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Dense particulate flow simulations using integral equation methods demandaccurate evaluation of Stokes layer potentials on arbitrarily close interfaces.In this paper, we generalize techniques for close evaluation of Laplacedouble-layer potentials in J. Helsing and R. Ojala, J. Comput. Phys. 227 (2008)2899-2921. We create a "globally compensated" trapezoid rule quadrature for theLaplace single-layer potential on the interior and exterior of smooth curves.This exploits a complex representation, a product quadrature (in the style ofKress) for the sawtooth function, careful attention to branch cuts, andsecond-kind barycentric-type formulae for Cauchy integrals and theirderivatives. Upon this we build accurate single- and double-layer Stokespotential evaluators by expressing them in terms of Laplace potentials. We testtheir convergence for vesicle-vesicle interactions, for an extensive set ofLaplace and Stokes problems, and when applying the system matrix in a boundaryvalue problem solver in the exterior of multiple close-to-touching ellipses. Weachieve typically 12 digits of accuracy using very small numbers ofdiscretization nodes per curve. We provide documented codes for otherresearchers to use.

Spectrally-accurate quadratures for evaluation of layer potentials close to the boundary for the 2D Stokes and Laplace equations