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A high-order accurate, explicit kernel-split, panel-based, Fourier-Nystr\"omdiscretization scheme is developed for integral equations associated with theHelmholtz equation in axially symmetric domains. Extensive incorporation ofanalytic information about singular integral kernels and on-the-fly computationof nearly singular quadrature rules allow for very high achievable accuracy,also in the evaluation of fields close to the boundary of the computationaldomain.

An explicit kernel-split panel-based Nystr\"om scheme for integral equations on axially symmetric surfaces