COMPARISON OF CHEBYSHEV AND ANDERSON ACCELERATIONS FOR THE NEUTRON TRANSPORT EQUATION

¹ DEN - Service d’études des réacteurs et de mathématiques appliquées (SERMA) CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France
² DEN - DTN/STMA/LMAG CEA Cadarache, F-13108 Saint-Paul-lez-Durance, France
³ EDF R&D/PERICLES Lab Paris-Saclay 7, boulevard Gaspard Monge, F-91120 Palaiseau, France, EDF

ansar.calloo@cea.fr
romain.le-tellier@cea.fr
david.couyras@edf.fr

Published online: 22 February 2021

Abstract

This work focuses on the k-eigenvalue problem of the neutron transport equation. The variables of interest are the largest eigenvalue (k_eff) and the corresponding eigenmode is called the fundamental mode. Mathematically, this problem is usually solved using the power iteration method. However, the convergence of this algorithm can be very slow, especially if the dominance ratio is high as is the case in some reactor physics applications. Thus, the power iteration method has to be accelerated in some ways to improve its convergence. One such acceleration is the Chebyshev acceleration method which has been widely applied to legacy codes. In recent years, nonlinear methods have been applied to solve the k-eigenvalue problem. Nevertheless, they are often compared to the unaccelerated power iteration. Hence, the goal of this paper is to apply the Anderson acceleration to the power iteration, and compare its performance to the Chebyshev acceleration.