Technique for reducing time in the calculation of eigenvalues and eigenvectors applied in neutron transport fixed-source problems

Abstract

In this work, a mathematical technique to accelerate the eigenvalue calculations, originally proposed for the Analytical Discrete Ordinates method (ADO), is applied to the coarse-mesh method Modified Spectral Deterministic (MSD), used in neutron shielding problems (fixed-source) in one-dimensional geometry. This technique consists in an arrangement of the neutron transport equation which leads to a reduced eigenvalue calculation on the intranodal analytical solution, where only the positive half of the eigenvalues and its respective eigenvectors are calculated, hence reducing the methods execution time. Precision and performance tests were performed in 2 model-problems, reducing around 80% of the execution time. All the codes were developed using the programming language C++.