Integral equation methods for Stokes flow in doubly-periodic domains

A fast integral-equation technique is presented for the calculation of Stokes flow in doubly-periodic domains. While existing integral formulations typically rely on a Fourier series to compute the governing Greens' function, here a method of images is developed which is faster, more flexible, and easily incorporated into the fast multipole method. Accurate solutions can be obtained with obstacles of arbitrary shape at a cost roughly proportional to the number of points needed to resolve the interface. The performance of the method is illustrated with several numerical examples.