An Incomplete Domain Decomposition Preconditioning Method for Nonlinear Nodal Kinetics Calculations

Abstract

Methods are proposed for the efficient parallel solution of nonlinear nodal kinetics equations. Because the two-node calculation in the nonlinear nodal method is naturally parallelizable, the majority of the effort is devoted to the development of parallel methods for solving the coarse-mesh finite difference (CMFD) problem. A preconditioned Krylov subspace method (biconjugate gradient stabilized) is chosen as the iterative algorithm for the CMFD problem, and an efficient parallel preconditioning scheme is developed based on domain decomposition techniques. An incomplete lower-upper triangular factorization method is first formulated for the coefficient matrices representing each three-dimensional subdomain, and coupling between subdomains is then approximated by incorporating only the effect of the nonleakage terms of neighboring subdomains. The methods are applied to fixed-source problems created from the International Atomic Energy Agency three-dimensional benchmark problem. The effectiveness of the incomplete domain decomposition preconditioning on a multiprocessor is evidenced by the small increase in the number of iterations as the number of sub-domains increases. Through the application to both CMFD-only and nodal calculations, it is demonstrated that speedups as large as 49 with 96 processors are attainable in the nonlinear nodal kinetics calculations.