A New Multigrid Finite Element Method for the Transmission Eigenvalue Problems

TL;DR

This paper introduces a multigrid finite element method for efficiently solving transmission eigenvalue problems, reducing computational complexity by solving eigenproblems on coarse meshes and boundary value problems on finer meshes.

Contribution

It develops a novel multigrid approach based on prior work, simplifying implementation and improving efficiency for computing transmission eigenvalues.

Findings

Method is simple and easy to implement.

Efficient for real and complex eigenvalues.

Numerical results confirm effectiveness.

Abstract

Numerical methods for the transmission eigenvalue problems are hot topics in recent years. Based on the work of Lin and Xie [Math. Comp., 84(2015), pp. 71-88], we build a multigrid method to solve the problems. With our method, we only need to solve a series of primal and dual eigenvalue problems on a coarse mesh and the associated boundary value problems on the finer and finer meshes. Theoretical analysis and numerical results show that our method is simple and easy to implement and is efficient for computing real and complex transmission eigenvalues.