Rayleigh Quotient Iteration with a Multigrid in Energy Preconditioner for Massively Parallel Neutron Transport
Abstract
Three complementary methods have been implemented in the code Denovo that accelerate neutral particle transport calculations with methods that use leadershipclass computers fully and effectively: a multigroup block (MG) Krylov solver, a Rayleigh quotient iteration (RQI) eigenvalue solver, and a multigrid in energy preconditioner. The multigroup Krylov solver converges more quickly than Gauss Seidel and enables energy decomposition such that Denovo can scale to hundreds of thousands of cores. The new multigrid in energy preconditioner reduces iteration count for many problem types and takes advantage of the new energy decomposition such that it can scale efficiently. These two tools are useful on their own, but together they enable the RQI eigenvalue solver to work. Each individual method has been described before, but this is the first time they have been demonstrated to work together effectively. 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 illconditioned matrices that cannot converge without the multigrid in energy preconditioner. Using these methods together, RQI converged in fewer iterations and in less time than all PI calculations for a full pressurized water reactor core. It also scaled reasonably well out to 275,968 cores.
 Publication:

arXiv eprints
 Pub Date:
 February 2017
 arXiv:
 arXiv:1702.02111
 Bibcode:
 2017arXiv170202111S
 Keywords:

 Computer Science  Computational Engineering;
 Finance;
 and Science;
 Computer Science  Numerical Analysis;
 Mathematics  Numerical Analysis;
 Physics  Computational Physics
 EPrint:
 arXiv admin note: text overlap with arXiv:1612.00907