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MMAS
2015
Springer

A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators

4 years 9 months ago
A Multiscale Butterfly Algorithm for Multidimensional Fourier Integral Operators
This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = Rd a(x, ξ)e2πıΦ(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)e2πıΦ(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. Key words. Fourier integral operators, the butterfly algorithm, hierarchi...
Yingzhou Li, Haizhao Yang, Lexing Ying
Added 14 Apr 2016
Updated 14 Apr 2016
Type Journal
Year 2015
Where MMAS
Authors Yingzhou Li, Haizhao Yang, Lexing Ying
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