Stability analysis of coarse group rebalance acceleration for multigroup two-dimensional diffusion equationsb

Abstract

For many problems of neutron and radiation particle transport, the standard source iteration algorithm converges quite slowly and requires an inordinate amount of computing time. Therefore, a need exists for accelerating this algorithm. Coarse Group Rebalance (CGR) is such a method that has been employed for this purpose. In this study for neutron diffusion equations, stability analysis for CGR acceleration is performed and tested by using numerical simulation and Fourier analysis. Two types of CGR acceleration schemes, additive (linear) CGR and multiplicative (nonlinear) CGR, are introduced. Although the multiplicative CGR acceleration scheme is a nonlinear method, it works for all cases. This analysis is based on linearizing the CGR algorithm for special class of problems and using a Fourier analysis to examine the stability of the linearized algorithm. Numerical tests show that the original (nonlinear) CGR and linearized CGR methods have basically the same convergence properties, and that theses properties are accurately predicted by the Fourier analysis. But the additive CGR acceleration scheme which is a linear method does not work (does not converge) for some cases.