Multi-group gmres algorithm for the exponential fuction expansional nodal SP3 method

To improve the accuracy of reactor core design, a parallel multi-group whole core pin-by-pin calculation code, EFEN, was developed based on the Exponential Function Expansion Nodal method. In this paper, we study the acceleration of EFEN with Wielandt shift algorithm and multi-group GMRES algorithm. Taking advantage of high dominance ratio of the PWR pin-by-pin problem, the Wielandt method was employed by making part of the fission sources into pseudo scattering source. However, this artificial up-scattering caused by the pseudo scattering would increase the burden of multi-group iteration for scattering source. Thus, instead of the legacy multi-group Gauss-Seidel algorithm, the multi-group GMRES algorithm that solve all on the energy groups simultaneously is used to deal with the artificial up-scattering problem. Verification and analysis of these methods were performed on 10-by-1 multi-assembly problem and a more realistic multi-group PWR core problem. The calculation results show that the number of power iteration can be reduce by a factor of about 6 or 10 by utilizing the Wielandt method with factor of 0.01. 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. However, the higher speedup of 14.0 can be obtained with multi-group GMRES method and previously developed CMFD method.