Asymptotic behavior of spectral of Neumann-Poincare operator in Helmhotz system

TL;DR

This paper investigates the spectral asymptotics of the Neumann-Poincare operator in the Helmholtz system, revealing its continuity at zero and convergence behavior as frequency and order vary.

Contribution

It provides new asymptotic analysis of the Neumann-Poincare operator's spectrum for Helmholtz systems, especially near the origin and for high orders.

Findings

Spectral of Neumann-Poincare operator is continuous at the origin.

Spectral converges to zero from the complex plane as frequency decreases or order increases.

Asymptotic behavior is characterized for small frequencies and high orders.

Abstract

In this paper, we are concerned with the asymptotic behavior of the Neumann-Poincare operator for Helmholtz system. By analyzing the asymptotic behavior of spherical Bessel function near the origin and/or approach higher order, we prove the asymptotic behavior of spectral of Neumann-Poincare operator when frequency is small enough and/or the order is large enough. The results show that spectral of Neumann-Poincare operator is continuous at the origin and converges to zero from the complex plane in general.