A wavelet algorithm for the solution of the double layer potential equation over polygonal boundaries

In this paper we consider a piecewise linear collocation method for the solution of the double layer potential equation corresponding to Laplace's equation over polygonal domains. We give a wavelet algorithm for the computation of the corresponding stiffness matrix and for the solution of the arising matrix equation with no more than O(N·[log N]8) arithmetic operations. The error of the resulting approximate solution is of order O(N-2·[log N]6).Finally, we give some remarks on the generalization of the algorithm to the piecewise cubic collocation and present numerical tests