leads tomore » the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.« less

Authors:
 [1];  [2];  [2];  [1]
  1. University of Wisconsin
  2. ORNL
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1041441
DOE Contract Number:  
DE-AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: PHYSOR 2012 Advances in Reactor Physics Linking Research, Industry, and Education, Knoxville, TN, USA, 20120415, 20120420
Country of Publication:
United States
Language:
English
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; COMPUTERS; CONVERGENCE; EDUCATION; EFFICIENCY; EIGENVALUES; NEUTRON TRANSPORT; QUADRATURES; REACTOR PHYSICS; SCATTERING

Citation Formats

Slaybaugh, R, Evans, Thomas M, Davidson, Gregory G, and Wilson, P. Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport. United States: N. p., 2012. Web.
Slaybaugh, R, Evans, Thomas M, Davidson, Gregory G, & Wilson, P. Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport. United States.
Slaybaugh, R, Evans, Thomas M, Davidson, Gregory G, and Wilson, P. 2012. "Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport". United States.
@article{osti_1041441,
title = {Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport},
author = {Slaybaugh, R and Evans, Thomas M and Davidson, Gregory G and Wilson, P.},
abstractNote = {Today's "grand challenge" neutron transport problems require 3-D meshes with billions of cells, hundreds of energy groups, and accurate quadratures and scattering expansions. Leadership-class computers provide platforms on which high-fidelity fluxes can be calculated. However, appropriate methods are needed that can use these machines effectively. Such methods must be able to use hundreds of thousands of cores and have good convergence properties. Rayleigh quotient iteration (RQI) is an eigenvalue solver that has been added to the Sn code Denovo to address convergence. Rayleigh quotient iteration is an optimal shifted inverse iteration method that should converge in fewer iterations than the more common power method and other shifted inverse iteration methods for many problems of interest. Denovo's RQI uses a new multigroup Krylov solver for the fixed source solutions inside every iteration that allows parallelization in energy in addition to space and angle. This Krylov solver has been shown to scale successfully to 200,000 cores: for example one test problem scaled from 69,120 cores to 190,080 cores with 98% efficiency. This paper shows that RQI works for some small problems. However, the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems. This result leads to the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.},
doi = {},
url = {https://www.osti.gov/biblio/1041441}, journal = {},
number = ,
volume = ,
place = {United States},
year = {2012},
month = {1}
}

Conference:
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