An efficient algorithm for simulation of stochastic scattering cross-sections

We present an efficient algorithm for uncertainty quantification of scattering cross-sections of stochastic configurations comprising multiple two-dimensional sound-soft particles whose locations and orientations are random. Our algorithm has two components. Firstly, we use a high order generalised polynomial chaos approximation of the stochastic cross-sections in the random variables that requires realisation of the exterior sound propagation model for high order quadrature sampling parameters. For each such realisation, we use an efficient spectrally accurate algorithm for deterministic scattering simulations based on solving a boundary integral equation reformulation of the acoustic model. We present numerical results for a stochastic configuration of particles with rough surfaces. Our numerical result demonstrate the high order accuracy of both components of the algorithm for simulation of moments of the scattering cross-section of the configuration.