Efficient Solution of the Simplified PN Equations

by Steven P. Hamilton, Thomas M. Evans

SP3 matrix sparsity pattern

SP3 matrix sparsity pattern for a 2×2×4 spatial grid and 4 energy groups.


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 the C5G7 MOX test problem as well as an operational pressurized water reactor model. Our results show that the most efficient approach is the generalized Davidson method, which is 30–40 times faster than traditional power iteration and 6–10 times faster than Arnoldi’s method.

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Publication Citation

Journal of Computational Physics 2015 pp 155-170