Roberts, Jeremy A.Forget, Benoit2014-09-262014-09-262014-10-01http://hdl.handle.net/2097/18343Several preconditioners based on multigroup di usion are developed for application to multiplying fi xed-source transport problems using the discrete ordinates method. By starting from standard, one-group, diff usion synthetic acceleration (DSA), a multigroup diff usion preconditioner is constructed that shares the same fi ne mesh as the transport problem. As a cheaper but effective alternative, a two-grid, coarse-mesh, multigroup diff usion preconditioner is examined, for which a variety of homogenization schemes are studied to generate the coarse mesh operator. Finally, a transport-corrected diff usion preconditioner based on application of the Newton-Shulz algorithm is developed. The results of several numerical studies indicate the coarse-mesh, diff usion preconditioners work very well. In particular, a coarse-mesh, transport-corrected, diff usion 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.en-USThis Item is protected by copyright and/or related rights. You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).https://rightsstatements.org/page/InC/1.0/PreconditioningNeutron transportKrylovDiscrete ordinatesArticle (author version)