A Type of Multigrid Method for the Steklov‐Lamé Eigenvalue Problems

ABSTRACT In this article, a type of multigrid method for solving Steklov‐Lamé eigenvalue problems is proposed. The basic idea is to avoid directly solving large‐scale Steklov‐Lamé eigenvalue problems. The main process is to transform the Steklov‐Lamé eigenvalue problems into a series of Steklov‐Lamé boundary value problems in a multilevel space sequence, and then correcting the approximate solutions for these boundary value problems in a low‐dimensional augmented subspace. Since the solution of the large‐scale Steklov‐Lamé eigenvalue problem, which involves the main computational work in the classical numerical method, is omitted, the efficiency of the solution can obviously be improved. Consistently we prove that the proposed scheme can obtain optimal approximation with linear computational complexity. Some numerical examples are given to verify the theoretical results.