A multiscale butterfly algorithm for multidimensional fourier integral operators


Journal Article

© 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) =∫ ℝ da(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.

Full Text

Duke Authors

Cited Authors

  • Li, Y; Yang, H; Ying, L

Published Date

  • January 1, 2015

Published In

Volume / Issue

  • 13 / 2

Start / End Page

  • 614 - 631

Electronic International Standard Serial Number (EISSN)

  • 1540-3467

International Standard Serial Number (ISSN)

  • 1540-3459

Digital Object Identifier (DOI)

  • 10.1137/140997658

Citation Source

  • Scopus