Multigroup diffusion preconditioners for multiplying fixed-source transport problems

JOURNAL OF COMPUTATIONAL PHYSICS

卷:274

Article

Roberts, Jeremy A.¹  Forget, Benoit² 

[1] Kansas State Univ, Dept Mech & Nucl Engn, Manhattan, KS 66506 USA

[2] MIT, Dept Nucl Sci & Engn, Cambridge, MA 02139 USA

关键词: Preconditioning;    Neutron transport;    Krylov;    Discrete ordinates;   

DOI  :  10.1016/j.jcp.2014.06.034

来源: Elsevier

【 摘 要 】

Several preconditioners based on multigroup diffusion are developed for application to multiplying fixed-source transport problems using the discrete ordinates method. By starting from standard, one-group, diffusion synthetic acceleration (DSA), a multigroup diffusion preconditioner is constructed that shares the same fine mesh as the transport problem. As a cheaper but effective alternative, a two-grid, coarse-mesh, multigroup diffusion preconditioner is examined, for which a variety of homogenization schemes are studied to generate the coarse mesh operator. Finally, a transport-corrected diffusion preconditioner based on application of the Newton-Shulz algorithm is developed. The results of several numerical studies indicate the coarse-mesh, diffusion preconditioners work very well. In particular, a coarse-mesh, transport-corrected, diffusion preconditioner reduced the computational time of multigroup GMRES by up to a factor of 17 and outperformed best-case Gauss-Seidel results by over an order of magnitude for all problems studied. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free