Integral Equation Methods for Stokes Flow and Isotropic Elasticity in the Plane

We present a class of integral equation methods for the solution of biharmonic boundary value problems, with applications to two-dimensional Stokes flow and isotropic elasticity. The domains may be multiply-connected and finite, infinite or semi-infinite in extent. Our analytic formulation is based on complex variables, and our fast multipole-based iterative solution procedure requiresO(N) operations, whereNis the number of nodes in the discretization of the boundary. The performance of the methods is illustrated with several large-scale numerical examples.