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In this paper, we present a nonnested augmented subspace algorithm and itsmultilevel correction method for solving eigenvalue problems with curvedinterfaces. The augmented subspace algorithm and the corresponding multilevelcorrection method are designed based on a coarse finite element space which isnot the subset of the finer finite element space. The nonnested augmentedsubspace method can transform the eigenvalue problem solving on the finest meshto the solving linear equation on the same mesh and small scale eigenvalueproblem on the low dimensional augmented subspace. The correspondingtheoretical analysis and numerical experiments are provided to demonstrate theefficiency of the proposed algorithms.

A Nonnested Augmented Subspace Method for Eigenvalue Problems with Curved Interfaces