A geometric nonuniform fast Fourier transform

Authors:
Ian Sammis;John Strain
Affiliations:
Department of Mathematics, 970 Evans Hall #3840, University of California, Berkeley, CA 94720-3840, United States;Department of Mathematics, 970 Evans Hall #3840, University of California, Berkeley, CA 94720-3840, United States
Venue:
Journal of Computational Physics
Year:
2009

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Abstract

An efficient algorithm is presented for the computation of Fourier coefficients of piecewise-polynomial densities on flat geometric objects in arbitrary dimension and codimension. Applications range from standard nonuniform FFTs of scattered point data, through line and surface potentials in two and three dimensions, to volumetric transforms in three dimensions. Input densities are smoothed with a B-spline kernel, sampled on a uniform grid, and transformed by a standard FFT, and the resulting coefficients are unsmoothed by division. Any specified accuracy can be achieved, and numerical experiments demonstrate the efficiency of the algorithm for a gallery of realistic examples.