Spectrally accurate fast summation for periodic Stokes<br/><br/>potentials

Monday, August 2, 2010 - 2:00pm - 2:30pm
Keller 3-180
Anna-Karin Tornberg (Royal Institute of Technology (KTH))
A spectrally accurate method for the fast evaluation of N-particle
sums of the periodic Stokeslet is presented. Such sums occur in
boundary integral- and potential methods for viscous flow
problems. Two different decomposition methods, leading to one sum in
real space and one in reciprocal space, are considered. An FFT
based method is applied to the reciprocal part of the sum, using
convolutions with a Gaussian function to place the point sources on
a grid. Due to the spectral accuracy of the method, the grid size
needed is low and also in practice, for a fixed domain size,
independent of N. The leading cost therefore arise from the
to-grid and from-grid operations, that are linear in N. Combining
this FFT based method for the reciprocal sum with the direct
evaluation of the real space sum, a spectrally accurate algorithm
with a total complexity of O(N log N) is obtained.
MSC Code: