Acceleration technique using Krylov subspace methods for 2D arbitrary geometry characteristics solver

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 form 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. To some degree, this is quite a favorable acceleration technique for the Method Of Characteristics (MOC) with the following advantages: firstly, it has great geometric flexibility by nature, thus, can theoretically be applied to accelerate absolutely arbitrary geometry MOC solver just like AutoMOC; secondly, it simply solves systems of linear equations and doesn't require any additional calculation, so it is convenient to implement. In our investigation, angular flux moments and incident angular fluxes from outer boundaries are involved in the linear systems and solved simultaneously, thus we can deal with boundary conditions and anisotropic scattering more accurately than linear systems which only involves scalar fluxes and incident currents. 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. The results could be improved by Lyusternik-Wagner extrapolation technique in some cases.