Acceleration of external iterations using Chebyshev extrapolation in neutron diffusion theory

Abstract

This research aims to analyze, compare, and validate the performance of Chebyshev polynomials applied to the acceleration of convergence of external iterations through extrapolation of the fission source. To solve the system of equations generated from the discretization via finite element method of the neutron diffusion equation, Crout's method was applied. Chebyshev's extrapolation method was implemented in the FORTRAN programming language. To validate this method, we used the IAEA and Homogeneous Reactor benchmarks, both two-dimensional defined at 2 and 3 energy groups, respectively. The results obtained from the tests with different mesh refinements demonstrate the effectiveness of the acceleration of the external iterations when different values are considered for the Chebyshev iterations, especially when compared to extrapolation via over-relaxation.

DOI:https://doi.org/10.56238/uniknowindevolp-108