A Fast Algorithm for Spherical Grid Rotations and Its Application to Singular Quadrature

We present a fast and accurate algorithm for evaluating singular integral operators on smooth surfaces that are globally parametrized by spherical coordinates. Problems of this type arise, for example, in simulating Stokes flows with particulate suspensions and in multi-particle scattering calculations. For smooth surfaces, spherical harmonic expansions are commonly used for geometry representation and the evaluation of the singular integrals is carried out with a spectrally accurate quadrature rule on a set of rotated spherical grids. We propose a new algorithm that interpolates function values on the rotated spherical grids via hybrid nonuniform FFTs. The algorithm has a small complexity constant, and the cost of applying the quadrature rule is nearly-optimal O(p log p) for a spherical harmonic expansion of degree p.