A Hausdorff-measure boundary element method for acoustic scattering by fractal screens
A. M. Caetano,
S. N. Chandler-Wilde,
A. Gibbs
et al.
Abstract:Sound-soft fractal screens can scatter acoustic waves even when they have zero surface measure. To solve such scattering problems we make what appears to be the first application of the boundary element method (BEM) where each BEM basis function is supported in a fractal set, and the integration involved in the formation of the BEM matrix is with respect to a non-integer order Hausdorff measure rather than the usual (Lebesgue) surface measure. Using recent results on function spaces on fractals, we prove conve… Show more
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