Session: 06-02 Nuclear Codes, Standards, Licensing, & Regulatory Issues Session 2

Paper Number: 134930

134930 - 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 sources 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, we construct linear and nonlinear equations, then calculate the spectral radius of the coefficient matrix formed using the Anderson and the Seidel iterative method respectively. The numbers of iterations of those two acceleration methods are compared. The basic principle that the Anderson acceleration method is superior to the Seidel method is analyzed theoretically.

Based on those compared results, the Anderson method with depth 1 and depth 2 is implemented in the source iteration process of the neutron diffusion calculation software respectively, where depth n represents the value of the previous n iterations. Depth 2 indicates that the current accelerated update value is calculated using the values of this and the previous two iterations. We calculate the first-cycle loading and the burnup calculation. 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.

The comparison results between different iteration depths of the Anderson acceleration method are as follows: the number of iterations of the depth 2 is less than that of the depth 1 iterative format, while there is not much difference in efficiency.  Because the least squares solution is the vertex of the parabola in depth 1 , that is, the position of the axis of symmetry, and the minimum squares solution needs to be calculated additionally in the process of acceleration at high depth, so the extra calculation time is lost.

Verified by sufficient comparison, the Anderson fixed-point acceleration method improves the efficiency of neutron diffusion calculation and provides a theoretical basis for other algorithm such as other fixed-point iterative accelerations. In the future, we plan to implement this algorithm to transport calculations or other fixed-point iterative accelerations, such as physics-thermal coupling calculations and so on，and add it to one of the basic algorithm modules of the digital reactor。

Presenting Author: Zhigang Li Nuclear Power Institute of China

Presenting Author Biography: Ping An, Ph.D. candidate in nuclear energy science and engineering.
She has been engaged in the research and software development of reactor core numerical algorithms for a long time, authorized 8 patents, published 32 SCI/EI publications, and led the development of more than 10 sets of software, with nearly 100,000 lines of code. It includes the supercritical water-cooled reactor physical-thermal-hydraulic coupling program system, and the three-dimensional neutronics calculation software CORCA-3D.

Authors:

Ping An Nuclear Power Institute of China
Wei Lu Nuclear Power Institute of China
Rui Liu Nankai University
Zhigang Li Nuclear Power Institute of China
Qifen Tang Nuclear Power Institute of China
Jie Shen NanKai University