Two-grid solution of boundary integral equations on closed curves

We propose two-grid iteration methods for boundary integral equations discretized by quadrature-collocation methods. Under some assumptions the optimal order of error estimate is achieved already on the first iteration. This enables us to introduce some solvers which are of the optimal convergence order and cheap in a practical implementation; the cost varies between O(N-2) and O(N log N) arithmetic operations. Numerical experiments confirm the approximation properties of the schemes.