Enhancing the convergence rate of the Minimal Residual method via Symmetric Gauss–Seidel preconditioning for solving neutron transport equation in spherical geometry

Abstract

This paper enhances the Minimal Residual (MR) method for solving the neutron transport equation in spherical geometry by incorporating Symmetric Gauss–Seidel preconditioning to accelerate convergence. The proposed preconditioned MR method is analysed both theoretically and numerically, demonstrating a substantial improvement in convergence speed—reducing the number of iterations required for convergence compared to the unpreconditioned approach and other classical methods. Numerical experiments confirm that this technique not only accelerates convergence but also significantly improves computational efficiency, particularly for large-scale neutron transport simulations. These findings highlight the potential of the preconditioned MR method as an effective tool for solving complex neutron transport problems, with critical applications in nuclear reactor physics, radiation shielding, and other areas of nuclear engineering.