A MULTISCALE BUTTERFLY ALGORITHM FOR MULTIDIMENSIONAL FOURIER INTE GRAL OPERATORS.

This paper presents an efficient multiscale butterfly algorithm for computing Fourier integral operators (FIOs) of the form (Lf)(x) = ∫...(x,ξ)e2πiΦ(x,ξ), where 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 pr ovided to demonstrate the practical advantages of the new algorithm. [ABSTRACT FROM AUTHOR]