Quasi-Monte Carlo Finite Element Analysis for Wave Propagation in Heterogeneous Random Media

We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficient simulation of wave propagation modeled by the Helmholtz equation in bounded region which refractive index is random spatially heterogenous. Our focus on case can contain multiple wavelengths. bypass usual sign-indefiniteness problem switching to an alternative sign-definite formulation recently developed Ganesh Morgenstern Numer. Algorithms, 83 (2020), pp. 1441--1487. The price pay that regularity analysis required QMC methods becomes much more technical. Nevertheless we obtain complete with error comprising stochastic dimension truncation error, finite element cubature results comparable those obtained diffusion problem.