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Title: Comparison of two Galerkin quadrature methods

Abstract

Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard S N method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard S N method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwise sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding S N equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.

Authors:
 [1];  [2];  [3];  [4]
  1. Texas A & M Univ., College Station, TX (United States)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  4. Univ. of New Mexico, Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1369451
Alternate Identifier(s):
OSTI ID: 1407871
Report Number(s):
SAND-2017-5262J; LA-UR-16-22029
Journal ID: ISSN 0029-5639; 653397; TRN: US1702537
Grant/Contract Number:  
AC04-94AL85000; AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Nuclear Science and Engineering
Additional Journal Information:
Journal Volume: 185; Journal Issue: 2; Journal ID: ISSN 0029-5639
Publisher:
American Nuclear Society - Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 97 MATHEMATICS AND COMPUTING; SN; Galerkin quadratures; anisotropic scattering; discrete ordinates; transport methods

Citation Formats

Morel, Jim E., Warsa, James, Franke, Brian C., and Prinja, Anil. Comparison of two Galerkin quadrature methods. United States: N. p., 2017. Web. doi:10.1080/00295639.2016.1272383.
Morel, Jim E., Warsa, James, Franke, Brian C., & Prinja, Anil. Comparison of two Galerkin quadrature methods. United States. doi:10.1080/00295639.2016.1272383.
Morel, Jim E., Warsa, James, Franke, Brian C., and Prinja, Anil. Tue . "Comparison of two Galerkin quadrature methods". United States. doi:10.1080/00295639.2016.1272383. https://www.osti.gov/servlets/purl/1369451.
@article{osti_1369451,
title = {Comparison of two Galerkin quadrature methods},
author = {Morel, Jim E. and Warsa, James and Franke, Brian C. and Prinja, Anil},
abstractNote = {Here, we compare two methods for generating Galerkin quadratures. In method 1, the standard SN method is used to generate the moment-to-discrete matrix and the discrete-to-moment matrix is generated by inverting the moment-to-discrete matrix. This is a particular form of the original Galerkin quadrature method. In method 2, which we introduce here, the standard SN method is used to generate the discrete-to-moment matrix and the moment-to-discrete matrix is generated by inverting the discrete-to-moment matrix. With an N-point quadrature, method 1 has the advantage that it preserves N eigenvalues and N eigenvectors of the scattering operator in a pointwise sense. With an N-point quadrature, method 2 has the advantage that it generates consistent angular moment equations from the corresponding SN equations while preserving N eigenvalues of the scattering operator. Our computational results indicate that these two methods are quite comparable for the test problem considered.},
doi = {10.1080/00295639.2016.1272383},
journal = {Nuclear Science and Engineering},
number = 2,
volume = 185,
place = {United States},
year = {Tue Feb 21 00:00:00 EST 2017},
month = {Tue Feb 21 00:00:00 EST 2017}
}

Journal Article:
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