Iterative computation of time-eigenvalues of the neutron transport equation

The Implicitly Restarted Arnoldi Method (IRAM) is applied to the computation of prompt time-eigenvalues of the neutron transport equation. Derivation of the eigenvalue problem is based on a least-squares functional combined with a spherical harmonics angular discretization and spatial finite elements. The method is applied to a mono-energetic homogeneous slab and compared to semi-analytical results. The results are found to be accurate if the angular discretization is sufficiently refined. The scheme is also applied to a model ADS geometry in both one and three energy groups. The IRAM is found to be very efficient but the solution of fixed source problems that are part of the algorithm need to be accelerated in the multigroup case to obtain an overall efficient method.