Anderson acceleration and linear diffusion for accelerating the [formula omitted]-eigenvalue problem for the transport equation

Abstract

This work focuses on the k-eigenvalue problem of the neutron transport equation to solve for the largest eigenvalue (keff) and the corresponding eigenmode, called the fundamental mode. 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 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. Past works have compared and contrasted the benefits of the Anderson acceleration method for the neutron transport equation, and the analysis is improved in this work by studying the impact of preconditioning acceleration techniques on the overall performance.In this work, the transport operator is inverted using the source iteration method with the discrete ordinates (Sn) method. Therefore, keeping in mind the need for improving the power iteration algorithm, we also focus on a different type of acceleration which is the diffusion synthetic acceleration (DSA) usually employed for improving the inner iterations. In this research effort, DSA is applied to the power iteration. Besides, Anderson and Chebyshev accelerations are combined with this external DSA scheme to evaluate the computational gain.All these methods have been applied to a benchmark case of a small pressurised water reactor, KAIST 3A.