Abstract

The most common assumption when solving wave scattering is to linearise and then solve for the frequency domain solution. This assumption mimics many experiment setups in which the incident wave is fixed to a single frequency and applied for a “long time.” The frequency domain solution captures the time-dependent problem, which may involve complex pulse reflections. In particular, rapid variations in parameters like reflection and indicative of this pulse reflection, and this can easily be simulated. The transformation from frequency to time domain also highlights the deep connection between linear wave scattering and complex analysis. For example, the evolution in time is represented by multiplication by an exponential. All these ideas will be illustrated by considering the most simple scattering problem, a one-dimensional wave equation with delta function masses. We will move from theoretical considerations to numerical simulations.