A conformal transformation is used to map the exterior of a scatterer of arbitrary shape into the exterior of a circle. This mapping replaces the problem of scattering from an awkwardly shaped scatterer in a medium of constant index of refraction (constant k2) by the problem of scattering from a circle in a medium of varying index of refraction (varying k2). The variation in the index of refraction is treated perturbatively by taking for the unperturbed problem the problem of scattering by a circle in a medium of constant index of refraction. Generally applicable bounds on the region of convergence of the perturbative solution are obtained and evaluated numerically for the case of Dirichlet boundary conditions. Error bounds on the remainder after n iterations are given. The method is illustrated by explicit calculation of the scattering from an infinite strip.
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Hill et al. (1973) studied this question.