An Algebraic Multigrid Method for Eigenvalue Problems and Its Numerical Tests

Abstract

In order to solve eigenvalue problems, an algebraic multigrid method based on a multilevel correction scheme and the algebraic multigrid method for linear equations is developed. The algebraic multigrid method setup procedure is used for construction of an hierarchy and intergrid transfer operators. In this approach, large scale eigenvalue problems are solved by algebraic multigrid smoothing steps in the hierarchy and by low-dimensional eigenvalue problems. The efficacy and flexibility of the method is demonstrated by a number of test examples and the global convergence, which does not depend on the number of eigenvalues wanted, is obtained.