In this talk we present a non-linear algebraic multigrid method applied to the partial eigenvalue problem arising from FE discretization of partial differential equations. We show that a coarse-space of modest size (obtained by aggressive coarsening) can be employed, provided its order of approximation is sufficiently high. With moderate demands on the order of approximation of the coarse-space and weak assumption on the input iterate (its Rayleigh quotient smaller than the second eigenvalue), we prove rapid convergence for large problems.
The nonlinear multigrid method that we use is a special type of the Exact Interpolation Scheme proposed by Brandt et al. in which the prolongator is constructed so that the current approximation belongs to its range. Unlike the previous work, however, we use a general purpose prolongator and simply add the current approximation as its first column. We demonstrate the effectivity of our method on realistic nuclear reactor criticality problems.