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We present a numerical method for computing the single layer (Stokeslet) anddouble layer (stresslet) integrals in Stokes flow. The method applies tosmooth, closed surfaces in three dimensions, and achieves high accuracy both onand near the surface. The singular Stokeslet and stresslet kernels areregularized and, for the nearly singular case, corrections are added to reducethe regularization error. These corrections are derived analytically for boththe Stokeslet and the stresslet using local asymptotic analysis. For the caseof evaluating the integrals on the surface, as needed when solving integralequations, we design high order regularizations for both kernels that do notrequire corrections. This approach is direct in that it does not require gridrefinement or special quadrature near the singularity, and therefore does notincrease the computational complexity of the overall algorithm. Numerical testsdemonstrate the uniform convergence rates for several surfaces in both thesingular and near singular cases, as well as the importance of corrections whentwo surfaces are close to each other.

Regularized Single and Double Layer Integrals in 3D Stokes Flow