2016/06/30 by Juan Carlos Araujo-Cabarcas, Araujo-Cabarcas, Juan Carlos, Christian Engström +1
Engineering · Physics and Astronomy · #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Vibration and Dynamic Analysis
paper · pdf · doi:10.48550/arxiv.1606.09635
openalex publication_date 2016/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we discuss problems arising when computing resonances with a\nfinite element method. In the pre-asymptotic regime, we detect for the one\ndimensional case, spurious solutions in finite element computations of\nresonances when the computational domain is truncated with a perfectly matched\nlayer (PML) as well as with a Dirichlet-to-Neumann map (DtN). The new test is\nbased on the Lippmann-Schwinger equation and we use computations of the\npseudospectrum to show that this is a suitable choice. Numerical simulations\nindicate that the presented test can distinguish between spurious eigenvalues\nand true eigenvalues also in difficult cases. Keywords: scattering resonances,\nLippmann-Schwinger equation, nonlinear eigenvalue problems, acoustic resonator,\ndielectric resonator, Bragg resonator\n