The Homogeneous B₁ Model as Polynomial Eigenvalue Problem

Abstract

The homogeneous version of the B₁ leakage model is a non-linear eigenvalue problem which is generally solved iteratively by a root-finding algorithm, combined to the supplementary eigenvalue problem of the multiplication factor. This problem is widely used for ordinary cross section preparation in reactor analysis. Our work approximates this problem with a polynomial eigenvalue problem, which can be easily transformed into an ordinary linear generalized eigenproblem of size equal to the initial one multiplied by the polynomial degree used for the approximation of a transcendental function. This procedure avoids recurring to numerical root-finding methods supported by extra eigenvalue problems. The solution of the fundamental buckling with increasing approximation order is compared to the reference value obtained by inverse iterations.

Keywords:

• Leakage model
• neutron transport
• homogeneous B₁

Notes

1 ${\delta }_{\mathcal{\ell }0}$ is the Kronecker function being equal to 1 if $\mathcal{\ell }=0$ and zero otherwise.