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Home / Publications / Journals / Nuclear Science and Engineering / Volume 185 / Number 2

Comparison of Two Galerkin Quadrature Methods

Jim E. Morel, James S. Warsa, Brian C. Franke, Anil K. Prinja

Nuclear Science and Engineering / Volume 185 / Number 2 / February 2017 / Pages 325-334

Technical Paper / dx.doi.org/10.1080/00295639.2016.1272383

First Online Publication:January 13, 2017
Updated:February 16, 2017

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.

 
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