Finite Element Approximation of the Modified Maxwell's Stekloff Eigenvalues

TL;DR

This paper develops a finite element method to accurately compute the modified Maxwell's Stekloff eigenvalues, providing rigorous analysis and error estimates, with numerical validation for inverse electromagnetic scattering applications.

Contribution

It introduces a new finite element approach for the modified Maxwell's Stekloff eigenvalues with proven error estimates on Lipschitz polyhedra, advancing computational methods in electromagnetic inverse problems.

Findings

Error estimates without extra regularity assumptions

Numerical validation confirms the method's accuracy

Applicable to inhomogeneous media in electromagnetic scattering

Abstract

The modified Maxwell's Stekloff eigenvalue problem arises recently from the inverse electromagnetic scattering theory for inhomogeneous media. This paper contains a rigorous analysis of both the eigenvalue problem and the associated source problem on Lipschitz polyhedra. A new finite element method is proposed to compute Stekloff eigenvalues. By applying the Babuska-Osborn theory, we prove an error estimate without additional regularity assumptions. Numerical results are presented for validation.