Application of the augmented block Householder Arnoldi method to the calculation of non-fundamental modes of the diffusion equation

Abstract

The determination of non-fundamental modes of the diffusion equation is required for computing CANDU reactor power distribution from analysis of in-core detector readings. They are also important for understanding subcritical mode instabilities occurring in boiling water reactors. The legacy method for computing these modes is the Hotelling deflation technique based on bi-harmonic decontamination. However, the Hotelling technique becomes unstable as the number of modes increase or as their eigenvalues become closer. Effective and fast alternatives are provided with Implicit Arnoldi Restarted Methods (IRAM). Among them, we investigated the Krylov–Schur method available in the SLEPc library, and we are proposing a custom implementation of the augmented block Householder Arnoldi (ABHA) method, similar to the Open Source implementation of Prof. James Baglama. In our work, the ABHA method is applied to the neutron diffusion equation, discretized with the Raviart–Thomas and Raviart–Thomas-Schneider methods or with the mesh-centered finite difference method.