Krylov sub-space methods for K-eigenvalue problem in 3-D neutron transport

Abstract

The K-eigenvalue problem in nuclear reactor physics is often formulated in the framework of Neutron Transport Theory. The fundamental mode solution of this problem is usually obtained by the power iteration method. Here, we are concerned with the use of a Krylov sub-space method, called ORTHOMIN(1), to obtain a more efficient solution of the K-eigenvalue problem. A Matrix-free approach is proposed which can be easily implemented by using a transport code which can perform fixed source calculations. The power iteration and ORTHOMIN(1) schemes are compared for two realistic 3-D multi-group cases with isotropic scattering: an LWR benchmark and a heavy water reactor problem. In both the schemes, within-group iterations over self-scattering source are required as intermediate procedures. These iterations are also accelerated using another Krylov method called conjugate gradient method. The overall work is based on the use of Sn-method and finite-differencing for discretisation of transport equation.