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

• Published in: Nuclear science and engineering Vol. 198; no. 6
• Main Authors: Calvin, Olin W., Choi, Namjae
• Format: Journal Article
• Language: English
• Published: United States Taylor & Francis 28.09.2023
• Subjects: Bateman equations; CRAM; depletion; Gauss-Seidel; MATHEMATICS AND COMPUTING; NUCLEAR FUEL CYCLE AND FUEL MATERIALS
• ISSN: 0029-5639; 1943-748X

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 the run time of the method. We analyzed the run time of CRAM 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 introduce the Gauss-Seidel method for solving the CRAM system of equations and compare its performance relative to DMI and SGE for depletion systems with varying numbers of nuclides. Additionally, we demonstrate that for practical purposes Gauss-Seidel is faster than SGE and DMI although this comes at the cost of the precision of the solution. All testing was performed using the CRAM implementation in the Griffin reactor physics analysis application.