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

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. The present report is concerned with the use of a Krylov Sub-Space method. called ORTHOMIN, 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 schemes are compared for two realistic 3-D multi-group cases: an LWR benchmark and the AHWR Critical Facility. The within-group iterations over self-scattering source are required in the solution of K-eigenvalue problem. They are also accelerated using another Krylov method called Conjugate Gradient method. In this work, the discretisation of Transport Equation is based on fmite-differencing and Sn-method and isotropic scattering is considered. (author)