Graduate Student / Postdoc Seminar

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Fast Fourier scheme for history compression in wave scattering problems

Speaker: Nour Al Hassanieh, Courant Institute, New York University

Location: Warren Weaver Hall 1302

Date: Friday, November 22, 2024, 2:10 p.m.

Synopsis:

 In this talk, we propose a high-order-accurate, fast algorithm to solve time-domain boundary integral equations (BIE) for the wave equation in scattering problems. Specifically, we consider problems where the spatial size can become sub-wavelength — a case where finite-difference time-domain (FDTD) methods may become inefficient due to small time steps. The method splits the solution representation into two parts: one that depends on the history of the solution in time and one that is local. We apply a fast-Fourier transform (FFT) filtering method to compress the history computation up to \(O(n^d\log n)\), where d is the dimension and n is the temporal Fourier content of data. We present numerical examples of 1D scattering from many springs as a stepping stone to problems in higher dimensions. Our results demonstrate the expected high-order accuracy and capture intricate scattering behaviors, such as wave localization and filtering effects.