  We present a numerical method for computing the single layer (Stokeslet) and
double layer (stresslet) integrals in Stokes flow. The method applies to
smooth, closed surfaces in three dimensions, and achieves high accuracy both on
and near the surface. The singular Stokeslet and stresslet kernels are
regularized and, for the nearly singular case, corrections are added to reduce
the regularization error. These corrections are derived analytically for both
the Stokeslet and the stresslet using local asymptotic analysis. For the case
of evaluating the integrals on the surface, as needed when solving integral
equations, we design high order regularizations for both kernels that do not
require corrections. This approach is direct in that it does not require grid
refinement or special quadrature near the singularity, and therefore does not
increase the computational complexity of the overall algorithm. Numerical tests
demonstrate the uniform convergence rates for several surfaces in both the
singular and near singular cases, as well as the importance of corrections when
two surfaces are close to each other.
