Leveraging Anderson Acceleration for improved convergence of iterative solutions to transport systems

In this note we demonstrate that using Anderson Acceleration (AA) in place of a standard Picard iteration can not only increase the convergence rate but also make the iteration more robust for two transport applications. We also compare the convergence acceleration provided by AA to that provided by moment-based acceleration methods. Additionally, we demonstrate that those two acceleration methods can be used together in a nested fashion. We begin by describing the AA algorithm. At this point, we will describe two application problems, one from neutronics and one from plasma physics, on which we will apply AA. We provide computational results which highlight the benefits of using AA, namely that we can compute solutions using fewer function evaluations, larger time-steps, and achieve a more robust iteration.