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The aim of this paper is to develop an algebraic multigrid method to solveeigenvalue problems based on the combination of the multilevel correctionscheme and the algebraic multigrid method for linear equations. Our approachuses the algebraic multigrid method setup procedure to construct the hierarchyand the intergrid transfer operators. In this algebraic multigrid scheme, alarge scale eigenvalue problem is solved by some algebraic multigrid smoothingsteps in the hierarchy and very small-dimensional eigenvalue problems. Toemphasize the efficiency and flexibility of the proposed method, here weconsider a set of test eigenvalue problems, discretized on unstructured meshes,with different shape of domain, singularity, and discontinuous parameters.Moreover, global convergence independent of the number of desired eigenvaluesis obtained.

An Algebraic Multigrid Method for Eigenvalue Problems in Some Different Cases