FOURIER ANALYSIS OF A NONLINEAR TWO-GRID METHOD FOR MULTIGROUP NEUTRON DIFFUSION PROBLEMS

摘要

We analyze a nonlinear acceleration method for solving multigroup diffusion equations in multidimensional geometry. It uses two energy grids: (ⅰ) original energy groups and (ⅱ) one coarse group. We perform theoretical studies of stability of the nonlinear two-grid (NTG) iteration method for fixed-source and k-eigenvalue problems. The Fourier analysis is applied to the NTG equations linearized near solution of infinite-medium problems. The developed analysis of the NTG method enables us to predict its convergence properties in various types of neutron diffusion problems. Numerical results of problems in 2D Cartesian geometry are presented to confirm theoretical predictions.