Multilevel Local Defect-Correction Method for Nonsymmetric Eigenvalue Problems

In this study, a multilevel local defect-correction method is designed for solving nonsymmetric eigenvalue problems. The main feature of our approach is the transformation of the nonsymmetric eigenvalue problems into several symmetric boundary value problems defined in a multilevel finite element space sequence and some low-dimensional nonsymmetric eigenvalue problems defined in a specially designed correction space. Moreover, the symmetric boundary value problems involved in our algorithm are solved by the local defect-correction strategy that divides the computing domain into small-scale subdomains. Since solving the high-dimensional nonsymmetric eigenvalue problems is avoided which is quite time-consuming compared with that of solving boundary value problems, the presented algorithm greatly improves the solving efficiency for nonsymmetric eigenvalue problems. Rigorous theoretical analysis and several numerical experiments are given to demonstrate the efficiency of our algorithm.