Krylov Subspace Iterations for Deterministic k-Eigenvalue Calculations

The Implicitly Restarted Arnoldi Method (IRAM), a Krylov subspace iterative method, applied to k-eigenvalue calculations for criticality problems in deterministic transport codes is discussed. A computationally efficient alternative to the power iteration method that is typically used for such problems, the IRAM not only finds the largest eigenvalue but also several additional higher order eigenvectors with little extra computational cost. Implementation requires only modest changes to existing power iteration coding present in an S_N transport program. Numerical results are presented for three-dimensional S_N transport on unstructured tetrahedral meshes to compare the IRAM results with those computed using the traditional, unaccelerated power iteration method. The results indicate that the IRAM can be an efficient and powerful technique, especially for problems with dominance ratios approaching unity.