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arXiv · 1606.09635

On spurious solutions in finite element approximations of resonances in open systems

Juan Carlos Araujo-Cabarcas·Christian Engström
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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

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Juan Carlos Araujo-Cabarcas, Christian Engström. 2016-06-30. On spurious solutions in finite element approximations of resonances in open systems. https://arxiv.org/abs/1606.09635

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