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We propose and analyse a hybrid numerical-asymptotic hp boundary element method for time-harmonic scattering of an incident plane wave by an arbitrary collinear array of sound-soft two-dimensional screens. Our method uses an approximation space enriched with oscillatory basis functions, chosen to capture the high frequency asymptotics of the solution. Our numerical results suggest that fixed accuracy can be achieved at arbitrarily high frequencies with a frequencyindependent computational cost.doi:10.1093/imanum/dru043 fatcat:fpis7hvvczfvdiokob3flronsi