Iterative Solution of Linear Systems Arising from the Boundary Integral Method

In this paper the behavior of some standard two-grid iterative schemes for the solution of linear systems arising from discretizations of second-kind boundary integral equations of potential theory is studied. When the boundary of the domain has corners, these schemes converge slowly, and in some cases even diverge. New iterative schemes are derived which always converge, and estimates for the accuracy of the solution to which they converge are given. Extensive numerical experiments are reported and discussed.