An Algebraic Multigrid Method for Eigenvalue Problems

An algebraic multigrid method is proposed to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. The algebraic multigrid method setup procedure is applied to construct the hierarchy and the intergrid transfer operators. In the algebraic multigrid scheme, a large scale eigenvalue problem can be solved by some algebraic multigrid smoothing steps in the hierarchy and some eigenvalue problems solving in a very small dimension. Some numerical experiments are presented to validate the efficiency of the proposed algorithm.

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