A simplified angular multigrid method to accelerate SN calculations

In problems with optically thick regions and high scattering ratios (c minus ratio = σs/σt), particles that are making a large number of scattering collisions in a single energy group contribute significantly to scalar flux distribution; consequently, the convergence of the source iteration (SI) method can become very slow. For certain cross-section libraries, groups in the thermal energy range may be very broad, and particles may undergo many scattering events before being removed from the group. One remedy to fix the slow convergence is to narrow the energy group ranges; however, this means that the transport equation must be solved for more groups, which may lead to further computational inefficiency. Hence, numerous techniques have been devised to accelerate the SI method, such as rebalance, diffusion synthetic acceleration (DSA), and multigrid acceleration schemes. Multigrid acceleration is a general type of acceleration method, which has been applied to transport calculations by using it directly for the SN equations and/or for the DSA equations. The basic principle of the multigrid method is to use a sequence of coarse and fine grids to obtain an accelerated solution on the fine grid. Here, the authors briefly explain the general idea of the multigrid method