The Ronen method (RM) has been successfully applied to obtain highly accurate approximations to the solution of the neutron transport equation in one-dimensional (1D) homogeneous and heterogeneous configurations, considering both isotropic and linearly anisotropic problems. Anderson acceleration (AA)–based algorithms have recently been applied the RM iterative scheme to improve its convergence rate. Specifically, an improved version of the AA, the damped Anderson acceleration with restarts and epsilon monotonicity (DAAREM), has been implemented and employed during RM iterations. AA works on Krylov subspaces built with the residuals from successive iterations. DAAREM makes use of a restart and an optimized regularization parameter to guess the target solution by extrapolation. This kind of acceleration is crucial to finding the fixed-point solution throughout the nonlinear RM iterations and avoids the issue of slow convergence.

This work provides a detailed description of the DAAREM implementation in the RM. A full comparison of the convergence performances between nonaccelerated RM, standard AA, and DAAREM applied to RM iterations is presented for a 1D full-core benchmark. DAAREM is also improved in this work by ensuring the monotonicity of its control parameters, thus achieving higher performance. A significant reduction in the number of iterations in achieving the flux distribution within the target tolerance is always obtained for the model problems considered.