Abstract:The computation of the hydrodynamic drag forces on bodies of arbitrary shape undergoing slow motions in an incompressible, viscous fluid is essential in various different applications. While several types of boundary integral methods are available for treating this problem, such as those of the Galerkin, collocation, spectral and wavelet type, these approaches may require basis functions that are difficult to construct, and which might exist only for certain classes of geometries, or may require weakly-singular integrations, which can be expensive. Some methods are restricted to bodies undergoing rigid motions only. In this talk, a boundary integral formulation and a family of Nystrom methods for the Stokes equations in exterior, three-dimensional domains with arbitrary Dirichlet data are presented. The family is based on the idea of a local polynomial correction, and at the lowest order, no weakly-singular integrations or coordinate transformations are required. Theorems on the solvability of the integral equation, representation of the surface traction, and convergence of the method will be described, and numerical examples that illustrate the conditioning and accuracy of the method will be given.