Analysis of the Acceleration Effect of Anderson’s Fixed-Point Acceleration Method in Core Neutronics Calculations

Abstract Fixed-point iteration is the most widely used iterative format in numerical calculations. The Seidel iterative method is a traditional acceleration method, which is generally used in the source iteration process of core neutronics calculations. During the fixed-point iteration process, the Anderson acceleration method is using the least squares method to find the direction that converges the fastest, based on previous iteration values. The Anderson acceleration method can replace the Seidel iteration directly. So, it can be easily implemented in existing numerical software iteration. In this paper, the Anderson method with depth n is derived, where depth n represents the value of the previous n iterations. The Anderson acceleration formats with depths of 1 and 2 are used to calculate neutron flux of the reactor core. We calculate Boron critical searching calculation of the first-cycle loading. The calculation results show that the Anderson method reduces the number of iterations by 20% and the calculation time by about 15% on average compared with the source Seidel iteration while ensuring the same convergence accuracy. This improves the efficiency of neutronics calculations and provides a theoretical basis for subsequent transport calculations or other fixed-point iteration acceleration methods.