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Title: A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification

Abstract

Rattlesnake and MAMMOTH are the designated TREAT analysis tools currently being developed at the Idaho National Laboratory. Concurrent with development of the multi-physics, multi-scale capabilities, sensitivity analysis and uncertainty quantification (SA/UQ) capabilities are required for predicitive modeling of the TREAT reactor. For steady-state SA/UQ, that is essential for setting initial conditions for the transients, generalized perturbation theory (GPT) will be used. This work describes the implementation of a PETSc based solver for the generalized adjoint equations that constitute a inhomogeneous, rank deficient problem. The standard approach is to use an outer iteration strategy with repeated removal of the fundamental mode contamination. The described GPT algorithm directly solves the GPT equations without the need of an outer iteration procedure by using Krylov subspaces that are orthogonal to the operator’s nullspace. Three test problems are solved and provide sufficient verification for the Rattlesnake’s GPT capability. We conclude with a preliminary example evaluating the impact of the Boron distribution in the TREAT reactor using perturbation theory.

Authors:
; ; ; ; ; ; ; ;
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1369425
Report Number(s):
INL/CON-16-40220
DOE Contract Number:  
DE-AC07-05ID14517
Resource Type:
Conference
Resource Relation:
Conference: M&C 2017 International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, Republic of Korea (South Korea), April 16–20, 2017
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; Generalized Perturbation Theory; Rattlesnake; TREAT

Citation Formats

Schunert, Sebastian, Wang, Congjian, Wang, Yaqi, Kong, Fande, Ortensi, Javier, Baker, Benjamin, Gleicher, Frederick, DeHart, Mark, and Martineau, Richard. A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification. United States: N. p., 2017. Web.
Schunert, Sebastian, Wang, Congjian, Wang, Yaqi, Kong, Fande, Ortensi, Javier, Baker, Benjamin, Gleicher, Frederick, DeHart, Mark, & Martineau, Richard. A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification. United States.
Schunert, Sebastian, Wang, Congjian, Wang, Yaqi, Kong, Fande, Ortensi, Javier, Baker, Benjamin, Gleicher, Frederick, DeHart, Mark, and Martineau, Richard. Sat . "A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification". United States. https://www.osti.gov/servlets/purl/1369425.
@article{osti_1369425,
title = {A Generalized Perturbation Theory Solver In Rattlesnake Based On PETSc With Application To TREAT Steady State Uncertainty Quantification},
author = {Schunert, Sebastian and Wang, Congjian and Wang, Yaqi and Kong, Fande and Ortensi, Javier and Baker, Benjamin and Gleicher, Frederick and DeHart, Mark and Martineau, Richard},
abstractNote = {Rattlesnake and MAMMOTH are the designated TREAT analysis tools currently being developed at the Idaho National Laboratory. Concurrent with development of the multi-physics, multi-scale capabilities, sensitivity analysis and uncertainty quantification (SA/UQ) capabilities are required for predicitive modeling of the TREAT reactor. For steady-state SA/UQ, that is essential for setting initial conditions for the transients, generalized perturbation theory (GPT) will be used. This work describes the implementation of a PETSc based solver for the generalized adjoint equations that constitute a inhomogeneous, rank deficient problem. The standard approach is to use an outer iteration strategy with repeated removal of the fundamental mode contamination. The described GPT algorithm directly solves the GPT equations without the need of an outer iteration procedure by using Krylov subspaces that are orthogonal to the operator’s nullspace. Three test problems are solved and provide sufficient verification for the Rattlesnake’s GPT capability. We conclude with a preliminary example evaluating the impact of the Boron distribution in the TREAT reactor using perturbation theory.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2017},
month = {4}
}

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