Stochastic finite-element approximation of the parametric dependence of eigenvalue problem solution

We present a stochastic finite-element approach for characterizing parameter dependence of minimum eigenvalue problems encountered in neutronic calculations. Our formulation results in solving a nonlinear system of equations, that is K times larger than the original problem and has K constraints, where K is the number of terms considered in the perturbative expansion of the solution. This approach allows us to calculate the behavior of the eigenvalue and the eigenvector in the entire parameter range, as opposed to a narrow region around a nominal value calculated by classical sensitivity analysis. Initial investigation for a small parameter space indicates that the method has the potential of substantial savings over Monte Carlo calculations that attempt to characterize the behavior of the eigenvector and eigenvalue over the entire parameter space.