Convergence of the adaptive finite element discretization based parallel orbital-updating method for eigenvalue problems

Abstract

It is significant and challenging to solve eigenvalue problems of partial differential operators when many highly accurate eigenpair approximations are required. The adaptive finite element discretization based parallel orbital-updating method, which can significantly reduce the computational cost and enhance the parallel scalability, has been shown to be efficient in electronic structure calculations. However, there is no any mathematical justification for this method in literature. In this paper, we will show the convergence of the method for clustered eigenvalue problems of linear partial differential operators.