Acceleration of k-Eigenvalue/Criticality Calculations Using the Jacobian-Free Newton-Krylov Method

Abstract

We present a new approach for the k-eigenvalue problem using a combination of classical power iteration and the Jacobian-free Newton-Krylov (JFNK) method. The method poses the k-eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a one-dimensional, one-group problem and two two-dimensional two-group problems and provide comparison to other efforts using similar algorithmic approaches.