  A local and parallel algorithm based on the multilevel discretization is
proposed in this paper to solve the eigenvalue problem by the finite element
method. With this new scheme, solving the eigenvalue problem in the finest grid
is transferred to solutions of the eigenvalue problems on the coarsest mesh and
a series of solutions of boundary value problems by using the local and
parallel algorithm. The computational work in each processor can reach the
optimal order. Therefore, this type of multilevel local and parallel method
improves the overall efficiency of solving the eigenvalue problem. Some
numerical experiments are presented to validate the efficiency of the new
method.
