Application of the Krylov-Schur method in three-dimensional nuclear reactor discrete ordinates criticality calculations

The accurate and efficient solution of the neutron transport equation is essential in nuclear reactor physics for understanding reactor kinetics, stability, and safety. This study investigates the application of the Krylov-Schur method to three-dimensional neutron transport criticality calculations within the Marvin code, comparing its performance to the traditional Power Iteration (PI) method. Using the Takeda benchmark problems, the Krylov-Schur solver demonstrated high accuracy in eigenvalue calculations and neutron flux distributions, closely matching reference Monte Carlo (MC) results. Additionally, the parallel efficiency of the Krylov-Schur method was evaluated, showing significant speed-up and better scalability compared to the PI method, particularly in large-scale computations. However, the method requires a larger memory footprint due to the need to store multiple Krylov subspace vectors and Schur decompositions. Despite this, the findings highlight the Krylov-Schur method's robustness and computational efficiency, making it a promising tool for neutron transport simulations in complex reactor configurations. Future work will focus on investigating the subtraction of high-order eigenvalues and eigenvectors using the Krylov-Schur method to further enhance neutron transport simulations.