  In this paper, we present a nonnested augmented subspace algorithm and its
multilevel correction method for solving eigenvalue problems with curved
interfaces. The augmented subspace algorithm and the corresponding multilevel
correction method are designed based on a coarse finite element space which is
not the subset of the finer finite element space. The nonnested augmented
subspace method can transform the eigenvalue problem solving on the finest mesh
to the solving linear equation on the same mesh and small scale eigenvalue
problem on the low dimensional augmented subspace. The corresponding
theoretical analysis and numerical experiments are provided to demonstrate the
efficiency of the proposed algorithms.
