IRAM combined with multi-group GMRES for solving Matrix MOC

In the Matrix MOC, a linear algebraic equation system can be constructed by sweeping only once, and then solving the linear system takes the place of repeatedly characteristics sweeping. In neutron transport critical problems, k_eff is traditionally computed by power iteration (PI), whose convergence rate is deeply dependent on the dominance ratio. Large problems of practical interest often have dominance ratios close to 1, leading to slow convergence of PI. In this study, k_eff is computed by the Implicitly Restarted Arnoldi Method (IRAM) combined with multi-group GMRES, in which multi-group problems coupled by upscatter are solved directly, avoiding upscatter iteration. Numerical results of several benchmarks such as 2D C5G7 demonstrate that IRAM combined with multi-group GMRES can obtain good accuracy and higher efficiency compared with PI. (authors)