Numerical Analysis: Fast Ewald summation for Stokesian particle suspensions

We have developed a numerical method for suspensions of spheroids of arbitrary aspect ratio which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using GMRES accelerated by the spectral Ewald (SE) method, which reduces the computational complexity to O(N log N ), where N is the number of points used to discretize the particle surfaces. Predictive error estimates, which can be used to optimize the choice of parameters in the Ewald summation, have been developed. Numerical tests show that the method is well conditioned and provides good accuracy when validated against reference solutions.

Further developments concerns a new and more accurate quadrature technique that can very accurately handle both the singular and nearly singular behavior of the double layer potential.