An efficient Gauss-Seidel-based acceleration method for solving the MMPA burnup equation system in nuclear reactors

Burnup calculation ensures the operational safety of nuclear reactors by determining the evolutionary behavior of radioactive nuclides through the solution of the burnup equations. The Mini-Max Polynomial Approximation (MMPA) method is an effective solution technique developed in recent years, and it offers several advantages over the Chebyshev Rational Approximation Method (CRAM). However, solving the MMPA system of equations using sparse Gaussian elimination (SGE) is computationally expensive because it involves repeated symbolic factorization, especially for large-scale problems. This study develops a Gauss-Seidel (GS)-based acceleration method, an iterative approach that avoids matrix preprocessing and reduces storage overhead by retaining only the necessary matrices and vectors. It offers fast convergence for diagonally dominant matrices. The method was rigorously implemented and verified through a light water reactor (LWR) pin-cell case, by utilizing three burnup databases containing the 71-, 221-, and 1487-nuclide inventories. The results obtained from all burnup databases indicate that once the approximation order exceeds 32, the average absolute relative difference of nuclide number densities reaches a magnitude of 10 -10 . The distribution of relative difference in nuclide number densities also becomes more concentrated and falls below 1.0×10 -11 , confirming excellent computational accuracy. In terms of efficiency, the GS-based acceleration method outperforms the SGE method across the approximation order range of 32 to 48. For the 1487-nuclide database, the GS-based acceleration method achieves a runtime reduction of nearly 50% compared to the SGE method. For computations involving the 221- and 71-nuclide databases, the GS-based acceleration method achieves a computational efficiency improvement of at least 70%. This method provides an effective solution for enhancing the computational efficiency of burnup equations, which in turn contributes to improving the efficiency of large-scale burnup calculations.