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We propose and analyze a quasi-Monte Carlo (QMC) algorithm for efficientsimulation of wave propagation modeled by the Helmholtz equation in a boundedregion in which the refractive index is random and spatially heterogenous. Ourfocus is on the case in which the region can contain multiple wavelengths. Webypass the usual sign-indefiniteness of the Helmholtz problem by switching toan alternative sign-definite formulation recently developed by Ganesh andMorgenstern (Numerical Algorithms, 83, 1441-1487, 2020). The price to pay isthat the regularity analysis required for QMC methods becomes much moretechnical. Nevertheless we obtain a complete analysis with error comprisingstochastic dimension truncation error, finite element error and cubature error,with results comparable to those obtained for the diffusion problem.

Quasi-Monte Carlo finite element analysis for wave propagation in heterogeneous random media