Nyström’s Method and Iterative Solvers for the Solution of the Double-Layer Potential Equation over Polyhedral Boundaries

In this paper we consider a quadrature method for the solution of the double-layer potential equation corresponding to Laplace’s equation in a three-dimensional polyhedron. We prove the stability for our method in the case of special triangulations over the boundary of the polyhedron. For the solution of the corresponding system of linear equations, we consider a two-grid iteration and a further simple iteration procedure. Finally, we establish the rates of convergence and complexity and discuss the effect of mesh refinement near the corners and edges of the polyhedron