New 'Monte Carlo Functional' Methods for Estimating k-Eigenvalues and Eigenfunctions

摘要

We have presented new hybrid (MCQD and MCF) Monte Carlo methods for k eigenvalue/eigenfunction problems. The new methods differ from conventional Monte Carlo methods by the use of estimates of nonlinear func-tionals of the flux to indirectly obtain estimates of the eigenfunction and eigenvalue. (The MCQD method described here has truncation errors, but the two MCF methods do not.) For the problems tested, the nonlinear func-tionals are much more accurate than the direct Monte Carlo estimates of the eigenfunction; for this reason, the MCQD and MCF estimates of the eigenfunction and eigenvalue have much smaller variance than in standard Monte Carlo. In future work, we plan to extend the MCF method to realistic multi-D problems with anisotropic scattering and energy dependence.