Abstract
Using perfectly matched layers for the computation of resonances in open systems typically produces artificial or spurious resonances. We analyze the dependency of these artificial resonances with respect to the discretization parameters and the complex scaling function. In particular, we study the differences between a standard frequency independent complex scaling and a frequency dependent one. While the standard scaling leads to a linear eigenvalue problem, the frequency dependent scaling leads to a polynomial one. Our studies show that the location of artificial resonances is more convenient for the frequency dependent scaling than for a standard scaling. Moreover, the artificial resonances of a frequency dependent scaling are less sensitive to the discretization parameters. Hence, the use of a frequency dependent scaling simplifies the choice of the corresponding discretization parameters.
Highlights
In this paper, we study acoustic resonances in open systems
We have studied the effects of the various parameters and sub-steps in the discretization process of a complex scaling method on the computed resonances of the Helmholtz equation in one and two dimensions and have classified the occurring spurious resonances into three categories: truncation resonances, which are an approximation to the essential spectrum, and interior and exterior spurious resonances, generated by the discretization of the interior and exterior domain respectively
In applications where resonances near the real axis are sought-after, the interior and exterior spurious resonances are the ones raising problems, especially since the location of the exterior spurious resonances delicately depends on the choice of the damping parameter
Summary
We study acoustic resonances in open systems. In this context an open system is an unbounded domain of wave activity, allowing for the existence of complex resonances (see e.g. [13] for examples). Since solutions to the Helmholtz equation on this complex manifold are exponentially decreasing, a truncation of the unbounded exterior domain into a bounded layer leads to an exponentially decreasing modelling error. This bounded layer can be discretized using standard finite element methods, which leads to a linear eigenvalue problem. The use of a frequency dependent scaling reduces the spurious resonances generated by the discretization of the exterior domain a lot. Two-dimensional problems are studied in Sect. 5, and a short conclusion completes the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
