GMRES as a multi-step transport sweep accelerator

Publisher Website
Google Scholar
Abstract
It is shown that GMRES can provide a multi-step transport sweep accelerator which operates by finding the linear combination of transport sweep iterates that minimize an estimate of the error in the flux. Because of the minimization process, a linear combination of only a relatively few transport sweep iterates can in fact well approximate a many-times collided flux. However, the number of iterations required increases with the optical thickness of the system; this reflects the need to capture the physics of the very highly collided particles present in the thicker system. Unlike a direct application of GMRES to the integro-differential form of the transport equation, which requires storage for several angular fluxes, the approach described here requires storage only for scalar fluxes in the case of isotropic scattering, or more generally only for those flux moments required for the order of scattering being used. In general it is not as efficient as DSA, but it is much faster than standard sweeps alone; it may therefore be very useful for discretization schemes where DSA cannot be applied. The number of iterations required of GMRES accelerated transport sweeps depends only weakly on the scattering ratio, and indeed has a dependance very similar to DSA. Furthermore, the general method can even reduce the number of iterations required for DSA, although, because of extra overhead, not necessarily the run time.

This publication has 3 references indexed in Scilit: