A spectral integral equation method for smooth genus-zero surfaces using spherical grid rotations

We present a scalable and accurate algorithm for evaluating singular and nearly-singular boundary integral operators on smooth, genus-zero, three-dimensional surfaces. Boundary integrals of this type often arise when solving, for example, the hydrodynamic interaction between particles suspended in a Stokes flow. Our algorithm relies on decomposing surface quantities in terms of spherical or vector spherical harmonics. We then apply a smooth quadrature rule in combination with spherical grid rotations to rewrite the desired operator in terms of known analytical integrals on the sphere. We validate our method against several benchmark tests for single and multiple particles with spherical, ellipsoidal, and radial-manifold shapes and demonstrate that our algorithm can achieve spectral accuracy and superalgebraic convergence while maintaining low computational complexity.