Juan Carlos Araujo-Cabarcas, Christian Engström
Published 2016-06-30Version 1
In this paper, we detect 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 show that this is a suitable choice. Estimates of the proximity of discrete and continuous eigenspaces and its consequences are discussed in the one-dimensional case. Then, the DtN formulation results in a quadratic eigenvalue problem and we discretize this problem as well as the linear eigenvalue problem from the PML formulation. Numerical simulations indicate that the presented test can distinguish between spurious eigenvalues and true eigenvalues also in difficult cases.
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