  The incorporation of analytical kernel information is exploited in the
construction of Nystr\"om discretization schemes for integral equations
modeling planar Helmholtz boundary value problems. Splittings of kernels and
matrices, coarse and fine grids, high-order polynomial interpolation, product
integration performed on the fly, and iterative solution are some of the
numerical techniques used to seek rapid and stable convergence of computed
fields in the entire computational domain.
