Abstract
We consider high-frequency multiple-scattering problems in the exterior of two-dimensional smooth scatterers consisting of finitely many compact, disjoint, and strictly convex obstacles. To deal with this problem, we propose Galerkin boundary element methods, namely the frequency-adapted Galerkin boundary element methods and Galerkin boundary element methods generated using frequency-dependent changes of variables. For both of these new algorithms, in connection with each multiple-scattering iterate, we show that the number of degrees of freedom needs to increase as $$\mathcal {O}(k^{\epsilon })$$ (for any $$\epsilon >0$$) with increasing wavenumber k to attain frequency-independent error tolerances. We support our theoretical developments by a variety of numerical implementations.
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