A multigrid method for SN calculations in x-y geometry

The standard source iteration method for obtaining iterative solutions of SN problems is known to converge slowly in optically thick, diffusive regions. Consequently, a class of acceleration schemes, synthetic methods, has been developed that has greatly increased the efficiency of SN calculations. The basic principle in the synthetic method is to use a suitable low-order operator to accelerate an iteration with a high-order operator. Initially, the low-order operator was a diffusion operator, which yielded a method known as diffusion-synthetic acceleration (DSA). Unfortunately, for the DSA method to be implemented in a stable fashion, a particular set of acceleration equations is required, which may be difficult to solve efficiently for complicated discretization schemes (e.g., nodal methods). Thus, in x-y geometry, DSA has only been implemented for the diamond-differenced SN equations. An effective means of accelerating iteration schemes, which (until now) has been almost exclusively applied to elliptic equations, is the multigrid method. The authors present a multigrid algorithm for solving low-order transport operators; specifically, a multigrid algorithm is used to solve the pseudo-S2 (PS2) equations, which result from a BPA method that was presented previously