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The Kirchhoff approximation (K-A) to calculate the acoustic backscattering ofa complex structure can be evaluated using a discretized version of its surface(i.e. a $\textit{mesh}$). From the computational viewpoint, the most accesibleapproach is the one based on flat facets. However, in the high frequency range,where the K-A provides good agreement and is therefore applicable, it requiresa mesh with such a large number of facets that it turns impractical. To avoidthese difficulties a mesh of curved triangles can be used to model thescatterer's complex structure. Previous computational implementations reportedin the literature did not accomplish satisfactory results for high frequency.In this work we propose a numerical model based upon an iterative integrationusing Gauss-Legendre rules. The model was validated against exact solutions andled us to achieve adequate results in the high-frequency range.

Modelling High-Frequency Backscattering from a Mesh of Curved Surfaces Using Kirchhoff Approximation