Application of Anderson acceleration to the neutron transport equation

International audienceThis work investigates the solution of the multigroup neutron transport equation with a discrete ordinatesmethod. More specifically, it focuses on the k-eigenvalue problem of the equation. In this case, the variablesof interest are the largest eigenvalue (keff) and the corresponding eigenmode is called the fundamentalmode. Mathematically, this problem is usually solved using the power iteration method. However, theconvergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case insome reactor physics applications. Thus, the power iteration method has to be accelerated in some ways toimprove its convergence.One such acceleration is the Chebyshev acceleration method [2] which has been applied to legacy codes. Inrecent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, these areoften compared to the unaccelerated power iteration method. Hence, the goal of this paper is to apply theAnderson acceleration method to the power iteration method, and compare its performance to the Chebyshevacceleration method