Acceleration Technique Using Krylov Subspace Methods for 2D Arbitrary Geometry Characteristics Solver

Abstract

The Generalized Minimal RESidual (GMRES) method, which is a widely-used version of Krylov subspace methods for solving large sparse non-symmetric linear systems, is adopted to accelerate the 2D arbitrary geometry characteristics solver AutoMOC. In this technique, a formulism of linear algebraic equation system for angular flux moments and boundary fluxes is derived as an alternative to traditional characteristics sweep (i.e. inner iteration) formalism, and then the GMRES method is implemented as an efficient linear system solver. Several numerical results demonstrate that the acceleration technique based on Krylov subspace methods can be applied to arbitrary geometry MOC solver successfully, and may obtain higher efficiency than the original characteristics solver does because of its spectacular effect on reducing both the number of outer iterations and the total computing time. Moreover, the results could be improved by Lyusternik-Wagner extrapolation technique in some cases.