We have implemented a new multilevel parallel decomposition in the Denovo discrete ordinates radiation transport code. In concert with Krylov subspace iterative solvers, the multilevel decomposition allows concurrency over energy in addition to space-angle, enabling scalability beyond the limits imposed by the traditional Koch-Baker-Alcouffe (KBA) space-angle partitioning. Furthermore, a new Arnoldi-based k-eigenvalue solver has been implemented. The added phase-space concurrency combined with the high-performance Krylov and Arnoldi solvers has enabled weak scaling to O(105) cores on the Titan XK7 supercomputer. The multilevel decomposition provides a mechanism for scaling to exascale computing and beyond.