Abstract
This paper treats the problem of determining equivalent homogenized cross sections that preserve a set of prescribed reference albedos obtained from a heterogeneous reflector. This equivalence problem is treated as an optimization problem where the minimum of a functional is sought. Duality is used for a direct estimation of the derivatives needed in the iterative calculation of the optimal homogenized cross sections. We analyze both diffusion and transport as low-order operators for the equivalence and propose several choices for constraining the unknown cross sections. Numerical results illustrate the new approach for one-dimensional PN core calculations.
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