Efficient Solution of the Simplified PN Equations

Abstract

In this paper we show new solver strategies for the multigroup SPN equations for nuclear reactor analysis. By forming the complete matrix over space, moments, and energy a robust set of solution strategies may be applied. Power iteration, shifted power iteration, Rayleigh quotient iteration, Arnoldi's method, and a generalized Davidson method, each using algebraic and physics-based multigrid preconditioners, have been compared on C5G7 MOX test problem as well as an operational PWR model. Our results show that the most ecient approach is the generalized Davidson method, that is 30{40 times faster than traditional power iteration and 6{10 times faster than Arnoldi's method.