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This paper is to introduce a type of full multigrid method for the nonlineareigenvalue problem. The main idea is to transform the solution of nonlineareigenvalue problem into a series of solutions of the corresponding linearboundary value problems on the sequence of finite element spaces and nonlineareigenvalue problems on the coarsest finite element space. The linearizedboundary value problems are solved by some multigrid iterations. Besides themultigrid iteration, all other efficient iteration methods for solving boundaryvalue problems can serve as the linear problem solver. We will prove that thecomputational work of this new scheme is truly optimal, the same as solving thelinear corresponding boundary value problem. In this case, this type ofiteration scheme certainly improves the overfull efficiency of solvingnonlinear eigenvalue problems. Some numerical experiments are presented tovalidate the efficiency of the new method.

A Full Multigrid Method for Nonlinear Eigenvalue Problems