Algebraic multigrid methods for solving generalized eigenvalue problems

Three algebraic multigrid (AMG) methods for solving generalized eigenvalue problems are presented. The first method combines modern AMG techniques with a nonlinear multigrid approach and nested iteration strategy. The second method is a preconditioned inverse iteration with linear AMG preconditioner. The third method is an enhacement of the previous one, namely the locally optimal block preconditioned conjugate gradient. Efficiency and accuracy of solutions computed by these AMG eigensolvers are validated on standard benchmarks where part of the spectrum is known. In particular, the problem of isospectral drums is addressed.