A High Performance Computing and Sensitivity Analysis Algorithm for Stochastic Many-Particle Wave Scattering

Abstract

We present a high performance computing framework for quantifying uncertainties in the propagation of acoustic waves through a stochastic media comprising a large number of three-dimensional particles. We subsequently describe an efficient postprocessing approach using our framework to statistically quantify the sensitivity of the uncertainties with respect to input parameters that govern the stochasticity in the model. The stochasticity arises through the random positions and orientations of the component particles in the media. Simulation even for a single deterministic three-dimensional configuration is inherently difficult because of the large number of particles; the stochasticity leads to a larger dimensional model involving three spatial variables and additional stochastic variables, and accounting for uncertainty in key parameters of the input probability distributions leads to prohibitive computational complexity. In the first part of our paper we describe a high performance computing framework for uncertainty quantification with fixed input parameters. In the second part of our paper we describe and analyze an efficient offline/online approach that allows characterization of the quantity of interest with respect to the variance of the input stochastic variables. Our approach provides a framework for high performance computing implementation to compute statistical moments for the three-dimensional model and can be used in conjunction with any method to simulate a single-particle deterministic model. We demonstrate the efficiency of our high performance computing implementation with Monte Carlo (MC) and quasi-Monte Carlo (QMC) realization numerical results for more than one thousand stochastic dimensions describing stochastic media comprising hundreds to thousands of nonconvex particles. Our demonstration of the efficient sensitivity analysis algorithm includes over a million MC samples of the backscattered cross section and thousands of generalized polynomial chaos-based realizations of the three-dimensional model with parallelization in both spatial and stochastic variables.