Tara M. Pandya

Massively Parallel, Three-Dimensional Transport Solutions for the k-Eigenvalue Problem

Abstract 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.

Hot zero power reactor calculations using the Insilico code

In this paper we describe the reactor physics simulation capabilities of the Insilico code. A description of the various capabilities of the code is provided, including detailed discussion of the geometry, meshing, cross section processing, and neutron transport options. Numerical results demonstrate that Insilico using an SPN solver with pin-homogenized cross section generation is capable of delivering highly accurate full-core simulation of various pressurized water reactor problems. Comparison to both Monte Carlo calculations and measured plant data is provided.

Scalable Parallel Prefix Solvers for Discrete Ordinates Transport in Multidimensions

Abstract The well-known “sweep” algorithm for inverting the streaming-plus-collision term in first-order deterministic radiation transport calculations suffers from parallel scaling issues caused by a lack of concurrency in the spatial dimension along the direction of particle travel. We investigate a new class of parallel algorithms that involves recasting the streaming-plus-collision problem in prefix form and solving via cyclic reduction. This method, although computationally more expensive at low levels of parallelism than the sweep algorithm, offers better theoretical scalability properties. Previous work has demonstrated this approach for one-dimensional calculations; we show how to extend it to multidimensional calculations. Notably, for multiple dimensions it appears that this approach is limited to long-characteristics discretizations; other discretizations cannot be cast in practical prefix form. Computational results on two different massively parallel computer systems demonstrate that both our “forward” and “symmetric” algorithms behave similarly, scaling well to larger degrees of parallelism than sweep-based solvers. We do observe some issues at the highest levels of parallelism (relative to the computer system size) and discuss possible causes. We conclude that this approach shows good potential for future parallel systems but that parallel scalability will depend on the architecture of the communication networks of these systems.

Eigenvalue Solvers for Modeling Nuclear Reactors on Leadership Class Machines

Abstract Three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadership-class computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy (MGE) preconditioner. The MG Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. RQI should converge in fewer iterations than power iteration (PI) for large and challenging problems. RQI creates shifted systems that would not be tractable without the MG Krylov solver. It also creates ill-conditioned matrices. The MGE preconditioner reduces iteration count significantly when used with RQI and takes advantage of the new energy decomposition such that it can scale efficiently. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. The combination of solvers enables the RQI eigenvalue solver to work better than the other available solvers for large reactors problems on leadership-class machines. Using these methods together, RQI converged in fewer iterations and in less time than PI for a full pressurized water reactor core. These solvers also performed better than an Arnoldi eigenvalue solver for a reactor benchmark problem when energy decomposition is needed. The MG Krylov, MGE preconditioner, and RQI solver combination also scales well in energy. This solver set is a strong choice for very large and challenging problems.