Complex scaling profiles for wave equations in open systems

Abstract

Open boundary simulations are the subject of great interest when considering wave phenomena. Methods using complex coordinate stretchings can be employed to generate exponentially decaying outgoing solutions in space for time-harmonic equations. Applying a Fourier transform to the resulting system in space leads to a system in time domain which can be discretized using the Finite Element Method and an appropriate time-stepping. In this thesis we consider different versions of complex scalings for the wave equation and the Klein-Gordon equation. We study the effects of using different coordinate systems and scaling functions and give numerical results in one and two dimensions.