Advances in Discrete-Ordinates Methodology

Multigroup diffusion preconditioners for multiplying fixed-source transport problems

“…Here, a brief summary is given of diffusion synthetic acceleration (DSA), a diffusion-based preconditioner that has long been used to improve source iteration [10] and was more recently applied to Krylov solvers for the within-group equations [3]. The development closely follows the excellent treatment of Larsen and Morel [11].…”

“…Of course, to apply P −1 in this case represents solving the original problem. Although preconditioners cannot in practice be expected to yield a set of eigenvalues equal to unity, any clustering typically improves convergence, and often just pushing eigenvalues away from the origin tends to improve convergence [11].…”

“…(1) in angle with the diamond-difference approximation in space [10]. By following the presentation of Larsen and Morel [11], the scalar flux is defined as…”

Computational transport methodology based on decomposition of a problem domain into transport and diffusive subdomains

“…In each particular case, they enable one to evaluate spatial ranges of various kinds of subdomains and areas between them where transport effects are weak but still important. We consider two different transport discretization methods: the QD method that uses the step characteristic (SC) scheme for discretization of the transport equation and a secondorder finite-volume scheme for the LOQD equations [10], the linear discontinuous (LD) finite element method [12].…”

The Tailored Finite Point Method

“…Numerical methods for the neutron transport equation have been developed for decades [39][40][41] as an active area. The discrete-ordinate transport equations are given by [41] …”