Time- and Frequency-Domain Wave Propagation Models: Reformulations, Algorithms, Analyses, and Simulations

Abstract

Efficient simulation of wave propagation induced by multiple structures is fundamental for numerous applications. Robust mathematical modeling of the underlying time-dependent physical process is crucial for designing high-order computational methods for the multiple scattering simulations. Development of related algorithms and analyses are based on celebrated continuous mathematical equations either in the time- or frequency-domain, with the latter involving mathematical manipulations.

Consequently, the meaning of the term "multiple scattering" varies depending on the context in which it is used.  Physics literature suggests that the continuous frequency-domain (FD) multiple scattering model is a purely mathematical construct, and that in the time-domain (TD), multiple scattering becomes a definite physical phenomenon. In recent years there has been substantial development of computational multiple scattering algorithms in the FD. In the context of computational multiple scattering, it is important to ensure that the simulated solutions represent the definite physical multiple scattering process. In this talk, we describe our recent contributions to the development of high-order wave propagation computational models in both time- and frequency-domains, and we argue that spectrally accurate FD scattering algorithms are crucial for efficient and practical simulation of physically appropriate TD multiple scattering phenomena in unbounded regions with multiple structures.