A Bootstrap Multigrid Eigensolver

This paper introduces bootstrap multigrid methods for solving eigenvalue problems arising from the discretization of partial differential equations. Inspired by full algebraic (BAMG) setup algorithm that includes an AMG eigensolver, it is illustrated how can be simplified case a discretized equation (PDE), thereby developing geometric (BMG) approach. We illustrate numerically efficacy BMG method for: (1) recovering eigenvalues having large multiplicity, (2) computing interior eigenvalues, and (3) approximating shifted indefinite problems. Numerical experiments are presented to basic components ideas behind success overall For completeness, we present error analysis two-grid Laplace-Beltrami problem.