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A multiscale butterfly algorithm for multidimensional fourier integral operators

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Date
2015-01-01
Authors
Li, Y
Yang, H
Ying, L
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Abstract
© 2015 Society for Industrial and Applied Mathematics.This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) =∫ <inf>ℝ d</inf>a(x, ξ)e2πiΦ(x,ξ)f(ξ)dξ, where Φ(x, ξ) is a phase function, a(x, ξ) is an amplitude function, and f(x) is a given input. The frequency domain is hierarchically decomposed into a union of Cartesian coronas. The integral kernel a(x, ξ)e2πiΦ(x,ξ)in each corona satisfies a special low-rank property that enables the application of a butterfly algorithm on the Cartesian phase-space grid. This leads to an algorithm with quasi-linear operation complexity and linear memory complexity. Different from previous butterfly methods for the FIOs, this new approach is simple and reduces the computational cost by avoiding extra coordinate transformations. Numerical examples in two and three dimensions are provided to demonstrate the practical advantages of the new algorithm.
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Journal article
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https://hdl.handle.net/10161/11655
Published Version (Please cite this version)
10.1137/140997658
Publication Info
Li, Y; Yang, H; & Ying, L (2015). A multiscale butterfly algorithm for multidimensional fourier integral operators. Multiscale Modeling and Simulation, 13(2). pp. 614-631. 10.1137/140997658. Retrieved from https://hdl.handle.net/10161/11655.
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Scholars@Duke

Li

Yingzhou Li

Phillip Griffiths Assistant Research Professor
This author no longer has a Scholars@Duke profile, so the information shown here reflects their Duke status at the time this item was deposited.

Haizhao Yang

Instructor* of Mathematics
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