An offline/online algorithm for a class of stochastic multiple obstacle scattering configurations in the half-plane

Efficient computational models are required to understand quantities of interest (QoI) such as the intensity of sound radiated by non-deterministic configurations (comprising multiple obstacles) in the half-plane. The stochastic nature of the configurations requires tens of thousands of realizations to compute the expected value and standard deviation of the random QoI. The acoustic wave scattering configuration usually comprises multiple deterministic structures, whose locations in the half-plane are non-deterministic. Thus understanding the nature of the deterministic structures is intrinsically an offline process, whilst understanding the nature of the resulting QoI is an online process. The online process includes interactions between the structures and the half-plane boundary. In accordance with the physical offline/online process, we develop a computational TT-matrix based offline/online reduced order model for large realizations of stochastic acoustic wave scattering configurations in the half-plane. We present results with more than 60 000 Monte Carlo (MC), quasi-MC (QMC) and generalized Polynomial Chaos (gPC) simulations, which are evaluated using our efficient online scheme for the acoustic scattering half plane model. Our offline/online deterministic and stochastic framework can be used in conjunction with any numerical method for the offline simulations of scattering from a single obstacle in free-space.