Theoretical and numerical analysis of the Minimal Residual Method for solving the neutron transport equation in spherical geometry

Abstract

This paper introduces an infinite-dimensional adaptation of the Minimal Residual method for solving the neutron transport equation in spherical geome- try. The method is based on a novel splitting strategy of the collision operator, designed to account for the distinct characteristics of the transport operator. We provide both theoretical and numerical analyses of the algorithm, demonstrating its convergence and computational efficiency. Compared to previous approaches Tizaoui 2007b, 2009, our method offers improved accuracy and a significant reduction in computational cost, particularly for large-scale systems. These results underline the potential of the MR method in solving complex transport problems, with applications in nuclear physics and engineering.