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For problems of time-harmonic scattering by polygonal obstacles, embeddingformulae provide a useful means of computing the far-field coefficient inducedby any incident plane wave, given the far-field coefficient of a relativelysmall set of canonical problems. The number of such problems to be solveddepends only on the geometry of the scatterer. Whilst the formulae themselvesare exact in theory, any implementation will inherit numerical error from themethod used to solve the canonical problems. This error can lead to numericalinstabilities. Here, we present an effective approach to identify and regulatethese instabilities. This approach is subsequently extended to the case wherethe incident wave is a Herglotz wave function, and we suggest how this couldpotentially remove frequency dependence of a T-matrix method.

Numerically stable computation of embedding formulae for scattering by polygons