摘要：In this talk, we shall propose an efficient and parallel interior eigensolver for computing eigenvalues of symmetric elliptic operators, which may compute efficiently more interior multiple and clustered eigenvalues other than only the first several smallest eigenvalues. The new method is parallel in two ways: one is to solve the correction equations inexactly by the two-level additive overlapping Schwarz preconditioner, the other is to solve different clusters of eigenvalues simultaneously in different computers. A rigorous theoretical analysis is given for the new method, which reveals that the convergence factor is independent of the fine mesh size and the internal gaps among the target interior clustered eigenvalues, depending on the distance from both ends of the target eigenvalues to others. Meanwhile, more subdomains lead to the better convergence factor. Numerical results supporting our theory shall be given. This is a joint work with Qigang Liang.