Section: New Results

Time-dependent wave splitting and source separation

Starting from classical absorbing boundary conditions, we (M. Grote, M. Kray, F. Nataf and F. Assous) propose a method for the separation of time-dependent scattered wave fields due to multiple sources or obstacles. More precisely, we propose a method to determine the separate outgoing components of the incident and scattered wave fields for time-dependent scattering problems. In the case of two superposed wave fields, our method applies to the following three typical configurations: two distinct localized sources with unknown time history each, a single (unknown) localized source with a nearby scatterer, or two separate scatterers illuminated by a known incident wave field. In all three cases, our method permits to recover the individual outgoing components from measurements of the total scattered field at a distance. In doing so, the particular nature of the scatterer, be it an im- penetrable well-defined obstacle or a penetrable localized inhomogeneity, is immaterial; only the purely outgoing character of the individual wave fields matters. In contrast to previous work, our approach is local in space and time, deterministic, and also avoids any a priori assumptions on the frequency spectrum of the signal. Numerical simulations in FreeFem++ in two space dimensions illustrate the usefulness of wave splitting for time-dependent scattering problems. This work was presented to several international conferences and was published in J. Comput. Phys. (2016).