Study on the accelerated method for solving the CRAM burnup equations based on Gauss-Seidel method

Abstract: [Background]: The reactor burnup calculation is crucial for the safe operation and fuel management of nuclear power plants. In recent years, the Chebyshev Rational Approximation Method (CRAM) has become a primary approach for solving burnup equations. When solving the burnup equations using the CRAM, the Sparse Gaussian Elimination (SGE) method is usually used for complex matrix calculation, and the improvement of computational efficiency is limited. [Purpose]: This study aims to develop a Gauss-Seidel (GS)-based acceleration method for solving the CRAM burnup equations to enhance the computational efficiency of the burnup equation solver. [Methods]: Firstly, based on the self-developed burnup calculation code AMAC, this study develops an acceleration method for solving CRAM burnup equations based on the GS method. Second, three burnup databases (containing 71, 221, and 1487 nuclides) were utilized to analyze the computational accuracy and efficiency of a light-water reactor benchmark. To evaluate computational accuracy, the results of the SGE and GS methods were compared, thereby demonstrating the precision of the GS method. Furthermore, with the Transmutation Trajectory Analysis (TTA) as the reference solution, detailed analyses of the computational results of the Partial Fraction Decomposition (PFD) and Incomplete Partial Fractions (IPF) formulations based on the GS method were conducted. Finally, a comparative analysis of the computational efficiency of the SGE and GS methods was performed. [Results]: The results show that the numerical precision of GS method is good for solving IPF and PFD burnup equations under different scale burnup databases, and can meet the accuracy requirements of actual burnup calculation. For the calculation of short-lived nuclides, the calculation accuracy of IPF is better than that of PFD. In terms of efficiency, the GS method significantly surpassed SGE, achieving up to 80.17% acceleration across the three databases. [Conclusions]: This study recommends the adoption of the GS-accelerated IPF formalism for practical burnup calculations to effectively balance computational accuracy and efficiency.