Fast Ewald summation for free-space Stokes potentials

Abstract

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

arXiv comment35 pages, 15 figures

References in corpus (4)

• How to mesh up Ewald sums (I): A theoretical and numerical comparison of various particle mesh routines
• Fast convolution with free-space Green's functions
• Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
• Fast and spectrally accurate Ewald summation for 2-periodic electrostatic systems

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