A parallel in energy Krylov solution algorithm for the variational nodal method

To reduce the computational expense caused by the large number of energy groups in thermal and fast reactor calculations, we researched using parallelization in energy (i.e. group) of the multi-group response matrix equations derived from the Variational Nodal Method. This study focuses on solving steady-state eigenvalue problems in diffusion theory that are typically needed for depletion and reactivity coefficient calculations. To examine serial and parallel performance, GMRES, a Krylov algorithm, is applied to the multi-group system of equations at each fission source iteration. We also study the impact of using Wielandt acceleration on the eigenvalue/eigenvector problem. Numerical results based on a 72 group thermal and a 216 group fast reactor core problems are obtained for both serial and parallel calculations. The results show reduced CPU times when using GMRES and Wielandt acceleration in both serial and parallel calculations. (authors)