Multigroup diffusion preconditioners for multiplying fixed-source transport problems

作者：Roberts Jeremy A^*; Forget Benoit

来源：Journal of Computational Physics, 2014, 274: 455-472.

DOI：10.1016/j.jcp.2014.06.034

• Preconditioning
• Neutron transport
• Krylov
• Discrete ordinates

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.

• 出版日期2014-10-1
• 单位MIT