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Three complementary methods have been implemented in the code Denovo thataccelerate neutral particle transport calculations with methods that useleadership-class computers fully and effectively: a multigroup block (MG)Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and amultigrid in energy preconditioner. The multigroup Krylov solver converges morequickly than Gauss Seidel and enables energy decomposition such that Denovo canscale to hundreds of thousands of cores. The new multigrid in energypreconditioner reduces iteration count for many problem types and takesadvantage of the new energy decomposition such that it can scale efficiently.These two tools are useful on their own, but together they enable the RQIeigenvalue solver to work. Each individual method has been described before,but this is the first time they have been demonstrated to work togethereffectively.  RQI should converge in fewer iterations than power iteration (PI) for largeand challenging problems. RQI creates shifted systems that would not betractable without the MG Krylov solver. It also creates ill-conditionedmatrices that cannot converge without the multigrid in energy preconditioner.Using these methods together, RQI converged in fewer iterations and in lesstime than all PI calculations for a full pressurized water reactor core. Italso scaled reasonably well out to 275,968 cores.

Rayleigh Quotient Iteration with a Multigrid in Energy Preconditioner for Massively Parallel Neutron Transport