On the stability of the Discrete Generalized Multigroup method

• Picard iteration with Discrete Generalized Multigroup found to be unstable in general.
• Krasnoselskij (relaxation) iteration scheme yields improved stability.
• Informed choice of group map improves convergence behavior.
• Better performance observed with larger number of groups.

This paper investigates the stability of the recondensation procedure of the Discrete Generalized Multigroup method and proposes alternatives to improve stability of the original formulation. Instabilities are shown to happen when employing a simple Picard fixed point iteration and an ill-informed group mapping scheme. This work presents a mapping procedure that improves stability of the original method for fine group calculations. Additionally, a relaxation scheme, Krasnoselskij iteration, is introduced to the fixed point iteration to further improve the stability characteristics and remove the need for fine group flux updates. Both improvements are applied on heterogeneous problems using the SHEM361 and the NG2042 group structures. The results indicate improved stability from a well-informed group mapping and demonstrate the possibility of eliminating the need for fine group flux updates.