\(P_N\) Synthetic Acceleration for the Source Iteration Scheme in Slab-Geometry Discrete Ordinates Transport Calculations

In this chapter, it is described an acceleration strategy for the source iteration (SI) scheme in slab geometry based on the coarse-mesh solution of the \(P_N\) equations as initial guess for the fine-mesh scattering source. The first part of this methodology consists of obtaining a local general solution for the \(P_N\) equations with arbitrary order N. In the second part, the local general solution for the \(P_N\) equations was used as an improved initial guess for the fine-mesh scattering source in the SI scheme used in the conventional Diamond Difference (DD) method. This methodology has been implemented in a computer code developed on the MatLab platform for Windows. As a result, the computer code generates numerical results for the scalar flux through the Diamond Difference method accelerated by the present \(P_N\) methodology. To evaluate the applicability of the \(P_N\) synthetic acceleration, as described in this paper, numerical results for a model problem are presented.