A Multigrid Method for Nonlinear Eigenvalue Problems

Abstract

A multigrid method is proposed for solving nonlinear eigenvalue problems by the finite element method. With this new scheme, solving nonlinear eigenvalue problem is decomposed to a series of solutions of linear boundary value problems on multilevel finite element spaces and a series of small scale nonlinear eigenvalue problems. The computational work of this new scheme can reach almost the same as the solution of the corresponding linear boundary value problem. Therefore, this type of multilevel correction scheme improves the overfull efficiency of the nonlinear eigenvalue problem solving.