Iterative Methods for Solving the Neutron Transport Equation in 1-D Spherical Geometry

摘要

In this note, we propose an iterative methods technique for solving the neutron transport equation in 1 -D spherical geometry. More precisely we analyze the theoretical and numerical aspect of Jacobi and Gauss-Siedel algorithms in an infinite dimension, and compare there with the classical method. These algorithms are based on a splitting of the collision operator taking into account the characteristics of the transport operator. One of the advantages of these algorithms is that give a good rate of convergence, and they are independent of the discretization chosen for the neutron transport equation.