Application of the Gauss-Seidel Method to the Chebyshev Rational Approximation Method for Solving Nuclear Fuel Depletion Systems

Abstract

The Chebyshev Rational Approximation Method (CRAM) has become one of the dominant methods for solving the Bateman equations for nuclear fuel depletion analysis. Since its introduction over a decade ago, several improvements have been made to CRAM improving its accuracy and reducing its run time. We analyzed its run time using two previously published methods for solving the CRAM system of equations, direct matrix inversion (DMI) and sparse Gaussian elimination (SGE), for depletion systems of varying numbers of nuclides to see how the two methods perform relative to one another. In addition to these two methods, we introduced the Gauss-Seidel (GS) method for solving the CRAM system of equations and compared its performance relative to DMI and SGE for depletion systems with varying numbers of nuclides. We demonstrated that for practical purposes, GS is faster than SGE and DMI and achieves a practical level of accuracy. All testing was performed using the CRAM implementation in the Griffin reactor physics analysis application.