A fully coupled two-level Schwarz preconditioner based on smoothed aggregation for the transient multigroup neutron diffusion equations: A parallel preconditioner for the multigroup diffusion equations

The multigroup neutron diffusion equations (an approximation of the neutron transport equation) are widely used for studying the motion of neutrons and their interactions with stationary background materials. Solving the multigroup neutron diffusion equations is challenging because the unknowns are tightly coupled through scattering and fission events, and solutions with high spatial resolution of full reactor cores in multiphysics environments are frequently required. In this paper, we focus on the development of a scalable, parallel preconditioner for solving the system of equations arising from the finite-element discretization of the multigroup neutron diffusion equations in space and an implicit finite-difference scheme in time. The parallel preconditioner (here referred to as the "fully coupled Schwarz preconditioner") is constructed by monolithically applying the overlapping domain decomposition method together with a smoothed aggregation-based coarse space to the coupled system. Our approach is different from the traditional block Gauss-Seidel sweep method that applies the preconditioner from the fast group to the thermal group sequentially, and we demonstrate that it provides significant improvements in terms of both the number of iterations required and the total compute time for a system of equations with millions of unknowns on a large supercomputer.