A Full Multigrid Method for Nonlinear Eigenvalue Problems

*Manting Xie (Academy of Mathematics and Systems Science, Chinese Academy of Sciences) xiemanting@lsec.cc.ac.cn

Nonlinear eigenvalue problems have been applied in many areas. I will introduce an effective method to solve them. The main idea is to transform the solution of nonlinear eigenvalue problem into a series of solutions of the corresponding linear boundary value problems on the sequence of finite element spaces and nonlinear eigenvalue problems on the coarsest finite element space. The linearized boundary value problems are solved by some multigrid iterations. I will prove that the computational work of this new scheme is truly optimal, the same as solving the linear corresponding boundary value problem. This shows that our new method certainly improves the overfull efficiency of solving nonlinear eigenvalue problems.