Complex Scaled Infinite Elements for Wave Equations in Heterogeneous Open Systems

Abstract

The technique of complex scaling is a popular way to deal with the wave equation on unbounded domains. It is based on a complex coordinate stretching in the time harmonic regime. In our work we consider settings, where the usual cartesian or radial scalings are not applicable due to inhomogeneous exterior domains (e.g. open waveguids in non-axial directions)We apply a scaling in normal direction. Moreover we use infinite elements to discretize the complex scaled equation instead of truncating the domain to benefit from superior approximation properties and omit an additional truncation error. We present numerical experiments to illustrate our results.