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A multiscale butterfly algorithm for multidimensional fourier integral operators

dc.contributor.author Li, Y
dc.contributor.author Yang, Haizhao
dc.contributor.author Ying, L
dc.date.accessioned 2016-02-28T03:45:09Z
dc.date.issued 2015-01-01
dc.identifier.issn 1540-3459
dc.identifier.uri https://hdl.handle.net/10161/11655
dc.description.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)e<sup>2πiΦ(x,ξ)</sup>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)e<sup>2πiΦ(x,ξ)</sup>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.
dc.relation.ispartof Multiscale Modeling and Simulation
dc.relation.isversionof 10.1137/140997658
dc.title A multiscale butterfly algorithm for multidimensional fourier integral operators
dc.type Journal article
pubs.begin-page 614
pubs.end-page 631
pubs.issue 2
pubs.organisational-group Duke
pubs.organisational-group Mathematics
pubs.organisational-group Trinity College of Arts & Sciences
pubs.publication-status Published
pubs.volume 13
dc.identifier.eissn 1540-3467


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