Acceleration of the exponential function expansion nodal SP3 method by multi-group GMRES algorithm for PWR pin-by-pin calculation

For PWR whole-core pin-by-pin calculation, a parallel multi-group neutron transport calculation code named EFEN was developed based on the Exponential Function Expansion Nodal SP3 method. Considering the large number of unknowns, it was accelerated by using Coarse Mesh Rebalance (CMR) method. However, its efficiency still requires further improvement. In this paper, the acceleration of EFEN with Wielandt shift algorithm and multi-group Generalized Minimal Residual (GMRES) algorithm are studied. To deal with the high dominance ratio for PWR pin-by-pin problems, Wielandt shift algorithm is employed by transferring part of the fission source to pseudo scattering source. However, the pseudo scattering treatment would lead to an extra up-scattering issue which would increase the burden of the classical multi-group iteration for scattering source. Consequently, instead of using the multi-group Gauss-Seidel (GS) algorithm, a multi-group GMRES algorithm that solves all the energy groups simultaneously is adopted to deal with the extra up-scattering problem. Verifications and analysis of these algorithms are performed on a 10 × 1 multi-assembly pin-by-pin problem and a more realistic multi-group PWR whole-core pin-by-pin problem. Encouraging conclusions are demonstrated by the numerical results. (1) The number of power iteration can be reduced by a factor of about 6-10 by utilizing the Wielandt shift algorithm with a shifting factor of 0.01. (2) Multi-group GMRES algorithm accelerates the multi-group iteration significantly. The combination of these two can provide a speedup of 3.6 for a typical 8-group pin-by-pin calculation with 289 × 289 × 56 meshes. In addition, higher speedup of 14.0 can be obtained by combining the multi-group GMRES algorithm with the existing CMR method.