A mixed-element two-grid discretization for Helmholtz transmission eigenvalues

TL;DR

This paper introduces a mixed-element two-grid discretization method for the Helmholtz transmission eigenvalue problem, providing theoretical error estimates and demonstrating efficiency through numerical results.

Contribution

The paper proposes a novel mixed-element two-grid discretization approach with proven error estimates for solving Helmholtz transmission eigenvalues.

Findings

The method achieves accurate eigenvalue approximations.

Numerical results confirm the theoretical error estimates.

The approach is computationally efficient.

Abstract

The Helmholtz transmission eigenvalue problem has received much concern in materials science, so it's significant to explore the efficient calculational method of the problem to mathematics and mechanics community. In this paper, based on a variational formulation proposed by Cakon, Monk and Sun, we introduce a mixed-element two-grid discretization and prove error estimates for this method theoretically. Some numerical results are presented to confirm the theoretical analysis and show that the method here is efficient.