Fast Ewald summation for free-space Stokes potentials
2017 (English)In: Research in the Mathematical Sciences, ISSN 2197-9847, Vol. 4, no 1Article in journal (Refereed) Published
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 (Lindbo and Tornberg in J Comput Phys 229(23):8994–9010, 2010. doi: 10.1016/j.jcp.2010.08.026 ), with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid (Vico et al. in J Comput Phys 323:191–203, 2016. doi: 10.1016/j.jcp.2016.07.028 ). 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 $$O(N \log N)$$ O ( N log N ) for problems with N sources and targets. Comparison is made with a fast multipole method to show that the performance of the new method is competitive.
Place, publisher, year, edition, pages
2017. Vol. 4, no 1
Research subject Applied and Computational Mathematics
IdentifiersURN: urn:nbn:se:kth:diva-203922DOI: 10.1186/s40687-016-0092-7OAI: oai:DiVA.org:kth-203922DiVA: diva2:1083032
FunderGöran Gustafsson Foundation for Research in Natural Sciences and MedicineSwedish Research Council, 2011-3178Swedish e‐Science Research Center