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We present a spectrally accurate method for the rapid evaluation offree-space Stokes potentials, i.e. sums involving a large number of free spaceGreen's functions. We consider sums involving stokeslets, stresslets androtlets that appear in boundary integral methods and potential methods forsolving Stokes equations. The method combines the framework of the SpectralEwald method for periodic problems, with a very recent approach to solving thefree-space harmonic and biharmonic equations using fast Fourier transforms(FFTs) on a uniform grid. Convolution with a truncated Gaussian function isused to place point sources on a grid. With precomputation of a scalar gridquantity that does not depend on these sources, the amount of oversampling ofthe grids with Gaussians can be kept at a factor of two, the minimum foraperiodic convolutions by FFTs. The resulting algorithm has a computationalcomplexity of O(N log N) for problems with N sources and targets. Comparison ismade with a fast multipole method (FMM) to show that the performance of the newmethod is competitive.

Fast Ewald summation for free-space Stokes potentials