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High-order algorithms for time- and frequency-domain wave propagation models

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MWSW03 - Computational methods for multiple scattering

Efficient simulations of  acoustic wave propagation in three dimensional regions with multiple structures are fundamental for numerous applications. Robust mathematical modeling of the underlying time-dependent multiple scattering  physical process  is crucial for designing fully-discrete high-order computational methods for multiple scattering simulations. Development of related algorithms are based on celebrated continuous mathematical equations either in the time- or frequency-domain, with the latter based on mathematical manipulations.Consequently, the meaning of the term “multiple scattering” varies depending on the context in which it is used. It has been argued in the physics literature 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.  From 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 argue that spectrally accurate FD  scattering algorithms are crucial for efficient and practical simulation of physically appropriate TD multiple scattering in unbounded regions with multiple structures. (This talk is based on collaborative work with Drs. Dominguez, Hawkins, and Le Louer.)

This talk is part of the Isaac Newton Institute Seminar Series series.

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