Domain decomposition methods for nonlinear nodal spatial kinetics

New solution methods suitable for efficient parallel computation of reactor spatial kinetics problems are presented. A transient fixed source problem is formulated at each time point by applying the theta time differencing method and a second-order precursor integration technique to the time-dependent neutron balance equation. The spatial solution of the fixed source problem is obtained by employing the nonlinear nodal method. The coarse mesh finite difference problems appearing in the nonlinear iteration are solved by a preconditioned Krylov subspace method. A preconditioner suitable for three-dimensional coarse mesh neutron diffusion problems is developed based on the blockwise incomplete LU factorization. Parallel computation of the nonlinear nodal solution is performed by employing three-dimensional domain decomposition. An incomplete domain decomposition preconditioning scheme based on the physics of neutron diffusion is formulated to incorporate efficiently the coupling effects between subdomains. A parallel spatial kinetics code capable of adaptive time step control and a one-dimensional thermal-hydraulic calculation is introduced and verified through benchmark calculations for the control rod ejection accident. Results obtained on a distributed memory machine demonstrate that for a modest fixed source problem, a speedup of 49 is achievable with 96 processors and for an adverse practical transient problem, a speedup of 30 with 72 processors