A multilevel Newton’s method for eigenvalue problems. (English) Zbl 1488.65594

He, Yunhui; Li, Yu; Xie, Hehu; You, Chun’guang; Zhang, Ning

Appl. Math., Praha 63, No. 3, 281-303 (2018).

Summary: We propose a new type of multilevel method for solving eigenvalue problems based on Newton’s method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue problems. Finally, some numerical examples are provided to validate the efficiency of the proposed numerical scheme.

MSC:

65N25	Numerical methods for eigenvalue problems for boundary value problems involving PDEs
65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65H10	Numerical computation of solutions to systems of equations
65N15	Error bounds for boundary value problems involving PDEs

Keywords:

eigenvalue problem; finite element method; Newton’s method; multilevel iteration