Accelerating The Monte-Carlo power iteration utilizing the Jacobian-free Newton Krylov methodology

Nowadays, Monte-Carlo criticality analysis is performed utilizing the power iteration that calculates the fundamental eigenpair of the steady-state/k-eigenvalue form of the neutron transport equation. Whereas this method guarantees the convergence to the fundamental Eigenmode, very often the convergence is slow. Consequently, it is of high interest to improve the convergence of the power iteration in order not only to increase the accuracy but also to reduce the computational cost. In this work an alternative version of the traditional Monte-Carlo power iterative algorithm is formulated, developed and analysed aiming to numerically accelerate the Monte-Carlo criticality analysis. More specifically, a Newton-based, matrix-free numerical method for solving non-linear systems, the Jacobian-Free Newton Krylov methodology, is adopted in the Monte-Carlo k-eigenvalue context attempting to accelerate the convergence. However, the computationally burdensome nature of a Monte-Carlo algorithm makes a straight forward implementation of this methodology rather impossible. The problem is overcome by suitably utilising a deterministic diffusion-based power iteration within the developed algorithm. Since the Monte-Carlo calculated quantities required by the introduced methodology are associated with statistical noise, a fact that creates questions about the performance of this new concept, the method is initially evaluated in simplified test-cases. (authors)