Before revision:  In this work, we finally provide a resolution to this issue for the two-dimensional case. We begin by deriving bounds which are tight as long as the cylinders are not too close together. When some cylinders are, in fact, in close proximity to one another, these bounds become pessimistic. To obtain a more accurate characterization of the convergence in this regime, we formulate a first-order scattering approximation and derive its rate of convergence. Numerical simulations show that this approximation provides a far more accurate estimate of the convergence in the closely spaced regime than the aforementioned bounds. Our results establish MEM convergence rates that hold for all  boundary conditions and boundary integral equation solution representations .
After revision:  In this work, we finally provide a resolution to this issue . While our focus in this paper is on the Dirichlet scattering problem, this is merely for convenience and our results actually establish convergence rates that hold for all boundary conditions and boundary integral equation solution representations .