Parallel implementation of Red–Black ordering preconditioners for accelerating GMRES solutions in neutron transport code PANDAS-MOC

Abstract

The PANDAS-MOC uses preconditioners like ILU(0) and SSOR to accelerate the convergence of the GMRES solution in the Multi-level CMFD solver. However, their sequential nature limits their effectiveness on parallel platforms. This paper investigates the performance of Red–Black preconditioners (RB-SSOR, RB-RSOR, RB-ILU) in accelerating the solutions of MG-GMRES and CG-GMRES in the PANDAS-MOC. It uses various benchmark reactors, including TWIGL-2D, C5G7-2D, C5G7-3D, and their corresponding subplane models (TWIGL-2D(5S), C5G7-2D(5S), C5G7-3D(5S)), with relaxed convergence criteria (10−3). The results show that all preconditioners significantly reduce the required number of iterations to converge the GMRES solutions. The paper also explores the strong scaling and hybrid MPI/OpenMP speedup performance of Red–Black preconditioners using the C5G7-3D(5S) problem. Preconditioners present similar sublinear speedup trends across tests for MG-GMRES and CG-GMRES respectively, but the speedup results in CG-GMRES are more than twice as high as those in MG-GMRES. RB-RSOR has an optimal efficiency of 0.6967 at (4,8), while RB-SOR and RB-ILU have their optimal efficiencies of 0.6855 and 0.7275 at (32,1) when executing 32 total threads (= MPI processors × OpenMP threads).