On spurious solutions in finite element approximations of resonances in open systems
Abstract
In this paper, we discuss problems arising when computing resonances with a finite element method. In the pre-asymptotic regime, we detect for the one dimensional case, spurious solutions in finite element computations of resonances when the computational domain is truncated with a perfectly matched layer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is based on the Lippmann-Schwinger equation and we use computations of the pseudospectrum to show that this is a suitable choice. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases. Keywords: scattering resonances, Lippmann-Schwinger equation, nonlinear eigenvalue problems, acoustic resonator, dielectric resonator, Bragg resonator
Keywords
Cite
@article{arxiv.1606.09635,
title = {On spurious solutions in finite element approximations of resonances in open systems},
author = {Juan Carlos Araujo-Cabarcas and Christian Engström},
journal= {arXiv preprint arXiv:1606.09635},
year = {2017}
}
Comments
Version 2, with mayor updates