Solution of the k-Eigenvalue Problem for Nuclear Reactor Analysis

Steven Hamilton, Emory University

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Solutions to the k-eigenvalue problem are of great interest in the design and analysis of nuclear reactors. In particular, we are interested in approximating the dominant eigenvalue and corresponding eigenvector of an eigenvalue formulation of the Boltzmann radiation transport equation. This problem is generally approached using the power method, possibly combined with some form of nonlinear acceleration. Slow convergence or instabilities frequently arise when using such approaches on particularly difficult problems. We are currently looking into the use of alternative eigensolvers (e.g. Rayleigh Quotient Iteration, Newton-Krylov methods or the Jacobi-Davidson method). Difficulties arise, however, in that such approaches require solving types of linear systems which have been largely unexplored in transport literature. In this study, we address these difficulties and propose some preconditioning techniques to facilitate the solution of such sub-problems.

Abstract Author(s): Steven HamiltonMichele Benzi