An 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. In this paper, we provide a mathematical justification for the method for clustered eigenvalue problems of linear partial differential operators, including the convergence and error estimates of the numerical approximations.